Analytic Extensions to the Data Model for Management Analytics

Chapter 1: Introduction to the Study

Introduction

This study explored the use of applied data-modeling concepts to refine the data

model for management analytics and decision support in a big data environment. The

study sought to address the challenges facing data analytics projects, which included, the

overwhelming availability of big data, the growing complexity of business domains, the

demands of operational accountability, and the explosion of analytic techniques (De

Smedt, 2013; McAfee & Brynjolfsson, 2012; Storey & Song, 2017). The issue was that

insights and solutions from these projects lost alignment to well-known data and the

intuitive cognitive models required for the management problem-solving.

Chapter 1 covers the following topics: background of the study, the purpose of the

study, the research questions, the nature of the study, the theoretical foundation, the

definition of critical terms; the scope, delimitations, and limitations of the study; and the

significance of the study to management theory, business practice, and social change.

Background of the Study

I was motivated to study this topic due to a combination of research and personal

experience showing that companies’ efforts in the areas of data analytics and decision

support were often neither effective nor efficient. Most management decisions and

actions of business analysts and executives used intuitions and cognitive models, and not

insights or solutions from data analytics and decision support systems (Yeoh & Popovič,

2015). The difficulty was the framing of specific management problems or opportunities

with available data. For this reason, management questioned the value proposition of

investments in data analytics and decision support systems. Strategic decision failures,

such as, the 2008 global economic collapse and many other such occurrences in history

were examples that made formal analysis and decision support systems suspicious as

viable management problem-solving tools (Bosch, Nguyen, & Buckle-Henning, 2014).

With the advent of business big data, the data analytics projects faced three

challenges: (a) taming the information chaos caused by the exponential growth of

information assets, (b) relieving the mounting pressure to use these information assets to

advance efficiency and predictability of decision-making, and (c) addressing acute

problems of information deluge on decision-making, including analysis paralysis,

escalating indecision, reification, and strategic ambiguity (Block, 2012; Tien, 2013).

From these challenges the following two problem scenarios arose. The more important

was the difficulty in the discovery of underlying structures and associations about

subjects of interest. The other issue was transforming these structures and associations

into actionable business insights and organizing them into scenarios to improve

management programs for predictable and positive outcomes (Resmini, 2012).

These challenges were reduced when the data were in models that connected

underlying elements and their associations (Hand, 2012; Thompson, 2011). A well-

constructed data model captured the structure, content, and context of the underlying

elements. Such models also captured mechanisms and situations responsible for the

outcome observations of the domain of interest (Burch, 2018). The data model provided

the stable and accurate representation of subjects within the enterprise (Johnson, 2014).

Furthermore, the data model provided the foundation for the continuous discovery of the

attributes of dominant subjects for management problem-solving (Beroggi, 2010;

Kwakkel, Walker, & Marchau, 2010). Additionally, the data model carefully rationalized

and integrated the attributes from all relevant data sources without compromising the

integrity of the data generation processes, therefore, provided the most comprehensive

collection of the subjects responsible for the performance of the enterprise.

With the advent of big data, input data structures came in many different forms. It

was not uncommon for data structures like online transaction processing (OLTP), online

analytic processing (OLAP), relational, object-relational, hierarchical (or graph),

network, document, and flat data structures to be part of a single data analytics project

scope. Because of the size and dimensionality of these data sources, it was typical for

contemporary analytic processes to partition and sample the data to limit complexity.

Partitioning led to the deluge of partial analytic solutions and data silos, for example,

static reports, dynamic reports (dashboards, scorecards), and analytic algorithms (Kalou

& Koutsomitropoulos, 2014). Sampling raised issues of representativeness, bias, and the

requirement of statistical validation. New and advanced data analytics methodologies

arose to overcome these concerns.

The advanced data analytics techniques included semantic data analysis, statistical

data analysis, symbolic data analysis, functional data analysis, topographical data

analysis, projection pursuit analysis, exploratory system dynamics and modeling, data

mining, and deep learning to name a few. These advanced data analytics techniques were

responses to the growing availability of data and the demand to use them to guide

knowledge and learning (Paganoni & Secchi, 2014). A unique challenge of these

advanced analytic methods was in the pre-processing of the data for the analytic

technique selected (Kaisler, Espinosa, Armour, & Money, 2014). This pre-processing

step required the selection of attributes, sampling of the data, and transformations of the

data in ways that caused loss of business interpretability and value (Kalou &

Koutsomitropoulos, 2014; Ma et al., 2014). For this reason, I chose the approach of

analyzing the data to determine how to extend the model to accommodate the unique

challenges posed by big data in data analytics projects for management problem solving

without the constraints imposed by analytic methodologies.

Problem Statement

Most business analysts and executives found the outputs from big data projects

inadequate for management analytics and decision support (Bendre & Thool, 2016).

From 2006 to 2016, an estimated average of 50% of these projects failed to deliver

acceptable and actionable outputs to business users (Gartner Inc, 2016). Also, the

percentage of failed data analytics projects continued to rise with the exponential growth

of data within organizations (Khan et al., 2014). The general management problem was

that the outputs did not reconcile the intuitive cognitive model of the problem situation of

business analysts and executives and the accustomed available data (Zicari et al., 2016).

In many cases, these outputs were incomplete, difficult to understand, and difficult to

translate into management actions because of their black-box nature (Günther, Mehrizi,

Huysman, & Feldberg, 2017). The outputs were also disconnected from available data

and from dominant cognitive conceptualization of the management problems and

solutions by analysts and executives (Flath & Stein, 2018; Ransbotham, Kiron, &

Prentice, 2017). The specific management problem was the inappropriate representation

of information by big data projects for management analytics and decision support

(Sivarajah, Kamal, Irani, & Weerakkody, 2017; Storey & Song, 2017).

Purpose of the Study

The purpose of this quantitative descriptive study was to examine the data model

of a typical data analytics project in a big data environment for opportunities to improve

the representation of information. I identified the data model as the primary focus of the

study because the expression of information in the data model was known to improve

understanding and application of the data (Burch, 2018). I adopted nonexperimental

design-based research (DBR) to study the data model for artifacts that would improve the

expression of the underlying management situations.

The research questions of this study focused on extracting expressions in the

available data to improve the discovery, identification, specification, and resolution of

management problems. Using 15-terabyte secondary data sets from U. S.-based

multinational medical product distribution company on orders, payments, products,

customers, sales channels, and marketing activities, I applied ontology learning to

identify operational concepts within the business domain. I used data engineering to

connect the concepts to available data through direct transformations, and analytic

formulations to abstract functional forms from the available data. This approach ensured

that any resulting analytic insights and solutions maintained the connection to the

available data.

I assessed the performance of the data model artifacts on empirical measures of

analytic importance such as information gain, intelligence density, decision yield,

cognitive gain, empirical lift, Bayesian yield, the weight of evidence, and strength of

association measures, as necessary. The results of this study could increase (a) the

acceptance of big data analytics outputs by business analysts and executives, (b) the

return on investment for big data analytics projects, and (c) the overall efficiency of data-

driven management analytics and decision support. The social change implication was an

increase in management engagement in social programs to sustain good corporate

citizenship within stakeholder communities, including sponsorship of community events

and social programs.

Research Questions

The research questions focused on finding artifacts within enterprise data to

model key business scenarios for management problem-solving as follows:

Research Question 1: Can data model extensions improve the discovery of

management scenarios from big data?

Research Question 2: Can data model extensions improve insights about the

management scenarios?

Research Question 3: Can data model extensions express the complex constraints

and rules needed to compose the acceptable and actionable solutions for analysts and

executives?

Research Question 1

I relied on the relational model as the primary approach to modeling enterprise

data. This modeling approach and subsequent enhancements solved significant problems

in the use of databases to deliver information systems. The initial relational data model

proposal unified data representation and addressed issues of data integrity. The proposal

also added enhancements, for example, the relationship and the data catalog (or

dictionary extensions) to improve the capture of the meaning of data and the use of the

database for analysis (Werro, 2015). However, the capture of meaning was limited to

low-order predicate logic, based on the quantities of attributes. Advanced analytics and

decision support required higher-order logic, ontological argument assertions, and

association reification to address complex analytic needs of management (Fried, Jansen,

Hahn-Powell, Surdeanu, & Clark, 2015). The premise of this research question was that

the manifestation of this higher-order logic, ontological argument assertions, and

association reification at the data level had the potential to improve the analytics and

decision support for management problem-solving.

Research Question 2

The challenge of representing business insights and solutions derived from big

data was the consequence of the increase in complexity of enterprise business processes

which manifested in applications, systems, and data environments. Addressing this

complexity in the use of databases for analysis led to data warehousing and business

intelligence applications. Data warehouses consolidated the data into single logical or

physical repositories, while business intelligence applications automated the exploration

of the data. From these systems and other sources, the creation of specialized datasets for

advanced analysis, for example, statistical analysis, mathematical programming, system

dynamics modeling, data mining, symbolic data analysis, functional data analysis, deep

learning, to name a few, became a necessity. This practice resulted in analytic silos which

constrained general expression of the enterprise within analytic solutions. The need to

segment analytic processing arose when the business analysis was limited to simple

aggregations in the presence of lots of data. The need also arose due to inadequate

computational power for all attributes and instances of the data in analytic processing.

Fortunately, these situations have changed in the modern enterprise, so high-

dimensionality analysis can be taken advantage of in creating insights for management

analytics and decision support (Liu, Liu, & Li, 2017). This new perspective allows

information about randomness, uncertainty, and dynamism to be expressed within

available data. It also allows the supporting data processing to adopt a distributed and

parallel approach, co-opting the resources needed for the computational task at hand.

Research Question 3

The success of algorithms in analytic processing was an essential contribution of

the last decade. In advanced analytic processing, extensions to properties of infinitely

differentiable functions are used to specify real complex lines and planes (Veech, 2014).

These extensions established analytic continuity and discontinuity (or breaks) in analytic

scenarios. The extensions contributed to analytic solutions such as complex response

surface topology, convoluted neural networks, restricted Boltzmann machines, and many

others that are capable of expressing difficult conditions and constraints as chains, trees

or forests of logic within the analytic space (Paganoni & Secchi, 2015). The implication

was that these techniques could be incorporated into the formulation of analytic

characteristics and associations to enhance data for management analytics and decision

support.

To address these research questions, I investigated methods of analytic data

representation. The investigation involved exploration of metadata, the underlying

ontology of the available data, and the intuitive cognitive conceptualization of the

management problem scenario. Since the business environment was not static, it was

critical to integrate continuous adaptation of the representation and annotation of the

characteristics and facts in the business domain. The implication was that contemporary

approaches to analytic data-modeling, which were mostly static, needed innovation to

capture changes in the attribution of concepts within the domain. The innovation was the

application of analytic formulation techniques to derive additional data from the source

data inputs while preserving the links between the input and derived data. Preserving the

links improved the explainability of the insights generated, when the derived data were

multi-valued, non-decomposable attributes, statistical moments, weighted scores (for

example, propensity scores, rank scores, linear weights or variates), domain markers,

patterns, profiles, perceptrons, coefficients, and so on. These derived data expressed

concepts and constructs not directly captured by the available data to broaden the scope

of the data for management problem-solving. Addressing the complexity of the derived

data in the data model was critical. I used partitioning, classification, segmentation,

grouping, and so on, to control the extant complexity under consideration, much the same

way as randomization and blocking during experimentation.

Theoretical Foundation

In this study, I integrated theories of information science and theories in applied

management and decision science. The key theories from information sciences were

relational, dimension, and information theories. I used these theories from Information

sciences to extend the theories from applied management and decision sciences in the

design of the data model for the management analytics and decision problem

representation. Specifically, information entropy and high-dimensional utility theories

were critical in the deconstruction of data for management problem-solving. A brief

discussion of these theories follows.

The relational theory provided the grounding for representing data as relations

and specializing these relations as facts and dimensions in the multidimensional data

model for analytic processing (Gosain & Singh, 2015). The multidimensional data model

fact relation types were the numerical attributes and dimension relations were categorical

attributes or derivations thereof which lacked formalized analytic space. With large and

complex business scenarios, classical multidimensional designs lost flexibility due to

high dimensionality and complex interdependencies (Al-Aqrabi, Liu, Hill, &

Antonopoulos, 2015).

Dimension theory addresses complex attribution and interdependencies through

the synthesis of the invariant properties required to specify the metric or vector space

expressed by available data (Rasetti & Merelli, 2016). The theory guided quantitative

expression of the dimensionality of the abstract space (Shen, Davis, Lin, & Nachtsheim,

2013). Its application resulted in the projection of classical multidimensional space into a

metric space for analytical processing. The techniques depended on the assumptions of

the nature of the space under consideration as follows. Programmatic methods (for

example, linear, stochastic, integer programming; time series) mapped well-defined

input-output spaces. Statistical (for example, analysis of variances, regression) and

probability (for example, bayesian, frequency) methods defined linear smooth metric

spaces. Numerical methods (for example, neural networks, decision trees, evolutionary

algorithms) defined nonlinear smooth metric spaces. Finally, algorithmic heuristics (for

example, data mining, deep learning, artificial intelligence algorithms) applied to

unknown metric spaces. However, the specification of the metric space required standard

measurements, which was lacking in management (Diamantini, Potena, & Storti, 2013).

Therefore, it was critical to use the available data to formulate the ontology to enhance

the representation and interpretation of expressions of underlying subjects of interest, as

proposed by information theory (Schutz, Neumayr, & Schrefl, 2013).

Information theory supports the recoding of available data to improve the

representation of a subject (Budhathoki & Vreeken, 2017). This application of

information theory abstracts available data into specific elements for the analytic

requirements. The application of information theory to data analysis created a number of

methods, including classical data analysis, semantic data analysis, symbolic data analysis,

functional data analysis, topological data analysis, projection pursuit analysis, symbolic

dynamics, complexity analysis to name a few. These methods contributed to data

abstraction as follows.

Classical data analysis described the standard data table which contains raw

information while semantic data analysis re-described the data using atomic and

molecular predicate logic in specific and intended decision-support problem-solving

scenarios (Kaytoue, Kuznetsov, Napoli, & Polaillon, 2011). Functional data analysis

represented information as mathematical and logical functions of underlying elements.

Symbolic dynamics captured multilevel, multiphase information for complex dynamic

analysis and decision-support problem-solving, with a well-developed construct of

symbolic extension which organized each level or phase of a subject into differentiated

zero-dimensional arrays. (Downarowicz, Travisany, Montecino, & Maass, 2014). In

complex analysis, analytic extensions are used to generalize the solution for infinitely

differentiable functions and variables without setting the thresholds beyond which

variables had no business analytic or decision significance and lost management

problem-solving value. The theories of applied management and decision science

established the significant threshold of analytic and decision value for management.

The integration of these analytic formulation constraints imposed by theories of

applied management and decision science transformed available data into the ontology

for management analytics and problem-solving. Rasch theory adds to this through the

construction of the measurements (or mereology and metrology) for management tasks

using latent variables (Bond & Fox, 2013; Sofroniou, 2011). Shafer-Dempster theory

generalized the Bayesian belief by integrating uncertainty reasoning into evidence

derived from available data (Beynon, 2011). Analytical hierarchical process theory

proposed steps for aligning the order of the contributing factors and influences exerted by

ontological and epistemological elements (Deng, 2017). The Blackwell theorem

expanded the application of information filters to isolate signals that were most critical to

decision making (Roy & Rao, 2017)

The organizational theory proposed that the factors and influences exerted by the

business elements occurred in the transactions it conducted. The opportunity to control

the behavior of organizations was in administering their transactions efficiently and

effectively (Powell & DiMaggio, 2012). Organizational theories evolved through task

specialization (or division of labor), behavioral, contingency, information processing, and

computational organization propositions. Each of these propositions established the

decision as the most critical cognitive activity of the organization. Therefore, the decision

theory was a framework for problem identification, specification, and resolution. The role

of data processing was central to decision theory formulations, which determined the

prevailing operational decision theory as rational, cognitive, behavioral, naturalistic,

garbage can, computational, or combinations thereof (Cegielski, Allison Jones-Farmer,

Wu, & Hazen, 2012; Pourshahid, Richards, & Amyot, 2011).

Nature of the Study

In this study, I examined the data model of a typical data analytics project in a big

data environment. I used design-based research (DBR) because of the focus on the design

of artifacts to support the research (Chakrabarti & Blessing, 2014). The focus was on the

design of data model for a typical data analytics project in a big data environment for

management problem-solving. The DBR approach had gained popularity in design

science disciplines like Information systems, Computer sciences, Engineering,

Cybernetics, Artificial intelligence, and others (Cronholm & Göbel, 2015). The research

approach focused on the scheme of the items within a subject under study to highlight

relationships and the impact of changes in the scheme on the overall expression of the

subject (Chakrabarti & Blessing, 2014). With DBR methodology, I was able to evaluate

and compare designs of the situation under consideration (Cronholm & Göbel, 2015).

I used a nonexperimental descriptive format. This format supported the discussion

of the methodology used in the progressive transformation of the data into the concepts of

the management problem. I applied ontology learning, data engineering, and analytic

formulation techniques to extend the data model. The ontology learning identified the

concepts and the cognitive map of the business problem domain. Data engineering

transformed the concepts to the available data. Analytic formulation fostered the

discovery and quantification of the associations and dependencies embedded in the data.

This approach ensured that representation of analytic insights and solutions retained the

connections to the available data.

To illustrate the data-modeling approach, I used secondary data from a U. S.-

based medical products manufacturer and distributor. This analysis scenario required an

integrated corporate action sequence of six different management areas of responsibility

within the enterprise: customer service, marketing, pricing, product development, sales,

and distribution. The case illustration reflected a typical data analytics project situation in

modern organizations where there were lots of data but no clarity on management

problems or the strategies to resolve them.

Definitions

This section includes definitions of key terms used throughout this study.

Analytic extension: The result of the process of expanding or continuing complex

function(s) or variable(s) into simpler function(s) or variables to derive solutions (Segura,

& Sepulcre, 2015).

Bayesian yield: The degree to which the data model facilitates the generation and

evaluation of alternatives, derived from the conditional entropy of Bayes (Deng et al.,

2014).

Classical data attribute: An attribute defined by the values captured at the lowest

level of granularity possible for item or individual of interest (Diday, 2012).

Classical multidimensional data model or data cube: A subject-based

arrangement of measures by categorical attributes to support online analytic processing

(OLAP) operations including slice, dice, roll-up, drill-down, and pivot (Kuznetsov &

Kudryavtsev, 2009).

Classical dimension attributes: A set of categorical attributes organized in a

hierarchy for the partitioning of measures during OLAP operations (Kuznetsov &

Kudryavtsev, 2009).

Classical measure or fact attributes: A set of numerical attributes which are

quantitative expressions of the subject(s) of interest (Kuznetsov & Kudryavtsev, 2009).

Cognitive gain: The degree to which data improved the understanding, reasoning,

and inference within the domain of interest (Curşeu, Jensen, & Chappin, 2013).

Data model extension: an appendage of a data model used to express specific

characteristics of underlying subjects to improve the depth of information representation,

for example, relationship, semantic, temporal, spatial, graphic, provenance, and others

(Smirnov & Kovalchuk, 2014).

Decision yield: The estimate of the likelihood of the use of the data in the

resolution of the decision problem because of the added precision, consistency,

simplicity, cost efficiency, and agility (Fish, 2012; Wu et al., 2012).

Empirical lift: The degree of expression of the critical empirical factors in the

data model, derived from information entropy concept of Claude Shannon (Deng et al.,

2014).

Enterprise data model: Rationalized integrated third normal form data model of

application and systems used to capture activities of the enterprise (Metz, 2014).

Enterprise data warehouse: Physical implementation of an enterprise data model

in as a database management system for analytic uses (Metz, 2014).

Intelligence density: The ratio of conceptually recognizable attributes to a total

number of data elements in the model (Bai, White, & Sundaram, 2011).

Symbolic data attribute: An attribute defined by values transformed from classical

data to express the characteristic of an attribute for specific analytic intentions (Diday,

2012).

Symbolic dimension attributes: A set of attributes that form an axis of analysis

used to qualify a subject of interest in specific terms for specific analytic objectives

(Noirhomme‐Fraiture & Brito, 2011).

Symbolic measures or facts attributes: Measures of a domain of interest used to

express numerical characteristics of a domain for specific analytic objectives

(Noirhomme‐Fraiture & Brito, 2011).

Symbolic extension: Specialized encoding of attributes that uniquely represents

the distinct state of existence of a subject of interest (Downarowicz et al., 2014).

Symbolic primitives: Functions automatically generated by data mining

algorithms, for example, symbolic regression, classification or time series, which include

fit functions, formulae, control commands, and so on, used in expressing the

mathematical relationship between attributes (Zelinka, Davendra, Senkerik, Kasek, &

Oplatkova, 2011).

Assumptions

Assumptions are conditions that a researcher holds as true with no demonstrable

proof. The first assumption in this study was that the available data for the data analytics

project in the big data environment were comprehensive and reflected the real world of

the enterprise and its management decision problems. The complexity of the enterprise

reflected its management problems, such that data model would offer the analysts and

decision makers the ability to establish the importance of operational concepts within the

management domain. This use of data-modeling preserved the lineage between the raw

data input and enhanced data generated for problem-solving (Caron, 2013).

The second assumption was that the abstraction of data preserved the validity of

the derived insights. The application of analytic formulation techniques to transform

attributes emphasized associations and influences that were specific to the analysis

situation under consideration. For example, analytic transformations such as class

assignments, use of nth order statistical moments, frequency estimates, probability

distribution functions, the coefficient of determination, correlation coefficient, and so on,

expressed association between the indicator and response attributes under consideration.

For example, joint probability estimates applied to situations where independence was

verifiable. Conditional probabilities were the preferred method of quantifying association

when independence was not verifiable.

The third assumption was that it was possible to extract insight from available

data. This perspective was different from contemporary research studies, in which the

data were from a controlled data generation process, an experiment. In this study, the

focus was on the data model of the available data for data analytics project. The data

combined information generated in the day-to-day operations of business integrated with

information captured by other sources external to the organization. In this scenario, the

data analyst had no control of the data generation process and was unable to manipulate

the situation directly. Data analysis and modeling required inferring influences of

attributes on one another to determine their consequences on management decisions and

business programs.

Scope and Delimitations

This study focused on the enhancements to the data model of the available data

for data analytics project in a big data environment. I did not construct a separate OLAP

multidimensional model or create an alternative analytical model building outside the

context of the data model. The former was the case with OLAP application system, while

the latter was the case with statistical and mathematical programming, system dynamics,

decision analytic processing, data mining, deep learning techniques, and algorithmic

heuristics applications and systems. This focus on the data model of the available data for

data analytics project in a big data environment was adopted because it offered the most

elegant solution to analytics in management compared to the alternative approach of

contrived subject-oriented OLAP models or constrained analytic algorithms. The OLAP

data model limited associations between the subject areas of the enterprise. Analytic

algorithms further limited data participation as required to control dimensionality of the

input data for computational and methodological purposes.

This data model research defined data structures that advanced data-driven

problem-solving in management. The tasks included decision discovery, scenario

generation, prediction, inference, evaluation, and choice tasks. The approach focused on

the abstraction of data elements from their raw form into structures, referred to as

analytic extensions, and their application to the creation of solutions to support these

tasks. This approach was different from the classical research approach in which

empirical study drove data generation and analysis. Instead, this work aligned the

objectives of the data model to structural, formal, and resolution expectations of the area

of interest. Through the data model, established relationships between the data objects

and analytic methods fulfilled the requirements of composing evidence and determining

effects and influences on entities.

I did not provide the detailed treatment of any of the analytical techniques used,

or their mathematical proofs because all the techniques were mainstream and did not

require justification as part of this study. I focused on the applied aspects of these

concepts and constructs, and their integration into the data model for management

analysts and decision makers.

Limitations

I used secondary data to illustrate the enhancements of the data model of the

available big data for analytics and decision-support in management. The source of data

for the study was proprietary, so the data was de-identified as required by the data owners

to protect the sources. The validation of the results, presented for the study, may not

account for all the situations of anomalies in the data or with the analytic formulation

techniques applied.

The interviews of business analysts and executives conducted established the

conceptual scope and the prevailing hypothesis of the analytic problem. The evaluation of

the resulting data model depended on management acceptance and actionability criteria

established by the business analysts and executives through the interviews. I also used

empirical measures of business and analytic significance, for example, information gain,

Bayesian yield, intelligence density, and other similar measures. This business result

orientation was different from traditional research where the statistical evaluation was

preferred.

I drew from my experiences as a management analyst and researcher for Fortune

10, 50 and 500 companies and government agencies in the United States, seeking

assistance with measurement, estimation, inference, and forecasting solutions to address

transactional, operational, or strategic problems. In this role, I needed to advance

capabilities in existing business intelligence and decision support systems to integrate

inferential capabilities (programmatic, diagnostic, predictive, intelligence) into their

decision-support environment and analytic processing workflow. Expectations included

the creation of a measurement and metrics framework for shared performance

management across diverse management domains. I designed and implemented

application systems to support management effectiveness and efficiency. The driving

force was to generate value from data assets and monetize them through the creation of

value-added information solutions and services, for both internal and external use. Since

these situations were specific subsets of data, analytics, and decision-support scenarios

faced in business management, the perspectives driving this work were from these

business settings. Therefore, the application of the study outside the business

management context would be limited. Extension of the data model may not be necessary

for data gathered through a controlled experiment or in situations where measurements of

underlying elements are well established as in science and engineering contexts.

Significance of the Study

Significance to Theory

In this study, I addressed gaps in data-modeling of extensive secondary data for

analytics and decision-support in management research. I advanced the use of ontology

learning, data engineering, and analytic formulation techniques to transform available

data from the classical data format in the form of scalar data types, through matrices and

arrays, to functionals with specific ontological commitments. This approach closed the

conceptual gap between analytical insights and cognitive concepts of domains of interest

which, Beroggi (2010) argued, lagged behind advances in information and computer

technology.

This study systematized an adaptive and progressive stepwise process of

designing data models that connect meanings and signals embedded in the data. This

framework generated derived data elements in specific analytic contexts. Many

conventional approaches to decision modeling such as the analytical hierarchical process

(AHP) of Saaty, generalized utility models, generalized risk models, and others which

required heuristic approximations by experts. A meticulous transformation of existing

data through ontology learning, data engineering and analytic formulation of the metric

space of the subject of interest replaced the rates and weights approach of decision

analysis methodologies.

The adaptive approach relaxed the controls and assumptions of traditional data-

modeling and allowed relationships captured within data to drive the formulation of

empirically rigorous, pragmatic data models that incorporated hierarchies not purely

based on cardinality and linear functional dependencies. This integrative approach to data

analytics in management maximized utilization of information and knowledge assets for

decision processing. It aligned the processing of available data to the ontology of the

subject under consideration specified by business analysts and executives.

Significance to Practice

The significance of this study was in the construction of a data model for data

analytics projects in a big data environment for management problem-solving. The focus

was the use of the data model to deconstruct complexity within available data and the

management problem-solving situation. The goal of this data model research was to make

transparent the discovery, evaluation, and resolution of management opportunities within

the domain.

The deconstruction of complexity was crucial to the creation of a useful data

model. Complexity is the state of lack of transparency between inputs (causes) and

outputs (effects) of nondeterministic systems. Complexity manifests as the interaction of

the inputs, the input output process, and the outputs themselves. Analytic deconstruction

of complexity is critical to decision processing, through programmatic (if known inputs,

outputs), diagnostic (if unknown input, known output), predictive (if known input,

unknown output), and intelligent (if unknown input, unknown output) means. The

construction of data models that accounted for the complexity of underlying data

elements and their interactions improved analytics and decision-support in management.

Making analysis more concrete and quantitative furthered Busemeyer and Townsend’s

(1993) decision field theory proposal. The decision field theory reflected some universal

propositions for resolution of choice problems through systematic perceptions of the

environment based on the information. It also included the utility of numeracy in the

decision makers’ coping to determine the need for decision-support by information

systems and technology (Peters, 2012).

The final area of professional application of this study was in the creation of

management support applications. The typical input to decision processes was a set of

rates and weights compiled from experts and surveys. Decision analytic techniques such

as hierarchical analytic processing, network analytic processing, info-gap decision

processing, and many others, required in-depth knowledge of the domain of interest and

the ability to reduce the knowledge into weights and rates of the decision problem. The

weights and rates formulated analytically from the available data were more accurate than

those defined by experts (Dezert & Tchamova, 2014).

Significance to Social Change

Business enterprises are essential instruments of societal prosperity because they

provide employment, support the needs of the population by providing goods and

services, and contribute to social efforts within many communities through donations and

volunteerism. The influence of business enterprises have increased due to globalization,

the information age, the convergence of business and politics (for example, the U.S.

Supreme Court Citizens United decision), and the adoption of free-market economics

around the world. These developments have added complexity to the working

environment for executives and managers of enterprises. The modern business enterprise

is not just expected to be solvent; it is also expected to contribute to the social aspects of

the communities in which it is doing business by improving the quality of life of

customers and community. The evidence needed to guide decisions and actions to

maximize benefits of the business enterprise to all its stakeholders and the public at large

was made possible by extending analytics to account for these considerations (Burns &

Jindra, 2013). Broadening the characterization of the influences of the enterprise

highlighted opportunities for management engagement in social issues. In many cases,

the issues that impact the marketplace also influenced the performance of the

organization. An example of social change that could be realized through the case

illustration includes social programs to improve daily activities of patients and residents

of health care institutions served by the company, especially incentives for sales

representatives to volunteer their time at facilities they covered.

Summary and Transition

This chapter introduced the study of a model of the available data for data

analytics project in a big data environment. The goal of the study was to search for data

model extensions to address the issues of representation of insights about problems and

solutions. This approach required organizing all available data into structures for that

mapped the available data to the cognitive conceptualization of the management problem

situation. This study is expected to contribute to reducing the high degree of failure in

management analytics and decision-support, which accounted for an estimated $2.7

trillion in wasteful spending in 2016. The link between available data and solutions of

management decision problems established a favorable relationship between investments

in data asset development, quality of decision-making, and the business value achieved.

In Chapter 2, I review the literature on online analytic processing

(multidimensional) data-modeling, the use of dimensional analytic techniques to achieve

functional form expression of available data, issues of big data analytic scenarios, and

challenges with computational and algorithmic analytic processing. In Chapter 3, I

describe the research methodology, including a justification for a DBR methodology, the

use of the descriptive, nonexperimental, quantitative format, the choice of the secondary

data, and the data abstraction methodology that integrated ontology learning, data

engineering, and analytic formulation techniques. The results of the study are in

presented in Chapter 4, and the discussion of the results are presented in Chapter 5.

Chapter 2: Literature Review

Introduction

The purpose of this descriptive nonexperimental quantitative, DBR study was to

examine the data model in a typical data analytics project scenario to address difficulties

encountered with the acceptance of big data projects outputs. The literature on data

models with data analytics revealed a very strong favorable association (Zohuri &

Moghaddam, 2017). The conceptual data model was the primary tool for communicating

the structure, content, and context of available data in organizations, yet big data

analytics projects favored an approach that bypassed this critical artifact. The result was

that business analysts and executives found the outputs from data analytics projects

inadequate for management analytics and decision-support (Bendre & Thool, 2016).

In this chapter, I describe the literature search strategy on big data analytics

process. I preview the state of analytic data-modeling, the role of functional form

expression in data models, the problem of representing large scenarios for analytic

processing, and the challenges with computational/algorithmic solutions in data analytics.

I conclude with a discussion of the issue of the dissociation of the data from resulting

analytic solutions which was my motivation for this data model approach to the

challenges of big data project outputs (MacLeod & Nersessian, 2018).

Literature Search Strategy

The primary source of material for the study was Academic Search Complete, an

EBSCO academic research database, available through Walden University. Searches

included Google Scholar, Elvsier, Association for Computing Machinery (ACM), and the

Institute of Electrical and Electronic Engineers (IEEE) digital databases.

The keywords used in the search included empirical model building, analytic

model building, multidimensional modeling, online analytic processing), exploratory

model building, exploratory system dynamics modeling, statistical database, business

intelligence, knowledge discovery from databases, data mining, data modeling, decision

models, domain models, big data modeling, business intelligence, expert systems,

symbolic data analysis, dimensional analysis, symbolic dynamics, artificial intelligence,

reasoning systems, artificial intelligence modeling, deep learning modeling, and symbolic

computation. The search was conducted from the year of study until about 600 articles

were retrieved and reviewed. Changes in popularity of these keywords over time

complicated the task of limiting materials included in the study to publications in the last

five years, as required by Walden dissertation guidelines. Some of the most relevant

materials cited publication dates as early as 1990, which indicates that the problem of

making sense of data emerged with Information / Systems era of this decade. Despite the

age of these materials, the concepts expressed aligned with contemporary usage and

understanding.

Of the roughly 600 articles I retrieved and reviewed. I cited 259 articles in this

document. Of these, 87% were peer-reviewed and published between 2013 and 2018

based on Walden library databases designations. Ten percent of these citations were

either books or conference materials.

Theoretical Foundation

This study integrated theories in information science and applied management and

decision sciences to extend the data model for management analytics and decision

problem representation. Relevant theories in information science included relational,

dimension, and information theories. The applied management and decision sciences

theories were organization and decision theories. A brief discussion of these theories

follows.

The relational theory provided the grounding for representing data as relations of

attributes such that every record within them was an instance of occurrence or members

of the relation. The relational theory also provided the constructs for specializing these

relations as fact relations and dimension relations in the multidimensional data model for

analytic processing (Gosain & Singh, 2015). The multidimensional data model facts

relations were the numerical attributes and dimension relations were categorical attributes

or derivations thereof, without any attempt to formalize the space defined. With large and

complex business scenarios, the classical multidimensional designs resulted in problems

of large dimension sizes and complex interdependencies (Al-Aqrabi, Liu, Hill, &

Antonopoulos, 2015).

Dimension theory addresses complex attribution and interdependencies through

the synthesis of the invariant properties required to specify the metric or vector space

expressed by available data. The theory guided quantitative expression of the

dimensionality of the abstract space (Shen, Davis, Lin, & Nachtsheim, 2013). Its

application resulted in the projection of classical multidimensional space into a metric

space for analytical processing. The techniques used depending on the assumptions of the

nature of the space under consideration as follows. Programmatic methods (for example,

linear, stochastic, integer programming; time series) projected well-defined input-output

spaces. Statistical (for example, analysis of variances, regression) and probability (for

example, Bayesian, Frequency) methods projected linear smooth metric spaces.

Numerical methods (for example, neural networks, decision trees, evolutionary

algorithms, etc.) applied to nonlinear smooth metric spaces. While algorithmic heuristics

(for example, data mining, deep learning, artificial intelligence algorithms) came in

useful in projecting unknown metric spaces. However, the specification of the metric

space required standard measurements, which was lacking in the field of management

(Diamantini, Potena, & Storti, 2013). Therefore, it was critical to use the available data

and subsequent derivations to formulate the ontology for the representation and

interpretation of expressions of underlying subjects of interest, using Information theory

proposals (Schutz, Neumayr, & Schrefl, 2013).

Information theory supported the re-coding of available data to improve the

representation of a subject. This application of information theory abstracted available

data into elements specific for analytic requirements. Many methods of data analysis

resulted from the application of information theory. Examples were classical data

analysis, semantic data analysis, symbolic data analysis, functional data analysis,

topological data analysis, projection pursuit analysis, symbolic dynamics, complexity

analysis to name a few. Essentially, these were methods of data abstraction that can be

integrated into the data analytics framework to drive extensions of the data model for

insight generation discussed below.

Classical data analysis described the data available in the classical data table,

while semantic data analysis extended the data analysis to the underlying atomic and

molecular predicate logic (Nalepa, 2017). Symbolic data analysis further abstracted

classical or semantic data for intended analysis and decision-support problem-solving

(Kaytoue, Kuznetsov, Napoli, & Polaillon, 2011). Functional data analysis provided the

framework for the representation of information as mathematical and logical functions of

underlying elements. Symbolic dynamics provided the framework for representing multi-

level, multi-phase information for complex dynamic analysis and decision-support

problem-solving (Downarowicz, Travisany, Montecino, & Maass, 2014). Furthermore,

SD has a well-developed construct of symbolic extension which organizes the data at

each level or phase of a subject into a zero-dimensioned array for differentiation. In

complex analysis, analytic extensions were used to generalize the solution for infinitely

differentiable functions and variables. However, the boundaries of analytic or decision

significance and management problem-solving value were not considerations of these

methods. The theories of applied management and decision science established the

significance and value threshold of analytic outputs in management.

The translation of available data into an ontology for managerial tasks required

the application of theories of applied management and decision science. Applied theories

like Rasch, Shafer-Dempster, analytical hierarchical process theories advanced the

integration of analysis into management and decisions sciences. Rasch theory was useful

in the construction of the measurements (or mereology and metrology) within the

management domain using latent variables (Bond & Fox, 2013; Sofroniou, 2011). Shafer-

Dempster theory generalized the Bayesian belief by integrating uncertainty reasoning into

evidence derived from available data (Beynon, 2011). Analytical hierarchical process

theory proposed steps for aligning the order of the contributing factors and influences

exerted by ontological elements (Deng, 2017).

The organizational theory proposed that the factors and influences, exerted by the

business elements, occurred in the transactions it conducted. The opportunity to control

the behavior of organizations lay in administering these transactions efficiently and

effectively (Powell & DiMaggio, 2012). For this reason, the organizational theories

evolved through task specialization (or division of labor), behavioral, contingency,

information processing, and computational organization propositions. Each of these

propositions held as its central theme that the decision was the most critical cognitive

activity of the organization. Decision theory provided the framework for problem

identification, specification, and resolution. This placed analytic processing at the center

of decision theory proposition. The degree of analytic processing was responsible for the

prevailing operational decision theory as rational, cognitive, behavioral, naturalistic,

garbage can, computational, or combinations thereof (Cegielski, Allison Jones-Farmer,

Wu, & Hazen, 2012; Pourshahid, Richards, & Amyot, 2011).

The integration of these theories converged on the utility of analytic processing in

the disambiguation of the business environment for analysts and executives. The essential

contribution of analytic processing compared to other analytic techniques (i.e., reporting,

modeling, algorithms, and computation) was complete automation of the data analytics

process from input to the generation of actionable insights and recommendations for all

levels of the enterprise. The requirement to integrate data and technology assets, i.e.,

database management systems, and computer application programs into seamless

processing were critical. Equally important was ensuring the outputs of the analytic

processing exercise was transparent in management decision making. The transparency

of analytic processing remained the primary challenge of applied management and

decision science practitioners and researchers, hence the primary motivation for this

study.

Literature Review

As noted above, analytical techniques provided frameworks for systematizing

analytic processing (Kwakkel at al., 2010). They helped determine the nature of

associations between attributes in the data to answer business and research questions

about underlying subjects (Chen, Chiang, & Storey, 2012). The structure, content,

context, unit of analysis and granularity of the data dictated their breadth, depth, and

application to management analytics and decision-support. In recent years, users have

challenged the utility of analytical techniques in addressing complex business questions

facing management (Gomes, 2014). The response to this challenge was online analytic

processing (OLAP). OLAP has two aspects: the multidimensional data model and

algebraic operations. The OLAP data model provided the framework for organizing data

the multidimensional structure. The multidimensional structure is an n-relational structure

or data cube. The OLAP algebraic operations specified exploration and navigation

procedures for the data cube (for example, slice, dice, drill, pivot). Currently, OLAP

remains state of the art in the analytic processing despite challenges of limited analytic

capabilities. To gain perspective on solutions to the challenges and issues with OLAP, I

review the literature on the synthesis of a logical representation of complex subjects and

large business analytic scenarios that advances high dimensional analytic processing. I

provide a discussion of multilevel ensemble formulation through

algorithmic/computational analytic processing. I highlight the absence of data models to

support these higher forms of analytic processing, which is the gap I am seeking to

address with this study.

Online Analytic Processing

Edgar F. Codd was the central figure in data-modeling literature for proposing

both relational and online analytic processing (OLAP) data-modeling techniques (Wade

& Chamberlin, 2012). Relational data-modeling drove advances in database technology,

including the principle of data definition and manipulation using declarative language

such as the structured query language (SQL). The framework of the relational data model

was the theory, algebra, and calculus of relations which were stable and closed. At the

core was the representation of data items as related sets, to which rules of normalization

were applied to ensure efficiency and accuracy of data capture and storage. The OLAP

proposal generalized the relational data-modeling approach from few to large relational

structures. The OLAP model was responsible for the rapid adoption of data-driven DSS

of the last decade, including a change in the role of the data warehouse from a passive

repository for static enterprise reporting to an active platform for dynamic real-time

analytics and decision-support.

At the core of the OLAP proposal was the multidimensional data-modeling

technique. This data-modeling technique organized numerical data as facts (or measures)

and categorical data as dimensions to form a multidimensional array (Gosain & Singh,

2015). This scheme enabled sophisticated navigation of large data sets and high-

performance data retrieval operations.

The original multidimensional data-modeling proposal by Codd was rather strict

about the designation of data attributes as measures or dimensions, and about the

relationship between fact and dimension relations. Intense research into multidimensional

data-modeling led to revisions. Gosain & Singh (2015) presented the most

comprehensive survey of such revisions, which identified 23 characteristics of the 16

most complete multidimensional models. Table 1 shows the characteristics of the

revisions.

Table 1

Characteristics of OLAP Multidimensional Designs

Aspect

Characteristic

Rationale

General

Atomic and non-atomic

measures

Capture of measures at whatever level of granularity available

Derived measure

Deriving new measures from existing ones, as needed

Derived dimension attributes

Deriving new dimension attributes, as needed

Flexible additivity

Support for full additivity, semi-additivity, and non-additivity

Non-hierarchical dimension

A single level dimension attribute

Cross dimension attributes

Dimension attributes that reference multiple dimensions

Degenerate facts

Measures that may not be accurate all the time

Degenerate dimensions

Dimension attribute with no content except its primary key

Sharing dimensions

Dimension shared by multiple fact relations

Sharing dimension levels

Dimension level sharing by multiple fact relations

Parallel hierarchies

Creation of more than one hierarchy in a dimension

Different roles of dimensions

Dimensions that serve different roles depending on the context

Fact-dimension

relationship

Incompleteness association

Allowing the occurrence of missing associations

Non-strictness association

Dynamic associations

Fact-dimension

relationship

Incompleteness association

Allowing the occurrence of missing associations

Non-strictness association

Dynamic associations

Inter-dimension

relationship

Generalization

Generalization/ Specialization relationship between levels of

dimension

Association

Functional dependencies between dimension attributes

Fact constellation

More than one fact in a dimensional model

Implementation

Technique

Modeling technique include ad-hoc, E-R, UML

Mathematical/analytical

constructs

Inclusion of mathematical/analytic operations

Transformation of hierarchy

Mapping for transforming hierarchies

Guidelines

Availability of an implementation guideline

According to Gosain & Singh (2015), the state-of-the-art analytic data-modeling

retained the basic n-dimensional schema of fact relations and corresponding dimension

relations. Representation of fact and dimension as relations allowed fact elements with

the same dimensional architecture to connect to dimension elements at the same group

level. This representation created the classical multidimensional structure commonly

referred to as snowflake schema design, providing significant flexibility over the earlier

proposal, the star schema design (Sharma & Sood, 2013).

Each dimension of the multidimensional schema represents sets of categorical

data elements with a partial order from top to bottom, such that one categorical data

element is greater than another if the members of the former are subsumed by the latter.

The topmost element of the dimension corresponds to the largest possible dimension

element size because it logically subsumes all the other elements in the dimension. The

partial order of the categories forms the hierarchy of the dimension. The hierarchy of the

dimensions was the navigational paths or graphs. Essential characteristics of these paths

or graphs are: (a) that they are acyclic paths or graphs which means no re-entry loop and

(b) that their direction reflects the cardinality of the relationship between the sets of

dimension elements based on their occurrence (Pedersen, 2013).

The practice was to apply Codd’s rules of normalization to the structuring of the

dimension elements to create homogeneous dimension levels. This practice allowed

multiple hierarchies for different navigation and aggregation paths on the data. It also

allowed specialization of the relationship between dimension levels into six types: (a)

covered relationship in which the lower dimension level subsumes all the elements of the

higher dimension level; (b) onto relationship in which there is a one-to-one

correspondence between the dimension levels, typically modeled implicitly within the

relation defined for the dimension level; (c) non-covering relationship which implies the

dimension level is in a path parallel to a considered dimension level, with skipped levels;

(d) non-onto relationships which are the absence of a parallel relationship at the one-to-

one cardinality; (e) self-into relationship in which there is a self-referential requirement at

the one-to-one level of cardinality creating an implicit hierarchy in the dimension level;

and (f) self-onto relationship, a situation where a self-reference returns an empty set,

which was the condition of a fully normalized dimension design (Pedersen, 2013).

The nature of the dimension is also an essential consideration in modeling. A

dimension can be universal or domain. Universal dimensions include time and location,

which can be modeled on their own or used to qualify other dimensions, as is the case in

the spatiotemporal data model. Domain dimensions are those that have a specific

significance in the subject under consideration; for instance, in the business domain,

examples of dimensions were Store, Product, Customer, and so on. It is also essential to

determine whether the dimension is static or dynamic and, if dynamic, whether it has a

cycle and whether the cycle is or is not stationary (Pedersen, 2013). Managing dynamism

in the design of dimensions creates the concept of slowly changing dimensions, which

have defined types as follows: (a) Type 0 – insert only; (b) Type 1 – update in place; (c)

Type 2 – dimension versioning; (d) Type 3 – use of dimension effective and expiry date;

(e) Type 4 – use dimension change or history relation to capture changes; and (f) Type 6

(hybrid of 1, 2, 3) with the current value, old value, start date, end date and current status

flag (Kimball & Ross, 2011; Leonard, Mitchell, Masson, Moss, & Ufford, 2014). The

assumption was that rapidly changing dimensions should not exist, but they did. For

example, the customer was a very popular dimension in the business domain model

which grew with changes in essential characteristics. The characteristics of the customer

were not part of the classical fact-dimension scheme of the multidimensional model. The

model did not explicitly reflect the change in state of the customer related to its activities

and did not establish a connection with related concepts like party, prospect, and so on

(so-called polymorphism).

The modeling of the dimensions was critical as it defined the axis of analysis or

navigation for the user and provided the analysis flow process the user could adapt to

formulate explanations to situations of interest progressively. However, some problems

emerged with this design of dimensions including (a) that the relationship between the

dimensions was primary key-foreign key reference; (b) that the dimensions are

independent of each other; (c) within each dimension the different dimension hierarchies

partition the dimension space equally or carry the same weight in terms of impact; (d) at

each dimension level the effect of the dimension values were equally weighted; and (e)

when there were elements in the dimensions that had a numerical value, they should be

treated as categorical attributes during analytic processing (Caron, 2013).

The measure or facts of the multidimensional data model are typically the

numerical attributes in the available data set. Fact or measures are assumed to be the

numerical translation of the results of the interaction of the dimensions at the appropriate

levels of details (Schutz, Neumayr, & Schrefl, 2013). For example, sales facts or

measures such as sale amount, sale quantity, sale price, or sale discounts are a numerical

representation of the interaction of customer and product dimensions within the business

domain.

Different approaches were used to derive the facts or measures. One approach is

the use of the concept of key performance indicators (KPI), which identifies measures

that were significant contributors to the performance of the domain of interest

(Diamantini et al., 2013). Another approach is the concept of the balanced scorecard

(BSC), proposed by Norton and Kaplan, as a measure of organizational growth and

learning that integrates operational and financial perspectives of organizations (Morard,

Stancu, & Jeannette, 2012). KPIs and BSCs were part of visual displays commonly

known as dashboards, which are constructed at different levels of an organization to

provide a point-in-time (cross-sectional) or progression-over-time (longitudinal) view of

performance. Current challenges with the definition of measures, related to the question

of constructing an appropriate measurement model for items and activities that were not

directly measurable. Morard et al. (2012) determined that the measurement model

derived deductively from available data differed from the BSCs and KPIs expressed by

management.

In a classical OLAP conceptual data model, there is no assumption of

independence in the facts or measures, so they should not be combined. Also,

contemporary designs advocate annotation of facts or measures such that there is

information on whether they are natural or derived. When they are derived, it is also

necessary to specify what operations (statistical, mathematical, or logical, for instance)

were applied. Because the classical OLAP data model design constrains the

implementation of hierarchies between measures, navigating the facts or measures in the

same way as dimensions were not allowed. The design became an important issue when

data gathered was at multiple levels of granularity and association between facts could

not be derived through the navigation of the dimensions. Contemporary OLAP designs

also assume that the value of the fact or measure is immutable and that the significance of

the value of the fact or measure is stable over time (Diamantini et al., 2013). For this

reason, there is no formal concept of changing facts and measures or adjustments to facts

or measures to ensure that change in the significance of the value is in the classical

multidimensional model.

Another important aspect of a multidimensional model is the relationships

between fact and dimension relations. The contemporary approach advocates relating the

fact to the dimension at the right level of granularity. The nature of this relationship is

essential to the accurate functioning of OLAP operations, especially aggregation

operations. An important reason for this is that aggregation operations navigate lattice

expressed by the intersection of the dimension and fact elements in three different ways:

additively (sum), non-additively (average, min, max), and by counts (cardinality). Other

considerations handled in contemporary design include (a) ranges by using value-

equivalent tuples with annotations to specialize OLAP operations on the ranges as slice

operations – time slice or space slice operations (Pedersen, 2013); (b) handling of

uncertainty in the data value and relationships as probability or conditional probability

using the probability operations applied, within and between fact relations and/or within

and between dimension relations (Cuzzocrea, 2011; Moole, 2005); and (c) heuristic

mapping of fuzzy attributes to actual dimensions and measures based on specified rules

(Fasel, 2014).

The process of determining the attributes in an OLAP data model was not

straightforward, mainly because the availability of data from multiple sources was

overwhelming (Romero & Abello, 2011). Data modeling methods took on two main

frameworks: demand-driven based on user requirements or supply-driven based on the

available metadata and data. A hybrid which integrates both frameworks was gaining

popularity (Romero & Abello, 2011).

According to Romero and Abello (2011), the demand-driven approach followed

the classical Information System (IS) engineering process which depended on the end-

users to provide input to inform the data-modeling process, while the supply-driven

approach depended on the available metadata. However, in real-world scenarios, end

users may not be aware of all the potential analysis opportunities and may overlook

critical requirements that could dramatically improve decision-making. Also, metadata

may not be comprehensive to allow the data modeler to infer all the attributes required

for analysis of the data elements. Also, available data was the noisy and unsupervised

discovery of features within the data was overwhelming and useless to decision-making,

and sometimes downright misleading. Most recent proposals called for the use of

ontologies to model data for analytics and decision-support (Padillo & Mazon, 2011).

Ontology, in the context of the data model, was the formalized conceptualization

of a subject within the domain of interest through its available data. Ontology was,

therefore, the most differentiated version of the “data about the data” or metadata

(Jareevongpiboon & Janecek, 2013). Contemporary documentation of data was in the

form of the data dictionary, which was limited to the name, description and the syntactic

attributes of the data including data type, uniqueness, nullable, and so forth. Data

glossaries expanded the number of semantic attributes that were captured to include

examples, concepts, constructs, to name a few. Thesaurus and vocabularies extended the

symbolic attributes further to include lateral relationships like types, similarity,

dissimilarity. Taxonomies captured dimensional attributes, including hierarchical

relationships within a set of concepts allowing partial ordering of these concepts.

Ontology brought all these characteristics together to achieve an ultimate

conceptualization of a subject of interest capturing all relevant concepts, constructs,

constraints, controls, and constants (Martinez-Cruz, Blanco, & Vila, 2012).

According to Pardillo and Mazon (2011), there were ten shortcomings of the

multidimensional model design, use of ontologies solved. Table 2 summarizes these

shortcomings and related solutions.

Table 2

Ontology proposals for OLAP Data Models

Situation

Current state

Rationale

Solution

Multidimensional

design

requirements

Limited to

classical

attributes

defined by the

users

Needs for specific

concepts that

provide meaning

to the analytics

and decision-

support situation

• Use of Foundation ontology

with representation and

interpretation mappings

Requirement for

data source

reconciliation

Direct or

syntactic

reconciliation

only

Semantic

reconciliation is

more appropriate

• Dimension and measure

discovery through matching and

subsumption,

• Selecting measure and

dimensions for defining facts

and classes,

• Establishing bases for searching

and pruning (grouping rules

etc.),

• Defining aggregation

hierarchies through part-whole

relationships,

• Use of heuristics on structural

aspects, for example, instance

counts,

• Inserting frequencies,

cardinality, etc.

(table continues)

Situation

Current state

Rationale

Solution

Data model

completeness

Syntactic

completeness

Semantic

completeness

• Use of published ontologies

and taxonomies to ensure

representation of

metonymy/homonymy or

hyponymy/hyponymy

relationship and other issues of

polysemy

Data types of

measures

Measures of

analysis

declared as

numeric

without any

sense of unit

or scale

Measures have

units and scales

normalized

• Use of levels of measurement:

nominal, ordinal, interval and

ratio, which improved the

implementation of aggregation

semantics for the different

measurement levels, for

example, mode and chi-squared

aggregation for nominal

measures, mean, standard

deviation, correlation, etc.

aggregation for interval data

Summarizability

Additivity

constraint

Semantic

summarizability

• Classification of measures:

additive, semi-additive and non-

additive;

• Classification of summary

attributes as flow (rate), stock

(level) or value per unit;

• Classification of non-additive

measures into ratios,

percentages, measures of

intensity, average, minimum,

maximum, etc.

Conformed

dimensions

Hub-and-

Spoke vs. Bus

approach to

design

Design consistency

that allows

complete

specification of

subject of interest

• Use of annotation and links that

map results to the input data

used

(table continues)

Situation

Current state

Rationale

Solution

Traceability

Loss of

traceability

between the

source and

model

semantics

Semantically

traceable data

models

• Integration of

transformation logic into

the data model

Reasoning

support

OLAP

algebra and

calculus

Reasoning

requires logic for

proof

• Integrate logical

propositions provided by

ontology into the data

model

•

Visualization

Issues of

visualization

of high

dimensional

hierarchical

data

Layered

visualization

with appropriate

visual gallery

• Semantic annotation of

measure and dimensions

for visualization

Security

Ad-hoc

• Inferred from ontology

about credentials,

permissions, and rights

Table 2 refined the approach to the determination of the content of the

multidimensional data model. The ontology approach emphasized the explicit

specification of knowledge available about the domain, either from internal sources or

public sources. The approach required inference of any domain-specific attribution not

available in the data. Hoang, Jung, and Tran (2014) advocated the creation of this

enterprise ontology, independent of the information systems development projects to

ensure that there was a systematic approach to qualification and quantification of the

elements relevant to knowledge of the domain of interest.

While ontologies captured comprehensive conceptualization of the domain of

interest, it provided no guidance on their essential and relative influence on the events

and activities of the domain of interest. It also did not provide a framework to reduce a

complex domain or concept into its components for examination. The dimensional

analysis technique provided such a framework by enabling functional form expression as

discussed below.

Functional Form Expression

The primary reason multidimensional models was so useful in analytics and

decision-support was their structural alignment to dimensional analysis and reasoning

than contemporary relational models(Savinov, 2013). Dimensional analysis generalized

linear algebra, reducing complex problems into simple forms for solutions (Shen et al.,

2013). The principal use of dimensional analysis was to deduce from data the final form

of quantities of dependent and independent attributes of the subject of interest devoid of

scale or units, according to Buckingham’s π-theorem. This dependence on normalized

standard quantities for expressing relationships preserved the concept of similarity and

prevented coincidence of equivalence and differences caused by measurement units and

scales. Using the similarity principle, it was possible to formalize the problem

mathematically and simplify the solution by reducing the space of the data matrix to

achieve a better functional form for underlying relationships.

The dimensional analysis required the manipulation of three classical constructs:

properties, quantities, and units to derive attributes whose units canceled out when

multiplied or divided, such that their absolute significance was maintained despite the

change in numerical magnitude (Bridgman’s principle) (Shen et al., 2013). The formula

that satisfied this principle of absolute significance of relative magnitude was the power

law form expression:

Q = αAaBbCc… (1)

where

• Q is the derived attribute

• A, B, C. are numerical values of base quantities

• a, b, c are real numbers whose values distinguish one type of base quantity

from another

• α invariant scale that guarantees similarity of Q and base quantities

(similarity coefficient)

These derived power form attributes were the dimensions. A dimension of the first kind

was from the base units of the numerical value of base quantities, and dimensions of a

subsequent kind from dimensions of the first kind, and so on. In this context, the

dimensions may not represent a tangible characteristic of the subject of interest. Each

base quantity, by definition, was its dimension. The dimension was, therefore, a

formulaic expression of how the value of the quantities transformed when the size of the

base units changed. For example, the dimension of a base quantity, Q,

[Q]=W (2)

Where

• [Q] represents a dimension of property Q

• W represents the concept of the measurement unit, in this case, the

concept of width

If the width unit size, W, increases by a factor of f, the numerical value of Q will increase

by a factor of f-l . Also, the dimension of a dimension conferred the same information

about the general form. A dimension, Q, defined by:

Q=α𝐿1

𝑙1𝐿2

𝑙2…𝑀1

𝑚1𝑀2

𝑚2…𝑡1

𝜏1𝑡2

𝜏2… (3)

Where

• Li, numerical values of certain lengths

• Mi, numerical value of mass

• ti, values of certain times

• α, exponents of real numbers

If the length unit changes by a factor, l, mass unit changes by m and time unit changes by

t, the value of Q changes to:

Q1=n-1Q (4)

where

n=(𝑛𝐿)∑𝑙𝑖(𝑛𝑚)∑𝑚𝑖(𝑛𝑡)∑𝑡𝑖

Q transformed like the numerical value of the base quantities with a unit whose size was

proportional to the sizes of the underlying units. When the numerical value did not

change with its base unit value, then the dimension was considered stable or

dimensionless.

In analytics and decision-support, one seeks functional relationships between

numerical values of quantities that describe, estimate, infer, or forecast the situation of

interest, devoid of coincidence of choice of units - dimension homogeneity. Dimensional

homogeneity implied both sides of the quantitative expression should have the same

dimension, and dimensionless, the quantities and the terms must be of the same

dimension or dimensionless, and any arguments of any exponential, logarithm,

trigonometric or other special functions that appear in the equation must be

dimensionless. Dimensional analysis demanded formulation of equations to capture the

functional relationships between sets of independent and dependent quantities expressed

in equation form as follows.

Q0 = f(Q1,Q2,…, Qn) (5)

Where

Q0 is the dependent quantity

Q1, Q2,…, Qn are independent quantities

f is the conversion factor that confers similarity to the expression

The relationships expressed in (5) above was the result of laws or policies

governing the occurrence of the quantities of the property of the subject of interest. This

relationship should hold despite the sizes of the base units of the quantities included, per

Bridgman’s principle. The system of units that defined the quantities determined its

dimension along with exponents that were dimensionless numbers following from this

definition. Assuming that

1. Q1, Q2,…, Qk were dimensionally independent subset of quantities, where none

of the members had a dimension that expressed the dimensions of the

remaining members

2. Qk+1, Qk+2,…Qn were the rest of remaining independent attributes expressed

regarding the dimensions of the subset Q1, Q2,…, Qk

3. Q0 remained the product of powers of Q1, Q2,…, Qk and Qk+1, Qk+2,…Qn to

achieve dimensionally homogeneous expression

4. k < n

Then

πi= 𝑄𝑘+𝑖

𝑄1

𝑁(𝑘+𝑖)1𝑄2

𝑁(𝑘+𝑖)2…𝑄𝑘

𝑁(𝑘+𝑖)𝑘 (6)

where

i=1, 2, …, n-k were dimensionless form of the dependent variable

and,

π0= 𝑄0

𝑄1

𝑁01𝑄2

𝑁02…𝑄𝑘

𝑁0𝑘 (7)

where

1 .. k was the dimensionally independent form of the dependent

variable, Q0

Then,

π0 = f(Q1,Q2,…, Qk; π1, π2, …, πn-k) (8)

According to Bridgman’s principle and following the Buckingham’s π-theorem, the

reduced form of the expression of the expression should be:

π0 = f(π1, π2, …, πn-k) (9)

This final form satisfied, the Buckingham’s π theorem which stated that when a complete

relationship between dimensional quantities was in the dimensionless form, the number

of independent quantities that appear reduced from the original n to n-k where k was the

maximum number of the original n that are dimensionally independent. This theorem

facilitated the discovery of the dimensions of dependent attributes, but not the form of the

dimension. The form had to be discovered deductively from both exploration of the

properties and the values of the data set, guided by existing knowledge of the subject of

interest, available data, theories, propositions, and experimentation (Shen et al., 2013).

Dimensional transformation of data in a pre-determined fashion ensured that the

underlying relationships remained intact and enhanced as needed for the analysis under

consideration (Shen et al., 2013). This analytic process eliminated coincidences of

similarity that may occur. Dimensional independence conferred statistical and

mathematical independence which made the analysis much more valuable and

informative. The reduction in the number of attributes eliminated redundancies

encountered with large data sets, (for example, redundant non-distinguishing dimension

attributes and records; identification of dimensions with similar effects of interest). Also,

dimensional transformation demanded numerical expression for dimensions, which is

different from the concept of dimension in a classical multidimensional model.

The requirement of numerical expression of attributes can be problematic with

non-numeric properties or attributes. Multivariate algebra, the grounding for multivariate

statistics, solved this problem through the coding of attributes, using functions. Examples

were enumeration, dummy coding (or identity coding), threshold-based coding, target-

based coding, the weight of evidence coding, cluster coding, smoothed weight of

evidence, etc. (Wickens, 2014, pp. 5-15). Other methods of categorical data

transformations include Rasch model of measurement based on tabulation of expected

frequencies and Shafer-Dempster model of evidence-based on the tabulation of the log-

odds of probabilities (Bond & Fox, 2013, pp. 15 – 28; Cuzzolin, 2012). The typical

dimensional analysis focused on extents of objects or subjects under consideration, as the

generalization of their linear algebraic expression. Extending this concept from defined

measurable objects or subjects to undefined abstract space covering the interaction of

objects and subjects, required specification and integration of subspaces. The

specification of large complex scenarios became the primary challenge of management

analytics and decision-support.

Expression of Large and Complex Scenarios

Data warehouses and OLAP applications evolved as a response to growing

complexity of information technology and data environments supporting business

functions and management activities. A typical enterprise data warehouse was made up

of many records with a large number of attributes. A simple mathematical estimate of

candidate models in an enterprise model design space can be calculated using the

formula, LA , where A is the number of attribute and L is the average number of levels (or

values) of the attributes. For a simple modeling problem with one hundred attributes at

two levels each, the number of solutions would be about 1030 (Michalewicz, Schmidt,

Michalewicz, & Chiriac, 2011, p. 25). Technically, the number of empirical model

candidates within a model design space was huge, but there were a limited number of

these models that would satisfy the design requirements of the analysis exercise.

Therefore, the characterization of the enterprise model design space required a

careful examination of the underlying analytics opportunities. Model spaces were the

factors and functions that drove the transactions to express states of existence (of entities,

domains, systems) responsible for the outcome variations, which made up the utility and

preference relations for the management decision maker (Hsu, Ito, Schweikert, Matsuda,

& Shimojo, 2011). Considering the potentially large number of solutions within an

enterprise model design space and the constraints imposed by subject based

multidimensional modeling approaches, the consensus in the literature converged on

multi-tier ensemble analytical architecture. Hsu et al. (2011) presented three-tier

architecture paradigm based on computational informatics perspectives to include: (1)

structure layer models for structural components of the domain, (2) function layer models

for functional components of the domain, and (3) application layer models for application

components of the domain. The application of this architectural approach to the analysis

of the brain system resulted in a computational fusion method for the assessment of

gender variation in facial attractiveness is shown in Figure 1 below.

Figure 1. Multilevel modeling applied to the brain system. From “Combinatorial Fusion

Analysis in Brain Informatics: Gender Variation in Facial Attractiveness

Judgment,“ by D. F. Hsu, T. Ito, C. Schweikert, T. Matsuda & S. Shimojo, 2011,

Heidelberg. Adapted with permission of the author.

Beroggi (2010, p. 12) discussed a three-step analytical formulation process:

structural, formal, and resolution steps, across three common modeling paradigms: data

(observation), domain (or system), and decision to create a 3X3 analytical model

architecture matrix. The first step of the analytical formulation was the structural level, a

graphical portrayal of the relations and dependencies which may be causal (non-

symmetric), correlational (symmetric), conditional (probabilistic) or informational

(definitional) allowing the subject of interest to reflect the underlying data structures. The

second level was the formal level where the relations and dependencies transformed into

attributes to calibrate or define the subject of interest. The third level was the resolution

level in which procedures were applied to generate solutions about the subject of interest.

At each level of the analytic formulation, the level of analysis determined the format,

content, and context of expressed relations. Appendices F and G were compilations of the

details of the approaches. Further, Hendry (2009, pp. 16-19) identified four practical

knowledge levels: measurement, estimation, modeling and forecasting levels, based on

the nature of probability distribution and data generation processes. Table 3 below

combined these proposals on representing complex subjects of interest from its available

data.

Table 3

Multi-Level Model Ensemble for Complex Subjects

Knowledge

Level:

Formulatio

n Steps

Dominant

approach

Modeling paradigm

Observation /

Record

Domain / System

Decision /

Application

Level A:

Structural

Measurement,

probability,

and statistical

theory

Underlying

transactions

organized to

expose effect

and coefficients

Underlying

processes that

connect the

transactions,

establishing input

and output

attributes

Underlying

mechanisms to

which the

knowledge of

transactions and

processes can

be applied

Level B:

Formal

Estimation

Measurement

and latent

models that

underlie the

coefficients of

interaction

captured in the

transaction

Functions and

equations for each

of the processes

within the domain

and system

Estimates

(heuristic,

probabilistic,

statistical,

mathematical)

that underlie the

mechanisms

Level C:

Inferential

Reduction,

Likelihood,

Expectation

maximization

Given specific

conditions,

determine what

inferences made

about the data

Starting with

initial values,

determine new

values for the

levels, flows, and

converters

Evaluate the

formal model

and determine

elimination,

integration and

recursive

approach

Level D:

Forecasting

Numerical

optimization,

simulation,

heuristics

Extend

conditions

beyond

representation

in the data to

include

potential

innovations

and emergence

Extend values

within the model

to new futures for

levels, flows, and

converters

Evaluate the

new futures for

applicability

and

implementation

In Table 3, an integration of the dominant approaches and modeling paradigms in

the literature cuts across disciplines from statistics to cybernetics. This matrix charts the

paths for data from the left upper corner through insights to foresight on the right lower

corner of the matrix. The modeling paradigms had modeling standards or patterns. The

data model paradigm represented the entity objects as the primary subject of interest,

while the domain (or system) models represented a collection of entity objects that

interact to achieve congruent outcomes. The decision (or application) model paradigm

represented the expression of relations to achieve alternative futures of existence for

specific goals and objectives.

The discussion so far established the multi-level design architecture as the

effective analytic representation in the presence of complexity. This architecture was

achievable through progressive reduction of the available data, and the exploration of the

results for candidate representations of the subject of interest. This approach included a

feedback loop for incremental updating of the model to improve its performance over

time. Analysis of the data, domain, and decision situations in complex areas of endeavor

required incremental construction and manipulation of models, such that one set of

models replaced another set of models. The ability to integrate and compare multiple

models in a domain of interest was critical to this type of empirical model building.

Analytic model building in complex domains demanded the construction of an ensemble

of models of various forms and specifications, for comparative analysis and integration

(Windschitl, Thompson, & Braaten, 2007). An epistemic comparison of the classical

approach and this alternate approach, multi-level empirical model building, was

synthesized in Table 4 below.

Table 4

Classical versus Layered Empirical Modeling

Model

characteristic

Classical

Layered

Goal

Find patterns in natural

phenomena

Find patterns and defensible

explanations for the way the natural

world works

Construction

Hypothesis often stated as

predictions about isolated

aspects of the phenomena

Adaptation often represented as

interaction of the phenomena within

the domain of interest

Validation and

Revisability

Evaluation of predictions

result in acceptance or

rejection of the prediction,

with limited opportunity to

revise them

Evaluation of hypothesis occurs in

the context of design, revisions to

the design allow further validation

of the predictions

Explainability

In the form of conclusions,

summarizing the trends and

patterns in the data

Uses patterns in the data to build

evidence for explaining the design.

The design serves as a tool for

explaining the phenomena

Extensibility

Insights on how the

phenomena could beyond

the scope of the data are not

possible

Provides insights into the

phenomena beyond the scope of the

data, through analysis of alternative

designs

Generative

New hypothesis or theories

are end-product

Alternative designs are the product

A necessary implication of the multi-level empirical model development in the

large enterprise space was the need to automate the generation and comparison of a large

number of models as part of the analytic processing. This created demand for

computational and algorithmic analytic processing techniques discussed below.

Computational/Algorithmic Analytic Processing

An emerging approach to handling large analysis scenarios was the adoption of a

computational or algorithmic approach. With this approach, computer scientists or

algorithm designers look at exploring large complex datasets as a computation or

algorithmic problem. The objective was the discovery of the models for the data using

statistical, machine learning (numerical heuristics), summarization (likelihood,

similarity), and feature extraction (frequent itemsets, similar items) methods. A large

number of algorithms had been developed to support computational extraction of models

from data. The most common algorithms being C4.5 and higher, k-means, support vector

machines, apriori algorithm, Expectation-Maximization algorithm, PageRank, AdaBoost,

naïve Bayes, Classification And Regression Trees (CART) (Wu et al., 2008). Other

algorithms included autometrics (Hendry & Mizon, 2011), neural networks, genetic

programming, grammatical evolution, multi-expression programming, evolutionary

algorithms, self- organizing migrating algorithm, differential evolution, simulated

annealing, analytical programming, Pareto genetic programming (Zelinka et al., 2011).

These algorithms integrated attribute manipulation, numerical simulation, numerical

optimization, bootstrapping, and other techniques in the evaluation of the data to discover

models that can be used to measure, estimate, infer or forecast a subject of interest.

A class of algorithms referred to as symbolic algorithms had become particularly

popular because they modify the underlying data model to improve the efficiency of

discovery of models within the data. Symbolic programming discovered symbolic data

from the available data (Syme, Granicz, & Cisternino, 2012). This approach constructed

symbolic structures from available data and used this structure in the discovery of

models. The structures in Figure 2 represent the result of implementing symbolic

regression or classification to produce fit functions, formulae, control commands

examples from Zelinka et al. (2011).

Figure 2. Examples of structures derived from symbolic algorithms.

This approach to analytic processing had been equally enabled and challenged by

data size and dimension explosion. Algorithms implement a static set of procedures with

established decision thresholds. The black box nature of their implementation required

that the user acquire a significant mathematical skill. Also, in many practical situations,

the nature of the available data was overwhelming, noisy, localized, inconsistent, and

incomplete. As such, the extraction of valuable insight through generalization of every

numerical relationship had limits. Input from expert to differentiate the raw input became

necessary to simplify the computational complexity of the algorithms. However, input

from expert had limits and introduced bias into the generation of useful generalizations of

relations within the subjects of interest. A much more comprehensive approach was

direct manipulation of the data model to discover the attributes that support analytic

continuation beyond the classical multidimensional space into formalized metric spaces

and subspaces.

Summary and Conclusions

In this chapter, I discussed different analytic processing methods. OLAP was the

only method with a well formalized for data-modeling process. I highlighted the issues

with OLAP data models, including, heterogeneous and irregular dimensions, handling of

different types of aggregation operations, handling time and uncertainty, symmetrical

treatment for dimension and fact elements, and support for different levels of granularity

in the facts and dimensions. Also, contemporary analysis scenarios handled with OLAP

were small and narrowly defined data cubes. As the size of data and complexity of the

analytic scenarios increased, specialized designs were introduced to improve their

analytics and decision-support capabilities, for example, planning, prediction, inference,

probabilistic, Gaussian, OLAM, programmatic OLAP (prolap), and many other OLAP

formats. Another critical issue was the determination of the proper attribution of fact and

dimension relations of the data cubes to ensure alignment with cognitive models of

underlying subjects. The classical multidimensional models and data cubes did not

address secondary issues associated with independence and parsimony of attributes in the

data model design. The result was sparse data cubes whose application was limited to

descriptive analytics.

Improving data models for advanced analytics and decision-support required three

key changes to the data-modeling process. It was important to learn the ontology of the

subject of interest from the available data, not the other way around as it has been the

case in contemporary ontology engineering. An important part of ensuring that the data

model has the right content for analytic processing was leveraging data engineering and

analytic formulation techniques to evolve the data to the right unit and level for analytic

processing, such that similarity principle critical to data analysis and decision-support

problem-solving would be applicable. Finally, refining the normed metric space through

rigorous specification of proper functional forms of relationships in the data ensured

reduction of the metric space to orthogonal expressions of underlying data to limit

interdependence of indicator or characteristic attributes.

The solution opportunities in the use of ontologies included representation and

interpretation mappings, and the use of measures and encoded indicator attributes in fact

relations. Ontologies would also establish the base for searching and pruning of

categorical and measure attributes in fact relations. Also, ontologies would use heuristics

to express structural aspects of the data. Other opportunities with ontologies were the use

of summary attributes and transformation logic and many others. Other solution options

were the use of data engineering and analytic formulation techniques, especially semantic

data analysis, symbolic data analysis and dimensional data analysis to establish the

ontology of the subject of interest within the analytic data models. Additionally, using

constructs from complexity analysis and symbolic dynamics, the analytic data model

should be transformed from a static artifact to an active one by expressing dynamism,

uncertainty, and fuzziness within the data model.

The mathematical constructs of Bridgman’s principle, Buckingham’s π-theorem,

and Blackwell theorem were helpful in the construction of extensions to express the

complex features embedded in the data. This integration of critical concepts from

dimension and complexity analysis into the relational data model to derive solutions in

management analytics and decision-support provided the basis for the analytic extensions

on relations adopted by this study. In the next chapter, I describe the research

methodology adopted to study this subject. I argue that data-modeling should be

considered a critical step in research involving secondary data, especially, when the data

exceed sizes typically considered adequate for normal distribution assumptions. A data

analytics project without a data model that accurately reflected the concepts and

constructs of the domain of interest cannot be expected to produce outputs that are

explainable or actionable by business analysts and executives.

Chapter 3: Research Method

Introduction

The purpose of this quantitative descriptive study was to examine the data model

of a typical data analytics project in a big data environment for opportunities to improve

the representation of information. I identified the data model as the primary focus of the

study because the expression of information in data models is known to improve

understanding and utilization of the data (Burch, 2018). I adopted nonexperimental DBR

to study the available data and to map it to the cognitive models of the underlying

management situation. This alignment of analytic outputs to cognitive models provided

the basis for the acceptance and actionability of data analytics outputs (Okoli & Watt,

2018).

In this chapter, I discuss the details of the research method. This study

emphasized design theories and concepts for extraction or extrapolation of knowledge

from the available data. Therefore, discussion of the specific issues of the industry of the

data source in this research was not relevant. Because the focus of the study was

constructing the data model that captured underlying concepts for management decision

problem-solving, requirements of population characteristics, sampling, and sampling

procedures were not relevant. The discussion of threats to validity focused on construct

validity since issues of external and internal validity or ethical considerations were not

significant to the methodology.

Research Design and Rationale

I used a quantitative, nonexperimental, descriptive design format for this study to

examine the data of the typical data analytics projects to find data model extensions that

would improve the discovery, identification, specification, and resolution of management

decision problems. The research questions guided the study:

Research Question 1: Can data model extensions improve the discovery of

management scenarios from big data?

Research Question 2: Can data model extensions improve insights about the

management scenarios?

Research Question 3: Can data model extensions express the complex constraints

and rules needed to compose the acceptable and actionable solutions for

analysts and executives?

The demonstration of the improvement in data analytics projects on the above

questions would indicate an affirmative response to them. For this demonstration, I used

secondary data from a typical enterprise data analytics project. In such a project scenario,

the specific the needs of the users are vague or non-existent. Additionally, the current

data analytics processes that occur in business intelligence, data mining, knowledge

discovery from databases, deep learning, and artificial intelligence tended to create

incomplete, nuisance and challenging insights and solutions. The secondary data used for

the demonstration was made up of 140 datasets from five different sources with about

1000 data attributes, 1.75 billion rows totaling about 15 terabytes.

The selection of a design research methodology informed the focus of this study,

which was building and evaluating data model designs to improve management analytics

and decision making. It is typical for the type of problem, the research objective, and the

expectations of the researcher to dictate research methodology and approach (Cooper,

Hedges, & Valentine, 2009). The type of problem may be normative, descriptive, and

prescriptive. The objective of research may be to test a proposition or hypothesis, explain

an occurrence, or qualify the impact of structure or function. The expectation of the

researcher may be to validate a theory, advance an acceptable explanation, and guide

practice (Bakker & Van Eerde, 2012; Hussain, Elyas, & Nasseef, 2013; Leech &

Dellinger, 2012; Reimann, 2011; Turner, 2010). The alignment of these factors was

critical in the selection of research methodology and design of the study.

Cooper et al. (2009) argued that the impact of these factors were reflected in the

classes of research methodology in the literature. There were three key classes of research

methods as follows. The first class was inquiry driven by theoretical formulations

(theory-based research), the contemporary scientific research approach. The second class

was inquiry driven by epistemic needs (case-based research) which was made popular by

social and behavioral sciences. The third class was inquiry driven by the need to improve

design (DBR) which was made popular by design and engineering sciences. These

classes of inquiry also determined the degree of interaction of the researcher with the

subjects under investigation. In theory-based research, a high degree of direct

interactivity and control is assumed to ensure that the measurements of the inputs capture

the characteristics (or attributes) of the subject, unencumbered by nuances of the

surrounding or the researcher. A high degree of indirect interactivity and control is

necessary with case-based research because the inquiry focuses on understanding

underlying epistemology (for example, phenomenology, ethnography, case study.). For

inquiries driven by the need to improve design (so-called DBR), any interactivity or

control biases the context (Kuechler & Vaishnavi, 2012). This study’s research approach

sought to capture the natural architecture and to determine changes in design to pursue to

improve knowledge expressed by available data for management problem-solving. The

researcher interacted with the scheme or configuration of elements (the design) in the

domain of interest to understand the problem and propose solutions to them as needed.

This research approach required the definition, construction, and test of the candidate

designs of the subject of interest to achieve outcomes that did not result naturally

(Kuechler & Vaishnavi, 2012).

The DBR approach was well established in Information Science and Engineering

research (Bakker & Van Eerde, 2012; Kuechler & Vaishnavi, 2012), and was considered

an important area of applied research for developing information, technology, and

engineering solutions using existing knowledge and artifacts (Blessing & Chakrabarti,

2009). Chakrabarti (2011) argued that this form of research allow the researcher to

develop new methods, constructs, and artifacts to simplify the application of knowledge

and engineering rigor for consistent results. This approach differed from the

contemporary research methodology of scientific evidence, which focused on the

theoretical development and statistical hypothesis testing. Fortunately, work in the last 50

years has increased the acceptance of DBR methodology because of its success in driving

advances in information and engineering disciplines (Kuechler & Vaishnavi, 2012).

The DBR to address several issues central to research studies as follows. The first

issue was the nature of and approaches to a subject in the real world rather than the

laboratory. It was also developed to address the issue of the use of a broader set of

measures of the subject that emphasize competency rather than theoretical knowledge.

The DBR was also positioned to address issues of the synthesis of recommendations for

design or process improvement based on the formative evaluations, compared to

summative evaluation of the classical research methodology. The DBR approach to

research allowed proper integration of the “difficulty with the complexity of real work

situations and their resistance to experimental control,” the availability of large amounts

of data, and issues related to “comparing cross designs” (Herrington, 2012). The role of

DBR in the researcher’s toolkit was to create practical knowledge to realize theoretical

formulations. It also allowed for formative research to test and refine designs based on

theoretical principles derived from practical measures, prior research, and progressive

refinement through assessment (Hogue, 2013).

According to Blessing and Chakrabarti (2009), DBR methodology occurs in four

parts. In the first part of the methodology, an existing design’s circumstances and

constraints were presented and analyzed (the analysis phase of design research). In the

second part, the researcher studied the interaction between the design and the results (the

design phase of design research). In the third part, the researcher deliberately manipulated

the design to change the interactions within the domain of interest by addressing design

constraints that may be responsible for the results (the evaluation phase of design

research). Finally, the researcher proposed and tested new designs and tools (the test

phase of design research). Design-based studies required the analysis of designs within a

robust framework of comparative inferences on structure and function. In this study, the

designs were the data models for management analytics and decision-support problem-

solving.

This research methodology required a quantitative format. The use of a

quantitative format for a study created explicit links between theory and results, limiting

the bias of the researcher (Creswell, 2011). In a quantitative study, the essential elements

of the analysis are mathematical constructs. Quantitative research techniques differ from

qualitative techniques, which use linguistic constructs (Creswell, 2011). Within the

domain of quantitative research, there were five main research design types: randomized

experiment, quasi-experiment, comparative, associational, and descriptive (Creswell,

2012). The first two types were experimental techniques, while the last three belong to

the non-experimental class of techniques. According to Creswell (2012), there were four

items to consider when selecting the approach to a quantitative design: random

assignment of subjects, intervention or treatment by the researcher, structure of the

criterion variables, and approach to the examination of relationships between variables.

In comparative study design, there is no randomization of the assignment of subjects to

the groups and no specific intervention against subjects in the study. However, there was

the requirement to define numerical quantities for comparison of the items studied. In a

descriptive study design, the expectation of comparison relaxed for the study to focus on

the design.

Methodology

Based on the framework discussed above, the choice for this study was a

descriptive approach. The secondary nature of data for the study dictated the selection of

the descriptive approach. The availability of suitable secondary data allowed progress

without the burden of collecting data. Secondary data also allowed a focus on the original

attribution of the subject of interest as represented by the available data sources, but

imposed constraints on the causal interpretation of the underlying effects and influences.

Population

In study design, the population refers to the group studied. The population in this

study was not typical. The data used in this study was sales data from a medical product

distribution company which captured purchasing habits of customers, selling

characteristics of agents, market demand, pricing actions on products, and marketing

actions to drive penetration of products within the marketplace. The scope of the data was

enterprise-wide, which meant, it contained all the information captured by the

organization from its business activities related to the products, pricing, sales, marketing,

and customer servicing. Each of these areas had sets of concepts which were extracted to

facilitate the analytic activities. I expanded on the Resources-Events-Agent (REA)

ontology framework proposed for business. See Appendices F & G for details.

Sampling and Sampling Procedures

This study did not utilize sampling or sampling procedures. Analytics and

decision-support problems in management required the participation of all data points in

the analytic processing. The focus of the study was to construct the data model that

leveraged every necessary data point in analysis and decision-support problem-solving.

This approach was selected to overcome the challenges of existing data analytics

processes where the use of sampling added complexity to the insights generated due to

the concerns of representativeness of the sample compared to the entire population of

items under consideration.

Archival Data

I used secondary data in this study. The data sources included SAP/R3 Enterprise

Resource Planning (ERP) system order processing module, along with additional sources

of product and market information gathered from second- and third-party sources. The

dataset spanned three years, from 2007 to 2009. Appendix A shows the list of data sets

included in the data use agreement approved by Institutional Review Board (IRB). The

IRB approval number 10-28-15-0015433 was issued October 25, 2015. The use of

historical data was deliberate and should not impact the outcome of the research. The

data came from a data asset repository used for exploratory data analysis and analytic

pilot projects. The data was completely de-identified. Randomly generated identifiers

related the different segments of the data together. The next chapter contains the

description of the data used to illustrate the data model extension approach. The chapter

also covers the anomalies in the data set addressed to ensure accurate transformation into

analytic and decision attributes.

Data Analysis Plan

A data analysis plan should present the description of the software, data cleansing

and screening procedures, details of the statistical tests, procedures, variables, and how

results will be interpreted. Because this study focused on data model designs for analytics

and decision-support problem-solving in management, the emphasis was on discovering

attributes of the data for managerial tasks. For this reason, I expanded this section to

include the processes of ontology learning, data engineering, and analytic formulation

which were critical to the data model extension methodology and the data analysis in

large complex analytic and big data scenarios.

Data Model Extension Methodology

As mentioned above, the data available for data analytics projects in a big data

environment came in different formats, data types, and data naming conventions. To

conduct a proper analysis of the underlying data model, I constructed data asset diagrams

at two levels: high-level and detail-level. The high-level data asset diagram provided a

panoramic view of all the data asset available for the analytic exercise, and the links

between the datasets. The detail-level data asset diagram showed the content of each data

asset, including the logic for the links between the data assets when they existed. The

dataset link logic was of three types: direct referential association (primary key – foreign

key association), indirect reference association through matching or associative relation.

The typical dataset for big data analytics described above contained duplication,

redundancy, inconsistencies, and other data issues. These data assets also embedded the

critical data, process, and business rules that are helpful in the application of the data

model to uncovering problem scenarios. To highlight these situations in the data, I

refined that data asset diagram using a generalized entity relation recognition algorithm to

restructure the data asset into a generalized entity relation model and generated an

accompanying entity relation diagram for visualization of the data model. At this level,

the data model applied all the normalization rules to ensure data quality and integrity in

the data. This data model reflected the piece of the “real-world” expressed by the

available data, as interconnected elements of a type system with one or more schema(s),

devoid of artifacts of physical implementation as databases, data-files, and applications.

(Puonti, Lehtonen, Luoto, Aaltonen & Aho, 2016).

For big data analytics, this real-world was complicated and contained tens of

schemas. Each schema formed the collection of relations within a data model connected

by association restrictions, including, domain, cardinality, and referential types. The data

model at this point still embedded the functional and transitive associations. Additionally,

the data model did not express the progression of the concepts with the data over time.

This classical data model was also limited to relations to real entities within the schema

as such the resulting design manifestation was known as the entity-relationship data

model (Puonti et al., 2016).

In this classical data model, given properties, P1, P2,…, Pn, a relation, R, was

defined by the n properties such that each instance or tuple had its first property from P1,

its second property from P2, and so on. A relation, R, was the subset of Cartesian product

P1, P2,…, Pn or ∏𝑃

𝑗

𝑛

𝑗=1 . Pj is the jth property of R with degree n, hence referred to as, n-

ary relation, with the following characteristics (Kumari & Singh, 2017):

1. Each row was an instance of the relation or tuple of R,

2. Row ordering was not consequential,

3. All instances or tuples of R were distinct or unique,

4. Column ordering corresponds to the ordering of the set of attributes of R,

5. Term label corresponding to the set domain conveyed the significance of each

attribute

6. The term labels applied to the attributes were unique and conferred some

interpretative value to its content

7. The combination of attributes covered by R uniquely described an entity, subject,

object, or class with the rows or tuples reflecting the membership in the collection

8. Property values assumed standard data types, including, integer, decimal,

character, and currency, all of which were of scalar type.

9. Advanced data types like user data types (UDTs), algebraic data types (ADTs),

statistical data types (SDTs) and functional data types (FDTs) were not allowed in

data models.

10. A typical data model of the enterprise units contained hundreds of relations within

tens of schemas.

The entity relations of the enterprise data model were not well differentiated.

They could represent people, groups, events, actions, transactions, resources, place, and

other ontological classes. To facilitate the translation of entity to ontology relations, I

derived a list of 16 possible ontology commitments for management analytic and

decision-support problem problem-solving shown in Appendix G. I used the list of

candidate ontology commitments to refine the relations and properties within each data

set into ontology classes and properties as data model extensions. These derived relations

differentiated the entity relations into higher forms encompassing complex associations

and constraints.

To derive data model extensions, I generalized the analytic continuity concept of

functions to the relations through analytic elements. Analytic elements were projections

of the properties of the relations beyond initial specifications, but which maintained

logical continuation as follows. Considering the data model as a collection of properties,

P, of relations, where each relation, R, was the generalized functional of a unique aspect

of an ontology, O, of a domain, D, in the universe, U. Each property, P, was an analytic

element, (a, l), where, a, was attribution represented by the property, and l was the

function or logic on a. The original analytic element in a data model was (a0, l0) and

subsequent derivation results in a matrix (a1, l1), …, (a i, lj) were extensions of each other

through the connection component, σ, of the set a0 ∩ a1 ∩, …, ∩ ax if l0| == l1| σ, …, == lx|

σ*. The analytic element defined by the pair, (a, l), therefore, continued to the boundary

point, ɛ, with ∂a ⸦ D. These elements continued the expression of the relation, R, beyond

the defined scope. This universal cover was the original scope for extensions of the

analytic elements of the relation, or the analytic space. The maximal analytic extension of

the relations was, therefore, an unambiguous holomorphic functional of complex

properties differentiable about every point in the domain. This new relation, σ*, specified

the region where the sum of terms of the sequences of the relation, or its infinite series,

became divergent. It extended the point beyond which values existed, and when the

expectation of the return of a single point was unrealistic (so-called mathematical

singularity).

The use of complex numbers reinforced extensions, especially, when defined on

more than one property of the relation. Complex numbers eliminated the need for

mathematical singularity or isolated points and favored algebraic or geometric varieties

with a mathematical plurality or cohomology. The dimension axioms defined expanded

the analytic space of the relation as follows. Given that complex numbers were

expressions of the form y0 + xi where x and y were real numbers, and i was the imaginary

unit, the solution to quadratic equation y2+1=0, and satisfied the equation y2 = −1.

Complex numbers extended the dimensionality of real numbers which were, technically,

points or zero-dimensional. For example, 1-dimensional number line was extendable to

the 2-dimensional plane by using the horizontal axis for the real numbers and the vertical

axis for the imaginary part of the complex number. The complex number y0 + xi

identified point coordinates (y, x) in the complex plane. A complex number whose real

part was zero was said to be purely imaginary, whereas a complex number whose

imaginary part was zero was a real number. Therefore, complex numbers were analytic

extensions on ordinary real numbers, converging on an area defined by a range of real

numbers within the domain, the germ, g, of the power series.

Assuming two germs, g1 and g2, were the sets of vectors, when the absolute

difference between the set of vectors was less than the radius of convergence of g1, and if

the power series defined by g1 and g2 specify identity relations on the intersection of the

domains, then g2 was an extension of g1, making up the point (or sheaf) of the extension.

The union of the germ sheafs identified from the power series of the domain by sets,

Ur(g), for all r > 0 and g ∈ G defined the basis for an open set for the topology on G.

Connected components of G, equivalence relations, formed the analytic extension map of

space. A map defined by φg(h) = h0 from Ur(g) to C where r was the radius of convergence

of g, represented the chart of the extension. The set of such charts formed the atlas for G

or the universal relation. Therefore, an analytic extension of the relation generalized the

power series defined from the sequences of the underlying properties. They created

objects within topological spaces of class equivalence with others of the same type with

shared local properties. Therefore, the converging power series of the relation properties

enhanced the underlying information and resulted in sets of vectors around the points or

space of expression within the empirical domain.

Analytic extensions on relations provided the paradigm for extension of data

models to include high-order logic. The extensions specified the analytic space through

the derivation of algebraic varieties of the domain ontology and topology was possible.

This algebraic variety ranged from simple ones like variables to intermediate types such

as features, identity vectors, and eigenvectors to name a few. Complex algebraic varieties

like tensors or co-dimensional entities resulted from the further projection of the

intermediate algebraic variety. At the level of the complex algebraic varieties, the

dimensions were degenerates of real dimensions with about half the number. That is, if

the dimension of the complex algebraic variety were, d, its real dimension would be 2d.

The real algebraic variety of equations with real coefficients became the dimension. The

real dimension referred to the maximum number of manifolds contained in the set of its

real points. Also, the real dimension was never greater than the complex dimension and

equals it if the variety was irreducible and had real points that are singular. For example,

the relation of a complex algebraic variety with dimension two would be a surface, but

with a real dimension zero. It had only one real point, (0, 0, 0), which was singular. The

relation representing a smooth complex hypersurface in complex projective space of

dimensions, n, was a manifold of dimension 2(n − 1). The complex hyperplane did not

separate a complex projective space into two components, instead, expressed them as

having real co-dimension of 2.

Based on this methodology, analytic extensions on relations were, inherently,

more robust than an analytic extension of functions, and enabled the differentiation of

data using analytical geometry. It transformed scalar data into algebraic varieties. The

additional properties improved the expressiveness of the relation for problem-solving

based on the set points or boundaries of differentiation that would satisfy the analysis

problem. Considering the properties of relations as analytic elements made them heuristic

translators, mapping one property to another, within the domain defined.

Composing an enterprise from relations of algebraic varieties transformed the data

model into empirical ontology with a well defined analytic topology. The progressive

differentiation and integration of these varieties expanded the characterization of the

domain but maintained a universal cover on the relation reducing analytic over-reach.

Analytic continuation or extension reached its boundary when the data model captured

very concepts of the domain in alignment with the intuitive cognitive model of the

business analysts and executives.

Expanded Data Analytics Process

The data analysis process started with the arrangement of the available input

datasets, followed by extraction of the underlying entities and relationships, and the

reconciliation of the attribution of entities and relationships across the datasets to achieve

a rationalized metadata model of the input data. Further abstractions of the metadata

captured characteristics of the underlying data not explicitly expressed by its metadata.

Contemporary literature on data analysis assumes the creation of a data model

should precede data collection. It also often assumes that the data is in a structured

format, mostly from databases. In the light of big data, these assumptions were no longer

valid. Relaxing these assumptions allowed data in any form and from any source to

participate in analytic processing. In this scenario, the data-modeling became the

dynamic process of discovering the characteristics and relationships between the

available data sources. This study used secondary data gathered without an explicit data

model of the analytic needs. I adopted a data analytics process made up of the five

following steps.

The first step of this expanded data analysis plan was to create the catalog of the

datasets that were available for analytic processing. This catalog specified the nature of

the datasets along with the format, the number of attributes, and the nature of attributes

available to establish the scope and boundaries of the analysis problem. The catalog

mapped datasets to the analytic processing objective. This mapping exposed gaps, when

they existed, within the available data sets. Connections between the datasets, included

referential keys, common attributes, hierarchical, temporal, or spatial association types.

The second step was to expand the datasets into entities and attributes. This step

involved a critical review of the structure of the datasets. It included the capture of user-

friendly names, descriptions, database data types, analytic data types, measurement scales

for each attribute in the dataset. The classical data models typically ignored measurement

scales, creating confusion with the interpretation of numbers.

The third step was to expand the metadata catalog to include relationships within

and between the datasets, such as extension (1:1), subsumption (1:M), and qualified

(M:N) relationships. These were cardinality relationships within the data model, which

were expanded to accommodate non-cardinality semantic, symbolic, and dimensional

expressions between and within entities in the data sets.

In the fourth step, attributes were organized into unique subject areas or

functional domains to understand the extent of representation of the subject area or

functional domains, as well as its association and dependence on other subject areas or

functional domains captured in the data sets. Analysis of the data within the entity

structure determined whether there were dynamic components of the attributes indicating

the data may be of a repeating nature, either longitudinal (single subject over time) or

cross-sectional (multiple data points at the same time from different sources). This

orientation of the data was critical to determining the appropriate types of data

engineering and analytic formulation processes to apply to the data. This decomposition

of the subject areas or functional domains into static and dynamic components furthered

the data model.

The fifth step was to establish the measurement frames for the concepts and then

generate new attributes or values needed to operationalize them with the available data.

The step continued for all the concepts of the decision-support problem. In classical

business analysis scenarios, the optimal data model should allow business users access

the attributes of the subject of interest in a way that aligned to the cognitive or conceptual

representation of the domain. This outputs from this data model should support business

analysts and executive in the tasks of management - plan, organize, lead and control

without any need to for technical knowledge of the analytic techniques or data

engineering method requirements.

Threats to Validity

Because this study employed DBR, which does not require interaction between

the researcher and the subject or the data collection process, the common threats to

validity did not apply. In studies where the researcher has direct or indirect interactivity

with the subject, it is critical to address threats to validity. Addressing these threats

prevent issues with study design (external validity), subject selection (internal validity),

and inference from sample to population (construct validity). External validity issues

include reactivity, interaction effects, specificity of variables, and interference. Internal

validity issues include self-selection, non-stationary effects, and subject retention.

Construct validity issues are related to statistical conclusion requiring correction. In

classical scientific studies, the validation techniques in these situations may be statistical.

In this study, I took an analytic and decision-theoretic approach to validity.

Analytic and decision-theoretic techniques evaluated models in the context of

specific analysis and decision needs of the users. The analytic and decision-theoretic

approach to model validation, though relatively new, has shown promise in alleviating

interpretation constraints imposed by pure statistical validation approaches (Welton &

Thom, 2015). The analytic and decision-theoretic approaches focused on determining the

strength of evidence for a model’s empirical power in the context of the specific analytic

and decision situation, without consideration of the generalizability (Jiang, Yuan,

Mahadevan, & Liu, 2013).

External Validity

The nature of the business data used in this research does not present situations

that would challenge external validity. The goal of the study was to support strategic

decisions in a domain of responsibility by establishing a methodology for data model

extension. The data-modeling exercise would explicitly define attributes to address the

reactivity, the interaction between subjects, the specificity of attributes, and the

interferences existing in the data to enhance analytics and decision-support requirement

of managerial tasks.

Internal Validity

Issues of internal validity also did not apply to this study because of the nature of

the data under consideration. The analysis provided insights for decision-support

problem-solving in management. In business analysis, absolute precision was not

necessary. However, management requires consideration of history, maturation,

regression, churn, and interaction, which are part of the practical expression of the subject

for decision-support.

Construct Validity

In this study, construct validation was limited to analytical and decision-theoretic

conclusions based on the significance to management analysis and decision-support. An

important criterion in construct validity was the degree of alignment of conceptual or

cognitive expectation of the management analysts or decision makers of the enterprise

functional unit or domain. For this reason, the measures used in this study focused on

business alignment, for example, intelligence density, decision yield, cognitive gain,

empirical lift, and Bayesian yield. When necessary, statistical reference attributes,

including f-statistic, t-statistic, f-statistic, and others were computed to assist the

interpretation of the strength of evidence.

Ethical Procedures

The source data used in the study came from the data warehouse I maintained for

analytic model and decision algorithms development. Personally identifiable information

was removed from the data. The study did not require human subjects or interviews. The

data was more than five years old. It was large enough for the study of extensions of

relational data-modeling needed to advance analytic processing in databases, beyond the

current state allowed by online analytic processing (OLAP).

Summary

The goal of this research was to study data model extension for management

analytics and decision-support using a DBR methodology. The choice of this

methodology aligned with the purpose and nature of the study. The quantitative non-

experimental descriptive research format provided the ideal approach to the study of the

data model and the opportunities to improve them through the implementation of analytic

extensions.

A critical component of this methodology was the modified data analysis plan,

which addressed the complexity of the available data for analytic processing. The data

analysis plan also addressed the links, both functional and non-functional, within and

between the datasets. Using the extended data analysis plan led to the identification of

conceptual data elements of the available data, which connected the available data to the

intentions of the management analytics and decision-support. These abstract and

conceptual data elements connected the measurement frames of subjects in the available

data. These measurement frames were the quantitative expression of effects, influences,

and other characteristics embedded in the data.

A point of the expanded data analysis plan was that large and complex domains of

an enterprise required reconciled attributes to map to the ontology of the underlying

subjects. The mapping from data to ontology helped align structural, formal, and

resolution expectations at appropriate levels of analysis. The mapping also allowed

measurement, estimation, inference, and forecast needed to resolve business questions

and management problems. Implementing analytic extensions at the data level

transformed data from raw input into attributes for cognitive processing. For this reason,

the focus of evaluation of these analytic attributes was on the empirical measures of

analytics and decision-support, such as intelligence density, cognitive gain, empirical

power, and others. Statistical measures of evidence such as statistical power, confidence

interval, p-value, parametric statistics, and others were secondary to the analytic and

decision-theoretic measures.

Chapter 4 contains further discussion of the analytic extensions, the details of

answers to the research questions, and an application in a big data analytics scenario of a

medical product distribution company. In Chapter 5, I provide a discussion of the

findings and the implications for research in applied management and decision science.

Chapter 4: Results

Introduction

The purpose of this quantitative descriptive study was to examine the data model

of a typical data analytics project in a big data environment for design alternatives to

address issues of misalignment of data analytics project outputs, available data, and the

prevailing intuitive cognitive model of the problem and solution scenarios. The objective

of the study was to improve the acceptance and actionability of data analytics outputs by

business analysts and executives. I identified the data model as the primary focus of the

study because the expression of information in data models was known to improve

understanding and application of the data to management problem-solving (Burch, 2018).

The research questions of this study were as follows:

Research Question 1: Can data model extensions improve the discovery of

management scenarios from big data?

Research Question 2: Can data model extensions improve the formulation of

insights about the management scenarios?

Research Question 3: Can data model extensions express the complex constraints

and rules needed to compose the acceptable and actionable solutions for

analysts and executives?

In this chapter, I discuss the results of the data model extension methodology and

the extended data analysis plan, as described in the previous chapter. I follow the

discussion of the results with an application of this data model approach to a typical data

analytics project in a big data environment.

Data Collection

Data collection in a classical research situation provides information on the data

collected for the analysis of the research subject including recruitment rate, response rate,

discrepancies from plan, baseline statistics, sample representativeness, and so forth. In

this study, I used secondary data and discuss the data collection process for a big data

project in a DBR context.

The data analytics projects in big data environment start with a list of available

data assets and a vague description of the business objective of the analytic and decision-

support exercise. The available data assets represented the universe of data for the

formulation of the analytic problem under consideration. The vague description of the

business objective stipulates the expectations of the analytic exercise. Detailed

requirements were problematic due to the overwhelming availability of data and the

complexity of the information about the business problem.

The key steps in big data analytics projects were the collection of all the datasets

available for the analysis, preparing the data for analytic algorithms, running the analytic

algorithms to generate analytic models, running the analytic models against new data to

determine its performance, reporting the performance of the models, reviewing the results

in the context of the business problem under consideration (Zicari et al., 2016). When

the results do not provide satisfactory answers to the business questions, this process is

iterated until an acceptable answer is produced. Using the data model extensions and

extended data analysis plan to update the data model throughout all these steps ensures

that progression of the data analytics process. The extensions of the data model created

the cognitive breadcrumbs needed to adapt the analytic processing for complex business

problem-solving. The data collection process went as follows.

Since the big data environment was the collection point for the available data in

the organization, and it ingested and maintained the data as-is from the source systems,

whether structured (data files, tables) or unstructured (documents, records, graphs,

multimedia) formats. The first step in the data collection was capturing the names of the

data assets, number of files in the set (if more than 1), partition logic (if multiple files),

format, size, number of rows, and the number of columns in all the datasets and

documents provided. For each of the files in data asset, I determined whether there were

links between the files, and if so, which attribute(s) established the link. I generated a

data set link inventory to sustain the connections between the data assets for further

processing.

I processed each data set further to gather details of the content. This included

data element labels, data type, number of unique values, and cardinality ratio. The data

element label was either the first row in the data set, declarations at the beginning of the

data set for filetypes like parquet or Avro, separate metadata files like flat files, or

database catalog of the primary source system. Data types were primary scalar data types

of numeric and non-numeric types. Variants of numeric data types like integer, big-

integer, decimals, money, float, and non-numeric datatypes like character, variable

character, text, binary, variable binary were derived when not explicitly provided with the

initial data set. A row in the data set was either a record for structured data or a line for

unstructured data. Unique values were derived by counting the unique occurrence of the

values of the data element either in a row of structured data or line of unstructured data.

The unique values were the tokens of the underlying subjects. I calculated the cardinality

ratio as the number of unique values divided by the number of the rows in the data set.

Using the cardinality ratio, I implemented the following relation identification algorithm

Table 5

Relation extraction algorithm

For each data set, set dataset name to dataset label

For all data elements in the data set

if there is a data element with cardinality ratio = 1 and

the data element is not a timestamp;

then assign this data element a relation property key status

assign the label of the data element as the name of the relation;

the sum of all cardinality ratios = 1

then assign all data elements relation property key status

assign the concatenated label of the data elements as a name of

relation;

the sum of all cardinality ratios > 1

then

find the combination of the sum of data element keys that add to 1

assign each combination a relation property key name

assign each combination a relation name that combined the name of

property names

data element with cardinality ratio = 1 and the data element

is a timestamp,

then

skip timestamp data element

find the combination of the sum of data element keys that add to 1

assign each combination a relation property key name

assign each combination a relation name that combined the name of

property names

If the sum of all cardinality ratios < 1

then

find a partition of the data with a combination of the sum of data

element keys that add to 1

assign each combination a relation property key name

assign each combination a relation name that combined the name of

property names.

no partitions were found that meet this criterion,

flag dataset for manual review

End;

The following relation types were collected through this process.

1. The primary relation which enumerated instances of items with similar

characteristics, for example, customer, product, sales representative, time,

location, and others.

2. The composite relations which captured the interaction of the primary

relations in the data model, for example, a sale became the relationship

relation of the interaction of product, customer, sales representative, time,

space, price, and so on.

3. Detail primary relation with high cardinality attributes of the primary

relation properties.

4. Detail composite relation with high cardinality relation properties of

composite relations.

The cardinality ratios separated the relations into two groups. The third normal

form relational data model that resulted from this process captured the universe of

attributes available for processing the goals and objectives of the data analytics project.

The collection of data about the data model extensions used the four types of

relations – primary, primary detail, composite, and composite detail, captured with the

relation recognition algorithm as input. Noting that the detail relation types extended the

primary relations, the connections between these relations were extensions.

For primary relations, the connection could be one-to-one, union (full or partial),

or none. If one-to-one, the relations were combined without any loss of data. If the full

union, that meant the two primary relations could be concatenated together without a

change of the number of properties in the resulting combined data set. If partial union, the

relations had common properties which were concatenated such that each relation had

properties that were unique to them and no values for the relation properties that were not

common. When the properties of two primary relations did not map to a single set of

properties, I combined their properties and allowed the attributes unique to each relation

to remain as missing values. The missing value treatment such as elimination or

imputation was applied at a later stage in the process as deemed appropriate. A relation

connection type of “None” indicated complete independence of the two primary relations.

Before declaring that the relations are completely independent, I searched for non-natural

connections between the relations, such as, geographical location or timestamp, and so

forth.

For each relation property within the relations of the data model, I created a new

property to represent the association between the relation properties. The realization of

these associations depended on the analytic formulation needed to quantify the

association. The applicable analytic formulation process depended in the assumptions

about the association which can be linear or non-linear, continuous or non-continuous

(see Appendix F). As such, I adopted a process of appending the name of the analytic

process to the name of the association. When multiple analytic formulations are

applicable, I used as many of the techniques as needed to facilitate capture the data about

the representativeness of the technique. I evaluated relation property values to discover

transformation that would result in new relation properties. I also evaluated each pair of

relation property values for form expressions of the association between them. The form

expression between these attributes resulted in new relation properties. Recalling from

Chapter 2 on the expression of large analytic domains that the formulation of form

expressions for every combination of attribute resulted in very large matrix, I limited the

discovery of form expressions to those that would advance the ontology learning of the

objective of the analytic processing.

With new relation properties, I labeled and integrated them into the data model.

This process continued until all the functional associations were discovered and

integrated into the data model. The universe of attributes expressed by the relations in the

data model at this point would be comprehensive for the discovery, identification,

specification, and resolution tasks for the data analytics project. I used the conceptual

model generated from the process to evaluate the appropriateness of the data for the

analytic exercise.

To evaluate the information within the data model, I used information entropy

calculation. For each relation and the relation property of the data model, the information

entropy was calculated as the sum of the proportions of the values multiplied by the

normal log of the proportions of the values. The relation or the relation property would be

1 when there was an equal proportion of all values and approach zero the more the

variation of the proportions of values are in the relation. For the ontology learning

process, relation properties with large information gain calculation had low ontology

classification. Also, low information gain represented high ontology class. This situation

of the ontology class was an indication of the generalizability of the concept across the

domain. The information gain distribution of the relation properties was used in the

determination of the ontological commitment for each property value in the data model

and the derivation of data model extensions.

Study Results

Using the data collected from the process described above and the information

entropy calculation discussed above, I grouped the relation property values into three

classes. Property values with information entropy > 0.75 were specialized ontology

concepts which were helpful in defining the dimensions of the subjects of the data model.

Those with analytic significance metric between 0.35 to 0.75 contained ontology

concepts that had moderate generalizability and were helpful in extending the data model

for specific analytic situations. Finally, the property values < 0.34 were helpful in

extending the data model for general expression. This data model extension approach

preserved the operations of relational algebra and calculus, including union, difference,

product, selection, projection, logic, and arithmetic. It, also, sustained the connection of

input data to the analytic expressions constructed for knowledge discovery, business

intelligence, and decision-support in management.

Recall that the analytic elements of the properties of the relation had an attribute

component (a) and the logic component (l), where the attribute element had value (v) and

scale (s) sub-components. The manipulation of the a, l components of the analytic

element resulted in the differentiation of the property or properties of the relation. These

extensions were higher-order conceptual relations or properties derived from lower-order

classical relation or properties using established data engineering and analytic

formulation techniques (Foster & Stein, 2013). The catalog of ontological element types

and analytic formulations are shown in Appendix F and G respectively. Further

discussion of the extensions follows.

Semantic Extension

Semantic extension formed interpretation continuity on attributes of the relation.

This extension involved manipulating the v-subcomponent of the a-compoentt of the

analytic element pair, (a,l), discussed above. This manipulation expanded the expression

of the relation property into a relation that captures all forms of representation based on

the value expression (Krogstie, 2012; Feilmayr & Wöß, 2016). Semantic extensions of

the data model transformed the scalar quantities of the relation properties into vector and

matrix formulations of the relation. The extension impacts non-numeric attributes the

most since their vectorization requires coding or transformation, such as dummy coding,

threshold coding, proportionality coding, probability coding, the weight of evidence

coding, Rasch coding, Dempster-Shafer coding, Likert scale coding, and so on and so

forth. The implementation of semantic extensions identified the cases and the states of

expression of characteristics of subjects within the data.

Semantic extension expanded the data model into its first-order logical

expression. First-order logic system were sets of propositions on concepts conferring

meaning to the underlying objects and subjects arising from the interaction of objects. In

turn, propositions were sets of atomic predicates connected with logic connectives into

compound predicates. The atomic predicates formed the units of expression of the object

or subjects and offered interpretation context(s) reflected in the term or name reference of

the predicate, the value assignment, data type, and scale of this value. The semantic

relation became the collection of propositions for the expression of the instances of the

relation with both conjunctive and disjunctive logic. Note that the typical entity relation is

of conjunctive normal form only.

Semantic extension transformed the entity-attribute-value structure of the data

model into the subject-predicate-variable structure of first-order logic. Semantic relations

were made up of elements whose instances were variables of well-formed atomic

formulas of first-order predicate logic with bounded values. For example, attribute, A,

was the predicate logic for the instance or variable of A, p (?a), within attribute domain of

A given entity, |a|, such that,

A: p(?a, |a|) = true & p(?a, not |a|)=[false | undefined]

Every attribute value was, therefore, the predicate logic assertion. For example, if

attribute A was “year”, its variable, ?year, with a domain, |year|= |2010, 2011, 2012,

2013|, an assertion for predicate, p(?year, 2010) = true and p ( ? year, 2014) = false

(closed world interpretation) or undefined (open world interpretation). The number of

distinct predicates became fewer than the number of variables. Essentially, every instance

or set of instances of attributes transformed into first-order predicate semantic relation.

The semantic expansion described above, based on first-order predicate logic,

transformation resulted in many variables in a relation, especially when dealing with

qualitative attributes of high cardinality or quantitative attributes whose magnitude had

significance. For these attributes, semantic continuity was established with count, order,

or ratio measures respectively. This improved expressivity of the semantic relations,

allowing aggregation of lower-order predicates over well-defined sets, supersets, and

higher levels of predicate cardinalities using following qualifiers:

• the many-sorted logic to partition instances into populations, groups, and

types;

• intuitionistic type logic to link variables to proof and dependency types;

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• Logic modal qualifiers, such as

o alethetic for the states of possibility, impossibility, necessity

o temporal for the timestamp, time span, time horizon

o spatial for point, area, space

o deontic for mandatory, obligatory, permissible,

o epistemic for propositional, hypothetical, theoretic, proven

o doxastic for temporal-spatial, situational, positional, and

o fuzzy logic for heuristic categories

Essentially, semantic extensions of the data resulted in atomic concepts of the

underlying data in a fully specified form. As noted above, this organization of data

favored the derivation of scalar quantities representing the magnitude of the properties of

the subjects as expressed in the data. The degree of connectivity of logic represented the

complexity of expression. The associations or correlations between the variables

provided the guide needed to answer complex questions about the subjects using the

available data. The estimate of the size of the semantic database was the product of the

sum of arities of all semantic relations and the number of relations.

The implementation of this extension of the data model required the following

transformations:

1. For attributes with assignment devoid of order or interval, each assignment

became a variable with binary values, commonly coded as one if present and

zero if absent respectively.

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2. For attributes with an assignment with order but devoid of the interval, the

value is translated into a rank order further transformed, normalized,

regularized as needed to capture the magnitude of expression.

3. For attributes with an assignment with order and interval, the value

transformations eliminated covariation (standardization), scale issues

(regularization and normalization) as needed

4. For attributes with characteristic assignment devoid of order with a large

number of values, were grouped

5. For attributes with a characteristic assignment with order and a large number

of values, were rank ordered

6. For attributes with numeric assignment devoid of order with a large number of

values, were grouped

7. For attributes with a numeric assignment with order and many values, were

rank ordered

Symbolic Extension

The symbolic extension formed subject-object relations which layered expression

of entity types and groups into conceptual boundaries for similarity, discriminant, or

other quantitative distance measures (Diday, 2012). They were extensions on the l-

complement of the (a,l) pair of the analytic element. With these extensions, the concept

of CUSTOMER became vector or spectrum of expression based on figurative

characteristics like purchase frequency, price sensitivity, lifetime value, churn

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probability, to name a few. This vector could compare to the PROSPECT vector to show

the flow between them in the PARTY vector of vectors. This result was the map of the

journey of a PARTY through the enterprise from the cradle to the grave. Superimposing

the actions of management responsible for changes in the characteristics of these vectors

over the lifetime of the PARTY brought clarity to the consequence of management

decisions and actions.

While the semantic extension evolved the data model into the relation of variables

and captured the logical association behind the expression of the subjects within the

domain of interest, the symbolic extension quantifies this expression for the comparison

of the subjects (Jiao, Zhou, & Chu, 2016). Symbolic extension of the data model adds a

transformation to records of the subject of interest to represent the distance from each

other, or to a normative reference. This extension derived attributes of the subject of

interest as a specific form of lossless encoding of the characteristics of the subject. The

results were mappings, π, from a space of expression, y, to that which defined it, x,

represented as follows:

π : y → x

y = π(x), that the subject of interest, y, encoded by the set of variables of the subject of

interest, x. It was not necessary for this mapping to be injective, that is, for the same

expression of the subject of interest transformed similarly by the same set of inputs (one-

to-one mapping between expression and input(s)).

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An emphasis on this extension was the capture of the space of expression that was

identifying the subjects of interest to make similarity or discriminant assessment

quantitative. Each element y ∈ Y determined a unique set x= π(y) ∈ X, where every x ∈

X was representative of one or more elements of y ∈ Y. Space, Y, was the Cartesian

product of finite metric spaces defining the boundaries of the topology of the subject of

interest. This space simplified the assessment of similarity compared to using the natural

metrics within the space, X.

With this extension, the enterprise transformed into an abstract topological

dynamical system, 𝒴 = (Y, T) where Y was a metric space and T is a continuous function

within the metric space. That is, 𝒴, had n-dimensional axis reflecting states of as subset

of the entire space, 𝒴 = (Y, 𝜎). This space consisted of finite form expression Y=(yn)n∈

𝒴 over a finite relation, which was transformed using a shift map σ(y)=(yn+1)n ∈ 𝒴. The

relation between 𝒴 and (Y, T) was the factor map which controls the translation of Y into

𝒴 dynamical system, such that the lower layer was made up of fine grain attributes that

encoded general characteristics of the subjects of the domain, while higher layers were

responsible for specific characteristics of the subject.

The first k attributes jointly represent the union of a unit of order k, with every

unit translating into a factor of the subject, independently. The units of the first order

form into disjoint blocks or groups, each unit of order k included a piece of the kth

attribute and a finite collection of attributes of lower orders. The result was an association

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or concept hierarchy based on criterion induced by order of expression which was subtler

than a strict hierarchical or graphical association based explicit criteria in the information.

To further explain the data model extension, let y1,...,yp be the set of variables, Dj

be the underlying domain of Yj and |Y|j the range of Yj for j=1,...,p., set of values for Y.

Given a symbolic relation, S, with p-tuple (y1,...,yp) with yj ∈ |Y|j for j=1,...,p. S ={

s1,...,sn} were the relation instances, then Yj(si) ∈ |Y|j for j =1,...,p, and i=1,...,n.

Therefore, the data array consisted of n relations, one for each instance si ∈ S, such that

(Y1(si),...,Yp(si)) for i =1,...,n. The data types of the symbolic variables took on additional

forms besides intervals and count integers of the semantic space, such as arrays of

different dimensions, functional expression/mapping, nominal and ordinal values, modal

values, standard numeric valued data types (Noirhomme‐Fraiture & Brito, 2011).

An important relationship in symbolic extension was the concept of full or partial

dependence. A symbolic relation, S1 may be fully or partially dependent on another

relation, S2, if it could only be applied when S2 takes expression within the all or given

set for S1. The relation, S1, was dependent on the relation, S2, if S1 made no sense for

some values of S2, and hence became non-applicable.

Dimension Extension

Dimension extension established the accurate and orthogonal axes of expression

of the abstract interrelated analytic spaces within the domain of interest given semantic

and symbolic differentiation and integration. This extension “dimensionalizes” the

domain into invariant quantities with the absolute significance of relative magnitude, per

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Buckingham π theorem and Bridgman’s principle (Shen, Davis, Lin, & Nachtsheim,

2014). Applied to the example of the PARTY, the complex dimension extension, defined

the multiple paths for the PARTY vector of vectors which connects to the different

outcomes within the domain, for example, customer tenure, type of order, purchase

frequency, willingness to pay threshold, to name a few. Dimensional extensions allowed

the definition of metrics like party conversion velocity and acceleration useful in

determining the progression towards management targets.

Mathematically, a dimension is an axis or aspect of the expression of a subject or

object defined in the geometric form. It is the derived extent on measures, metrics,

moments, and coefficients of expression such as length, breadth, volume, height, to name

a few of a subject or objects assuming its geometric realization. Dimensional extension

represented these extents in the form of invariant quantities (or points) in an abstract

space allowing accurate inference, projection, simulation, and optimization of the

characteristics of the realized geometric form. In this sense, this extension applied to

subjects and algebraic rules governing quantities, such that, calculations and derivations

maintained correspondence with the properties of the subjects represented. It assumed an

abstract space of expression defined by the dimensions inherent in the available data in

which each record occupied a point in the space. The dimensional extensions provided

the abstract coordinate system for analytic exploration of a subject of interest based on

available data, allowing the manipulation of the numbers without concern of the units of

measurement underlying the properties under consideration.

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The construction of a dimensional extension to the data model required the

abstract assignment of input and output features of the subject of interest, based on the

provenance of the subject or the objective of the analytic exercise. Output features

represent the result of the interaction of inputs. Consider, the input dimension elements

denoted as X1,..., Xp and the resulting response element denoted as Y0, the conventional

dimensional model became:

Y0 = f(X1,...,Xp),

Xis were the symbolic attributes or the features of the subject of interest standardized to

avoid mathematical issues with unit differences. f was the function expressing the

association of the two sides of the relationship.

Additional assumptions of dimensional extension included the base quantities

which constitute a subset of the inputs, denoted X1,...,Xt, where t ≤ p, to satisfy non-basis

quantities, [X0],[Xt+1],...,[Xp] expressed by the combinations of the dimensions of the

base quantities, [X1],...,[Xt], in the form of the power law. It is important to note that

basis quantities cannot combine dimensions of other base quantities. Furthermore,

assume that [X0] can be expressed by the combinations of [Xi] for i = 1,...,p, otherwise it

violates dimensional homogeneity. This assumption led to the existence of the basis

quantities that may not be unique or independent. To address this, the transformation of

the attributes uses basis quantities based on Buckingham’s Π-theorem. For example,

[Xi] = [X1]di1...[Xt]dit for i = 0,t + 1,t + 2,...,p.

Consequently, the transformed quantities are

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Πi = Xi((X−di1)1···(X−dit))t for i = 0, t+1, t+2, ... , p

where

[Πi] = [((XiX−di1)1···(X−dit))t ] = [X1]di1...[Xt]dit[X1]−di1...[Xt]−dit = 1

The response function can be rewritten:

Y0 = f(X1,...,Xt,Xt+1,...,Xp).

Using Πi instead of Yi, the following expression resulted

Π0((Xd0)1 ···(Xd0t)t)= f(X1,...,Xt,Πt+1Xdt+1,1 1 ···Xdt+1,t t ,...,ΠpXdp1 1 ···Xdpt t),

and

Π0 = (X−d01)1 ···(X−d0t)t ·f(X1,...,Xt,Πt+1Xdt+1)1 ···(Xdt+1,...,ΠpXdp1)1 ···(Xdpt)t )

where f is the function to be estimated.

Or,

Π0 = g(X1,...,Xt,Πt+1,...,Πp)

where

Πi,i = 0,t + 1,...,p are quantities and

X1,..., Xt are considered independent of one another

Based on Buckingham’s theorem, Πi represented the final expression of the output

regarding the dimensions of the input.

Resolving the Research Questions

The research questions are restated here:

Research Question 1: Can data model extensions improve the discovery of

management scenarios from big data?

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Research Question 2: Can data model extensions improve the formulation of insights

about the management scenarios?

Research Question 3: Can data model extensions express the complex constraints

and rules needed to compose the acceptable and actionable solutions for analysts and

executives?

Research question 1. To answer the research question 1, I examined the datasets

that resulted from the use of the extended data model for the management scenarios.

Within this data model, management scenarios were connections which expressed

associations between sets of data elements about resources (for example, products), and

agents (for example, sales representatives) in transactions (for example, sales

transactions) leading to business outcomes (for example, profit margin). These were

multi-dimensional association matrices of the semantic, symbolic, and dimension

attributes of the available data. Within the multi-dimensional association matrices, the

semantic attributes expressed degrees of similarity or dissimilarity to other values of the

property, symbolic extensions established the congruence of properties to each other, and

the dimensional extensions established the distance between relation instances.

Management scenarios, G*, such that each management scenario, G, was

represented as

(V, E = {𝐸0, 𝐸1, …, 𝐸𝑚 ⊆ (V xV)}),

a multi-dimensional relational matrix where

A ∈ {0 … 1}𝑛.𝑛.𝑛{0…1} and

(11)

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𝐴𝑖,𝑗

𝑘 > 0 if (i, j) ∈ 𝐸𝑚: 1 ≤ k ≤ m or 0 otherwise

Thus, each extension data element E represented an adjacency matrix, and the

combination of m adjacent matrices formed a complete expression of the management

scenarios. Within this scenario space, the multidimensionality of the associations

characterized the different conditions that apply to the scenario. Each condition became

the unique path of connections with a unique set of functions and constraints which

mapped to unique outcomes. Using the analytically extended data model representing all

relevant multi-relational paths within the available data between all data elements, the

paths with the same starting point and end-point formed the scenarios when there are

discriminating combinations of initial value and end outputs. Based on this analysis, an

analytically extended data model provided the relevant scenarios for management

analysts and executives, through the extension attributes which connected inputs to

outputs. Simply, a scenario was the path from a specified input point to a specified output

point within the data model. The data model extension improved the discovery of

management scenarios from big data.

Research Question 2. To answer research question 2, I studied the type of

information any management analyst or executive would consider an actionable insight.

Important requirements of insight were explainability, interestingness, and relevance. An

insight was considered explainable if it was capable of being understood within the

domain of interest. The capability to understand represented the alignment of the analytic

results to the intuitive conceptualization of the subject of interest. That is, an insight was

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considered explainable if it connected well-established concepts within the domain of

interest. When an insight revealed new connections and new concepts, the insight was

found to be interesting. An insight was considered relevant by management analysts and

executives when the connection to resources and agents had utility since these were the

items the management analyst or executive could manipulate to solve the management

case.

The extensions that connected the resource (for example, product, price,

marketing, customers), agent (sales representatives, customer service representatives,

product development, Pricing analyst) and transaction (sales) ontology elements

addressed explainability, interestingness, and relevance. At the data level, the insights

were the quantities that qualified the associations between the transactions and the

interaction of resources and agents that provided the management analyst with clarity on

where optimization opportunities existed in achieving the satisfactory outcome.

The extended data model captured the different levels of insights depending on

the analytic objective of the exercise. The insight was descriptive if it provided

perspective on current and historical occurrences. It was inferential when it provided

information on one situation for the estimation of another. For example, inferential

insight was diagnostic when it used existing information to provide a reason for an

ongoing condition. It was predictive inferential insight when it used information of a

current and past situation to make guesses about the future. The insight was considered a

forecast when it took into account a point in the time in the future for which these

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assumptions could be realized all things being equal. The data model extensions

improved the formulation of insights about management scenarios.

Research Question 3. As noted above, constraints and rules were expressions of

different forms of logic. Constraints were logic of limits, and rules were logic of

associations or projections. Complex constraints and rules are, therefore, n-order logic, in

which lower order predicates or propositions were nested to create higher order

predicates and propositions. As stated above, the classical relation could be considered

the collection of first-order predicate logic at the attribute level, and first-order

propositional logic at the tuple level. Data-model extensions grouped and nested the

predicate and propositional logic in different combinations for the discovery,

identification, specification, and resolution of management problem scenarios. In the

extended data model, the logic of limits, associations, and projections were data points.

The data model extensions captured complex constraints and rules needed to improve the

acceptance of analytic outputs by management analysts and executives.

Application

This section contains the application of data model extension and extended data

analysis methodologies to a big data analytics project scenario in a U.S. based global

medical equipment manufacturer and distributor. A brief overview of the company and

management needs set the context for the analytic exercise. The primary goal of the data

analytics exercise was to identify the contributors to profit margin and overall growth of

the company. The company consistently missed its annual revenue and profit goals, so

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management wanted the project to discover what was responsible for the situation and

provide a recommended remediation plan.

Case Overview

The company was a huge manufacturer and distributor of medical supplies,

uniquely positioned to provide products, education, and support services across the

continuum of healthcare. It marketed as much as 100,000 products, including hospital

furniture (bed, mattresses, seats, and tables of all types and specifications), durable

medical equipment, housekeeping supplies, exam gloves and garments, and many others.

Its customer base included hospitals, long-term care facilities, physician offices/practices,

home health providers, and retail outlets. For large customers, they offered inventory,

supply chain, logistics, technology and analytics and equipment customization solutions.

Its more than 11,000 sales representatives marketed the products and services through

some 200 distribution centers in 13 countries in North America, Europe, and Asia /

Oceania. It operated a delivery fleet for high throughput routes and used delivery services

to drop ship purchases as necessary. The company operated manufacturing plants in the

China and Singapore. Its manufacturing plant in the United States closed about five years

before this analysis.

Executive management was concerned about its stagnation of revenues and

profits. The profit margins were much lower than peers in the same industry. The

executive management considered its poor performance on key market valuation metrics,

for example, price per share, earning per share, price to earnings ratio, price change, price

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change percentage, and market capitalization as indicative of the erosion of profit

margins. They believed that their forward guidance of the market was responsible for the

pessimistic view of the company by the market, the result being its low market valuation

and stock pricing. Management believed that a better attribution of the profit margin

would provide the tool to manipulate their operational activities to achieve higher levels

of profitability which should command market valuation that was better than its peers.

The prevailing belief was that the company had a pricing issue, much more than a

cost issue. An earlier profit strategy study proposed revenue estimates, targets and

forecasts based on price increases and commission reductions only. Management wanted

validation of these strategic proposals, quantitatively. They also wanted to design

programs to achieve a consistent growth of the company and increase product footprint in

existing and new customers over time which would translate into a higher market

valuation of the company. They needed a comprehensive solution that can achieve profit

margin expansion while minimizing the downside impact of price and commission

changes on the customers and sales force.

Data

The enterprise transaction processing system (SAP/R3 Enterprise Resource

Planning (ERP) system) of the company was the primary data source for the study.

Additional data sources included data from GHX Market Intelligence, Distribution

Feedback Reports, and Health Product Information System (HPIS) data which was the

source for standardized health care product codes, along with competitive and

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complementary product information. Also, reports generated to support sales, customer,

pricing, and product management contained information needed for analysis. Many of

these reports were monthly and quarterly snapshots which had been saved off as

documents for management use. Examples were active account reports provided as

active_account.xls, Credit analysis by Reason Code report, provided as Credit analysis by

Reason Code report.pdf, and so on. The data were representative of the complexity of

enterprise data in modern organizations. Table 5 contains the summary of data assets in

the study.

Table 5

Study Data Overview

Item

Value

Comment

The total size of data

15 terabytes

(TB)

Considered Very Large Data Set (VLDS) for analytic

modeling

Total number of fields in

all data sets

700

A large number of fields means that the dimensionality

of the dataset would be very high, which would make

computability difficult

Number of datasets

137

All data sets would be linked to compose a complete

universe of data asset for the analytic modeling

exercise

Number of sales

transaction records

1.7 billion

A large number of sales transactions means that the

observation set for the analytic case of very robust, and

it is likely to reflect the different mechanisms and

subjects that underlie the data generation process

completely

Timespan

3 years

More than one business cycle for analysis since

systems aligned well with the calendar year

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% of numeric attributes

As much as 210 numeric data elements are available as

candidate variables

% of character attributes

As much as 490 characteristic variables are available

candidate variables

The range of character

attribute levels

1 – 5,000

A large number of levels of the natural classes, and

potential explosion of dimensionality and contraction

of degrees of freedom

Range of numerical

attributes

-100,000 to

+5,000,000

A large number of the cardinality of numerical

attributes. Negative numbers meant quantities or

money flowing in the opposite direction of what was

expected. For example, negative order quantity was

order quantity returned by customers, negative

payment amount was amounts returned to the

customers

The total data size was 15 terabytes, made of 1.7 billion sales transactions over

three years. A total of 139 datasets and documents were available for the analysis, with

358 data elements. A ratio of 3:7 of numeric to characteristic attributes. The characteristic

attribute levels ranged from 1 to 5,000, while numeric attributes ranged from -100,000 to

+ 5,000,000. Table 6 shows this diversity of data assets.

Table 6

Data Formats in Input Dataset and Documents

Data asset Type

Data Asset description

File source

# of data assets

DAT

Database output file

ERP data archive

DBF

Database file

ERP system

Mdb

Microsoft Access Database file

User Application

Xlsx

Microsoft Office 2000 Excel

File format

Extracts from ERP and other

systems

Xls

Microsoft Office Excel File

format

Extracts from ERP and other

systems

CSV

Character separated values file

Extracts from ERP and other

systems

PDF

Adobe Acrobat Portable

document format file

Internal and third party reports

RAR

Compressed file

Data file archive

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SPOOL

Database or Application output

file

ERP and other applications

DOC

Microsoft Office Word File

format

Reports and analysis

DOCM

Microsoft Office Word Macro

File format

Reports and analysis

TXT

Text file

Extracts from ERP and other

systems

Total number of data assets

140

As noted in the table above, available data also included several documents with

unstructured or semi-structured information. The documents contained information

needed for the analysis, so it became necessary to extract this information from the

documents. I converted PDF, DOC, DOCM documents to unformatted texts documents

before using the Open SourceText Mining algorithms within Pentaho Data Integration to

process and ingest the data into the PostgreSQL database, which was capable of handling

structured, unstructured, and hierarchical data representation. The conversion of the

different data formats were vital activities of the data analysis process. The meticulous

process of converting the non-structured data assets into structured data facilitated their

integration with the structured data was an essential and significant undertaking. It is

worth noting that the need for a document database like MongoDB or Graph database

like Neo4j did not arise as the relational database selection had capabilities of handling

these structures as relational constructs.

Appendix A displays the data use agreement obtained from the study showing the

detail list of available data. Table 6 summarizes the data formats used in the study, and

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Figure 3 shows the data diagram of the data-files, documents, and database extracts. The

data diagram guided the arrangement for further data model development, by organizing

140 different data assets (data files, database tables, and documents) into a scheme with

the linkages between the data assets. The diagram highlighted data assets from the SAP

R/3 ERP system, which contributed most of the data. The non-SAP R/3 data assets

included those from GHX Market Intelligence, for example, Distribution Feedback

Reports and HPIS product data.

The data diagram represented groups of data assets with similar structure and

source. The items in the box were the instances of data assets. For example, SALES

ORDER data were in data sets of monthly data because of the size of the files, so were

pulled into a single group. In this situation, it was necessary to break up the extraction

process into monthly chunks for massively parallel extraction routines which minimized

the window needed for the extraction process.

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Figure 3. Study data asset diagram.

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A significant number of the data files provided for the analysis contained sales

order data (59 data files). Distribution feedback reports from an external source came in

14 files, and price history data came in 9 files. These three data file groups made up the

top 3 datasets for the analysis.

Data Modeling

Base Relational Model. Each data file group was further processed to identify

entity or entities it contained using the entity recognition (ER) algorithm described in the

data collection section above. The ER algorithm produced classical and associational

relations in a 3rd normal form with its primary key column and any foreign key columns

identified. This output generated the data model made up of 30 entity relations, connected

by 32 referential constraints. For the data dictionary of the data model, see Appendix B.

The generated data model addressed cardinality between the entities of the data

sets within and between the datasets, as well as duplicates in the join keys that can

inadvertently result in Cartesian unions. The data model brought together the available

data from different sources and domains into a rationalized framework addressing data

integration issues.

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Figure 4. Study data model.

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Data model extensions

Semantic extension of the data model expanded the attribution of relations for

characterizing profit margin of sales from the universe, shown in Appendix E. I derived

semantic extensions for each of the non-numeric attributes. I encoded the attribute

relations to capture occurrence and non-occurrence of the attribute value. The figure

below illustrates an example of semantic relations for PAYMENT ADVICE and the

SALES ORDER PRICING relations including, BILL TYPE, BILL DATE, SALES

ORDER TYPE, SALES OFFICE, SALES ORDER REASON, PLANT, PRICING

CONDITION CODE, PRICING DATE, and SALES UNIT OF MEASUREMENT. The

use of these semantic relations generated matrices of Boolean, nominal, ordinal, or ratio

scale values of the underlying subjects within the sales domain.

I further extended the data model by adding symbolic elements. As noted in the

section above, these symbolic elements are specific to the analysis problem under

consideration. I determined items derived from domain of interest, listed in Appendix D.

For example, the symbolic extension for the ORDER entity captured the additional

attributes, for example, price blocks, returns (orders with negative sale amount),

promotion sales (sale with special price type), samples (sales with zero amount and

pricing type is sample), new sales reps (sales reps with tenure less than 1 month),

specialized sales reps (sales reps with doctorate degrees for specialized equipment

demonstrations and sales), and so on and so forth.

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Finally, the dimension extensions captured the further expression of the enterprise

as abstract units. For example, the frequency of the order, order to order size change,

order to order price change, change in price impact on customers, price change impact on

orders, and so on were dimensional extensions. It is typical for these expressions to be

dimensionless (i.e., devoid of units) so that their applications are not constrained, and so

that the quantities represent the absolute value of relative quantities. Ratios, percentages,

coefficients, moments were used to formulate them in the data model. The final analytic

data model resulting from the implementation of the extensions discussed above for

margin expansion and growth was extensive, and too large for display here. Using the

extended data model, I constructed datasets that made the profit margin the subject of

interest or the outcome (target or dependent) variable of the data model. All other

classical attributes and the analytical extensions derived from the available data were the

indicator or input variables. Appendix I shows the catalog of analytic processes that are

useful for continued formulation the management problems and solutions to arrive at the

results in the management analysis and recommendation discussed below.

Management Analysis and Recommendations

Figure 5 below shows the conceptual determinants of profit margin, along with

their interaction effects. I constructed the determinant from analytic extensions of the

base data model. To determine the contribution of the different attributes to the profit

margin, I utilized a random forest regression method. This analytic formulation method

was selected since profit margin had a noncontinuous, nonlinear association with

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attributes within the management domains. As shown in the figure, there were no

dominant contributors to the profit margin levels in the available data. The factors

contributed between 1.98% and 3.50%, as such management intervention had to be broad

to achieve any effect.

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Figure 5. Profit margin determinants

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Figure 6. Summary of determinants by management area

The summary of the determinants of the profit margin by the different

management areas showed marketing the lead contributor. The others area in order were

pricing, customer and finally product management areas.

The profit margin coefficients estimated the impact of each of the concepts in the

figure below. I, also, extracted these contributions using a random forest regression

algorithm.

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Figure 7. Profit margin coefficients

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Figure 8. Profit margin coefficient by management area

Figures above show the impact of the concepts on profit margin level

(determinants) and the profit margin change (coefficients). The determinants identified

the critical aspects of the business driving profit margin levels. The profit management

coefficients identified the contribution of each management area to the increase in the

profit margin. Combining these two measures created the following order of influence on

profit margin: marketing, customer, product, pricing, and sales/distribution management

areas as shown in the pie chart below.

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Figure 9. Management area influence of profit margin

The following charts show further decomposition beyond the management areas

based on the key concepts derived from the ontology learning, data engineering and the

analytic formulation methods against the available data.

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Figure 10. Bar chart of customer management area details

Figure 12 above represents the decomposition of the customer management area

into the concepts discovered in the area. Within the customer management domain, the

most important contributor to the profit margin was the customer size based on their

revenue. There was also the tendency for sales agent engagement with the customers to

produce orders, especially, when the company collaborated with the customer to develop

specific products for the customer, for example, special hospital beds for geriatric

patients and disabled patients and so on.

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Figure 11. Bar chart of pricing management area detail

The pricing management area decomposition identified the impact of different

pricing concepts. The price elasticity, relative price of a product to comparable products,

the type size price differential as well and the revenue leakage based on pricing policies

all impacted profit margins and profit growth.

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Figure 12. Bar chart of sales and distribution management area details

A look at the sales and distribution management area revealed that the primary

concept impacting the profit margin was the sales representative promotional

performance. These were promotions initiated directed by the sales agents in

collaboration with the sales and marketing team. The average margin per sales

representatives was significant the overall profit margin. Also important was the

preferences expressed by the sales agents related to the products they were responsible

for driving sales.

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Figure 15. Bar chart of the product management area

The product management concepts of importance where the freight cost which

seemed to add to the overall invoiced cost of sales, rebated products was also critical to

the profit margin improvement of the company. Rebated products were products that

were distributed by the company. The rebated products turned out to better priced than

products the company manufactured.

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Figure 14. Bar chart of the marketing area details

Marketing area details showed most important concept in this area was the special

pricing promotions conducted by the company, followed by the special products

promotions. Also important was promotional activities at community events.

Based on the analysis conducted on these management area concepts the

following programs were recommended for implementation. Each program had well-

defined outcomes expectations:

Special pricing and product promotions with sales representatives – The

management analysis above indicated that marketing contributed poorly to the profit

margin growth. It also highlighted the most effective marketing promotions in achieving

improvements in profit margin to be special pricing and special products promotions

conducted with the sales agents within each of the sales territories. This program

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proposed a marketing process that gathered input from the sales representatives in each

territory to determine the best approach, the product and the potential prospects to target.

The manager of each of the sales territories established targets for the number of

promotions to complete and the return on investment to target for continued investment

on marketing within that sales territory. This program also identified companies to target

for marketing, sales, and investment activities. It included actual investment in customers

by extending products credits and allowing tiered payment cycle of 3, 6, 9, 12, 18, and 24

months to help improve the cash flow situation and growth of customers.

Group pricing arrangement and rebating program –This program administered group

discount pricing arrangement to ensure compliance. The program monitored the volume,

identifying customer groups that did not meet agreement for a rebalancing of the price to

the actual volume. If the group exceeded the volume arrangement, rebate or credits were

triggered. Not meeting the conditions of volume arrangement triggered reverse rebate or

debits from the customer to the company. This program improved margins by 13% in the

first year of implementation.

Onsite supply management program expansion: This program was implemented

for the very large clients, to ensure retention. The company accepted responsibility for

supply management, for exclusive multi-year supply arrangements. This program became

so popular that it became a standard offering of the company. This program resulted in

20% increase in product penetration in existing clients, as well as 80% retention of

rapidly growing clients

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Pricing block improvement program: This program addressed the problem of the

price blocks which occurred when the offer price is much below the standard price. The

sales representatives used this to lower the price so they can get a volume that allowed for

their commission to be competitive. Price blocks also delayed the delivery of items to the

customer who added to challenges of customer satisfaction. This program established the

policy that all price blocks should be cleared within 1 hour of the occurrence of the block

by the sales representative or escalated to the Regional pricing manager. This lead to the

recapture of an average of 7% of the profit margin which was eroded by price blocks.

Product manufacturing improvement program – this program targeted

manufactured products to determine how to make the manufacturing more competitive.

The target was for products manufactured by the company to be cheaper by about 20% so

these products can compete effectively. This lead to many manufacturing strategic

decisions, including outsourcing of manufacturing operations which allowed the

achievement of the objective of getting manufactured products to 20% of the cost of

comparable distributed products

The case overview showed that using analytic extensions to the data model to

derive semantic, symbolic and dimensional attributes related to the profit margin

problem, it was possible to apply advanced analytic processing techniques to discover the

management scenarios underlying the problem. Though the business problem was vague,

using the analytic extensions to enhance the data model, I was able to construct analytic

attributes to represent the concepts described in Appendix D. These concepts like

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customer size, customer tenure, customer payment behavior, and many others were better

at representing the management scenarios responsible for the problem. In relatiom to

research question 1, these data model extensions improved the discovery of the

management scenarios of underlying problems from big data.

Using the management scenarios discovered, it was not very difficult to connect the

management scenarios to management insights needed to address these challenges

imposed by the scenario. In the case above, the insights about marketing that led to the

recommendation of special pricing and product promotion campaign with the sales

representative at key clients was from the finding that this integrative approach to

marketing contributed more to profit margin than other forms of promotion. About

research question 2, the data model extensions and the additional analytic processing

improved the insights about the management scenarios, and provided credible

explanations and solutions for the problem under consideration.

The use of analytic extensions enabled the construction of attributes that captured

complex rules and constraints needed to represent the domain knowledge. Analytic

attributes like order to order interval, order to order quantity change, order to order price

change, and many others allowed the capture of the complex business rules and

constraints related to the behavior of the different participants in the transactions. Also

special policies related to price block management were reflected in the data by

identifying transactions in which these policies contributed negatively to the management

situation under consideration. Therefore, the answer to the research question 3 was that it

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was possible to use data model extensions to represent complex constraints and business

rules needed for the composition of acceptable and actionable solutions for analysts and

executives.

Summary

In the study, I demonstrated that the use of the analytic extensions improved

discovery of management scenarios, insights about these scenarios, and the representation

of complex business rules and constraints needed compose acceptable and actionable

solutions for business analysts and executives The use of analytic extensions supported

the realization of quantities for management analysis. The approach expanded the

representation of information for management analysis and reduced the complexity of the

model. Using different analytic formulations, I was able to define and operationalize

critical concepts within the management domain needed to formulate solutions for

management analysis and decision-support. The concepts I derived and quantified using

analytic extensions to the data model captured difficult and complex conditions and

constraints existing in the domain of interest for analytic problem-solving. Management

problem-solving required the design and execution of business and technology programs

to address the conditions and constraints within the enterprise preventing the achievement

of desired outcomes. The need to improve the utilization of data in the design of

management processes continued to increase with improvements in data gathering,

storage, and retrieval techniques. Through significant work had been done in the

construction of statistical databases for very large datasets as well as in knowledge

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discovery from databases, using data models to formalize the data architecture for these

solutions remained a gap.

In this study, I worked on extending the classical relational data model with

attributed with specific ontological commitments using semantic, symbolic and

dimensional expression forms. While the classical data model saw the attributes as a

primitive expression of the subjects within the enterprise domain, this approach of

implementing extensions to the data fostered the capture of concepts which represented

patterns, profiles, features, and facets directly within the data model.

This approach to the extension of the attribute space simplified the analysis of the

contribution of the different elements to the behavior of the domain of interest. An

illustration of this approach to management problem solving in the medical products

distribution company led to recommendations that were well accepted by analysts and

executives in the business. The programs included special pricing and product promotion

campaigns with the sales representatives to expand market share, group pricing

arrangement and rebate program monitoring to minimize profit leakage. Other

recommendations included Onsite supply management program to increase customer

loyalty, active price block administration to minimize inadvertent underpricing and

overpricing scenarios, and product manufacturing process evaluation to target

manufacturing cost for some of the products that were being cannibalized by rebated

distributed products.

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These recommendations aligned to the intuitions of the business analysts and

executives. The approach avoided the issue of the use of esoteric technical and

assessment methods with limited business and management value. In empirical

management analysis, there was no value in comparing the results to chance or

theoretical distributions to determine the significance of the problem or the outcome

expectation. In classical research, the statistical power and significance of the variables

are basic requirements. Using the data model, I was able focus analysis and

recommendations on business impact of the attributes within the management domain.

The validation of business effects of attributes was critical for the executive decision

maker. These business effect estimates were important drivers of the design, execution,

and administration of management programs that transformed the company to

profitability.

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Chapter 5: Discussion, Conclusions, and Recommendations

Introduction

The purpose of this quantitative nonexperimental descriptive DBR was to

examine data model of a typical enterprise data analytics project to determine data model

extensions that would improve the formulation of management problems for analytic

processing. I focused on a typical data analytics project in a modern data-rich

organization. These projects dealt with very large and complex analytic scenarios

expressed with big data. The management analysis and decision-support requirements

were ambiguous and sometimes unknown. This situation made the classical data analysis

process and analytic processing techniques unsatisfactory. Hence, there were high levels

of failure of these projects in the fulfillment of management needs to resolve business

problems through well-informed recommendations that were acceptable and actionable

by management analysts and executives.

In this chapter, I interpret the findings and the limitations of the study, followed

by recommendations for further studies into the business knowledge discovery and

modeling for management analytics and decision-support research. I conclude the chapter

with a summary of further research opportunities for data analytics and decision-support

in management.

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Interpretation of Findings

Contribution to Knowledge and Research

In Chapter 2, I reviewed the literature on data-modeling for analytic processing. I

also discussed the challenges of increasing complexity of the data and the size of analytic

scenarios in data analytics projects.

The data analytics started with the static composition of data as reports and the

use of reporting databases. The static outputs evolved to more functional expression in

data warehouses, data marts, and business intelligence systems. In the last decade, more

sophisticated analytical expression based on statistical and mathematical methods in

software packages provided important advancements to the data analytics practice. The

most recent progress has been in programmatic or computational expression using

algorithms to evolve logic from associations within the data.

Despite this progress in analytic solution development, challenges remained in

knowledge discovery, business intelligence, and decision-support for management

problem-solving. Significant gaps existed between data, management problems and

analytic solutions proposed. In this study, I demonstrated an approach to the problem

with big data analytics with progressive transformation of the data and the creation of

extensions to the data model for management problem formulation. This approach also

allowed management analysts to apply the analytic insights in the composition of

solutions for management problems. In this study, I emphasized the data model to

establish the boundaries of analytic transformations and search for associations in the

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data. The absence of this analytic transformation boundary was the critical gap with

existing algorithmic analytic processing approaches, which tended to create solutions that

were difficult to translate to management programs which were needed to address

business problems.

The confluence of big data, advances in analytic algorithms, and abundance of

computational power provided the opportunity for transparent enterprise empirical

modeling for intelligent management. This situation buffered issues, like (a) concerns of

representativeness from using part of the data (sampling), (b) the need for theoretical

distribution to estimate parameters or probabilities (curve-fitting), (c) the curse of

dimensionality requiring variable selection, (d) the need for data fabrication or imputation

of missing values to fill gaps in the data, and (e) the need for data reduction to match

computational power availability that are important considerations on existing data-

analytics projects. With these advances, the primary challenge of research in applied

management and decision science becomes the design of data analytics processes that

overcome legacy scenarios of limited data and computability. The approach to the study

of this problem was to extend the data model to enhance the expressiveness of the

underlying schema for the formulation of management problems and the design of

solutions to these problems. The analysis indicated that this approach improved all types

of analytic solutions developed to support management.

Data solutions supported the creation of the exact schema for the problem and

solution scenarios. Analytic extensions to data solutions improved heuristic solutions by

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enabling the discovery of exact rules to replace approximate rules of heuristics. It also

benefited analytical solutions which depended on exact theorems (or formulae, functions)

by identifying the right combinations of propositions that make up the theorems.

Numerical and computational solutions’ dependence on exact procedures and algorithms

required on proper representation of the information in the data model to support the

different permutations of logic that make up the algorithm. In general, data models and

their extensions enhanced the creation of relevant schemas with relevant rules and

theorems and connections, which improve the algorithms and computational solution

generation.

Enterprise data was fraught with complexity imposed by the data generation

process including the lack of explicit connection between cause and effects, functional

dependencies and associations. Data model extensions provided the tools to realize these

embedded features for management problem-solving. Accurate insights on the

performance of enterprise functions on value delivery to the marketplace were critical to

sustaining viability. To this end, the perspective of enterprise outcomes should neither be

completely random nor completely systematic. If the former were the case, management

would be at the mercy of nature, locked in a game of chance, governed completely by the

statistical and probabilistic processes. Conversely, if the latter were the case, management

would be a pure game of quantitative choice governed by deterministic mathematical and

numerical processes.

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The findings of this study support the consensus in the literature that management

is a game of strategy involving the creative design of enterprise programs to guide the

interaction of resources and agents to create events and transactions for the fair exchange

of goods and services (Colman, 2016; Weirich, 2017). The formulation and execution of

this game were, therefore, the most critical activity of management, and defined the

management actions in specific problem-solving situations.

Technically, management problems are constrained optimization problems of the

form:

∫

These were problems of integration of functions that minimize or minimize multiple

objectives subject to constraints. The resulting complex Lagrangian functional

represented the generalized coordinates with partial derivatives expressing changes in

underlying variables and interactions over time. Figure 17 shows a conceptual diagram of

its data model.

min|max f(a, b, …)

subject to g(a, b, …) >=0

(10)

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Figure 14. Generalized data model for the management problem formulation.

Note: a – attributes; c – coefficients, b, d – constraints; u, l – boundary data

Essentially, the data model was sets of attributes, coefficients, constraints,

constants, and controls for each objective within the management domain. Because many

of these were not the natural attributes of the domain of interest, their derivation

depended on evolving them from data available, hence the need for the data model

extensions.

Contribution to Data Analytics

As noted earlier, the use of schema-based analytic solutions was responsible for

the rapid adoption of data warehousing and business intelligence systems in the last

decade. The functional reorganization of data resulted in the adoption of analytics and

decision-support technology in the enterprise. Differentiation of relations into fact and

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dimension relations provided rearrangement of the data for exploration. Unfortunately,

their implementation in OLAP tools limited the application of advanced analytic

programming.

The approach of analytic extensions to the relational data model discussed in this

study overcame the constraint imposed by OLAP. With these extensions, the

reorganization of the database schema was unnecessary. The additional translations of the

data were layered onto the basic relational data schema, to enhance the representation of

the underlying information. These layers of transformation contain the semantic,

symbolic, and dimensional attributes needed to express similarity among values of the

property of a relation, the congruence between two or more properties of a relation or the

association between two or more relations in the data model.

The semantic extension focused on the logical continuation of values of the

attributes and expressed the atomic concepts of the data. As discussed in the previous

section, this involved implementing a data encoding process to derive variables which

continue expression of concepts as arrays or vectors. This extension eliminated the fixed

fact and dimension relations. Semantic extension considered any attribute as a fact or a

dimension depending on the objective of the analysis. Analytic problem solving became

much more flexible than currently possible with the OLAP multi-dimensional data

model. These extensions allowed question-answering regarding values of the attributes

represented by the data.

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The focus of the symbolic extension was on connecting classes to alternative

intentional logic to expand their expression. This extension was useful in imposing

equivalence over property expression space to answer complex questions. That is, this

extension organized data for the interpretation of association of the sets with breaks in

semantic continuity but where there was congruence. The extension was akin to

organizing characteristics of various levels or states of expression of a dynamical system,

such that each level or state was a shift from another level. Symbolic extension fostered

innovative aggregations of data allowing sophisticated description and redescription

processing for profile classification, niche finding, analogical reasoning, story

construction, schema matching to name a few.

With the dimension extension, the focus was on identifying the empirical

dimensionality of the subject of interest based on the data. For example, the distribution

of customers at every price point became the customer dimension of the price. This

perspective of dimension was different from the classical definition of dimension in

multidimensional modeling or dimensional analysis. In multidimensional modeling, the

concept of a customer dimension for the price was not achievable at the attribute level.

These data model extensions made the answering of questions using the data

directly possible at the all levels of knowledge and business intelligence: strategic,

tactical, operational, and transactional. The schemes reflected the precise empirical

ontology of the enterprise as proof systems (theorems) or automatic procedures

(algorithms) for problem-solving. Using them, business analysts and executives could

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compose programs, test their feasibility, assess the expectations, and estimate the

benefits. Data-driven and result-oriented management program development created

predictability and efficiency in the practice of management.

Contribution to big data management research

Another contribution of this study was the application of the design-based

methodology to data analytics in management research. The typical management research

methodology advocated a process of identifying the problem, formulating the research

questions, operationalizing the research questions as hypotheses, and identifying the

variables for which data can be collected to test the hypothesis. Where necessary, the

researcher designed the experiment and created the measurement instrument for the

research. The researcher then gathered data, applied analytic techniques to fit the data to

theoretical distributions, and determined whether the evidence in the data was significant.

This DBR started with the data and then learned from the data what was useful in

solving the problems presented by the interaction of factors within the data generation

process. With DBR, the problem did not need specification at the start of the research.

The requirement was to learn the problems and the solutions from the data or direct

manipulation of the data generation process or the learning environment. The learning

requirement made the availability of big data, advanced analytic algorithms, and

computing power critical to the advancement of this emerging research methodology.

This methodology was robust to address the data analytic problems that increase in

complexity with the nature of analytic problems. This research approach challenged

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variable selection, model selection processes, sampling, data reduction, data treatment

applied to achieve better performance in model results, and many other research practices

in the contemporary scientific inquiry. It also challenged the use of mathematical

solutions and statistical routines. Mathematical solutions were needed when there was no

data to express complex function. Statistical routines were useful when the data was not

enough to support an assumption of accurate population representation. In the modern

data-rich organization, none of these situations existed.

The use of DBR in this study illustrated the opportunity in using the data to

discover and express issues existing in any domain of interest. It also demonstrated the

use of the same data to seek solutions to the problem that would satisfy the end users of

the analytics. Through the iterative transformation of the data, it was possible to quantify

many of the concepts for cognitive processing of the domain of interest. The use of

analytic extension eliminated the need to persist logic in the form of mathematical

expressions. Rather these can be converted into attributes in a data model that can be

analyzed and used in decision making. The use of the data form rather than the functional

(or mathematical) form of the expression improved the interpretation of the results and

the acceptance of the recommendations that were derived.

Limitations of the Study

The limitations that arose from the study regarding the generalizability, validity,

and reliability of the research design, research methodology, and the study outcomes are

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discussed in this section. These were the issues discovered only after all the data had

been analyzed.

The use of data model to broaden the characterization of the domain of interest for

management problem-solving limited the solution scope to the available data. Influences

that could not be extracted directly or indirectly from the available data were not

considered. Anecdotal evidence that could not be substantiated with the business data

could not be included in the analysis. For example, in the illustration, management

analysts and executives believed that the nature of group purchasing contracts and

arrangements contributed to revenue leakage. Since contract data was not available for

analytic processing, their potential influences were not reflected in the recommendations

and the resulting management programs.

The data model was the consequence of the data generation processes and the

controls established within them to ensure the accuracy of the information captured. The

nature of the data generation process, also, determined the representativeness of the

underlying mechanisms and observations about the subjects within the captured data.

Therefore, results of the analytic processes were limited by the context, content, and the

relationships within the data generation process. These in turn limited the solution

proposed for management problem-solving. This limitation was moderated by the use of

big data which ensured the inclusion of all the data elements gathered about the subject of

interest without consideration of methodological and computational needs.

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The selection of the data from medical equipment manufacturing, supply, and

distribution company as the source of the data for illustration of the data modeling

approach was a consequence of the objective of the study which required the use of big

data. The complexity manifested in the large number of products marketed by sales

representative and the different classes of customers and markets in the United States.

This selection of this industry was a natural and unavoidable limitation of the study.

However, this selection limited the relevant business concepts to those of the industry.

For example, there were different types of medical equipment and supplies for many

different medical management scenarios. Some of them were used for therapeutic and

others for diagnostic purposes. The equipment required different levels of skills from the

sales representatives. These differential characteristics of the products had to be

explicitly modeled for management analysis and decision-support. However, only those

differential characteristics that were influential within the data set were reflected in the

analytic results and management action recommendations. The specific extended data

model constructed for the management problem-solving may not generalize to other

management problem-solving scenarios within the industry or to other industries.

However, the modeling approach which expanded the conceptualization of subjects and

their alignment to the cognitive model of the domain of interest improved the

management analytics and decision-support problem-solving in general.

Furthermore. the data model for management analytics and decision support for

profit margin problem solving may only be limited to similar situations of profit margin

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optimization with complex interaction of products, pricing, customer, sales and

marketing characteristics. However, the description of the methodologies adopted for

ontology learning from available data, the application of data engineering to quantify

abstract concepts, and the use of analytic formulation techniques to determine the

functional association between sets of attributes have broader application.

The selection of the data was representative of a typical big-data environment

with data size of more than 1 terabyte. The selection of large data meant that concepts

would occur at a frequency that were statistically powerful, and therefore, relevant for

management analytics and decision support. The approach of analyzing all the available

data, instead of a subset of the data required the construction of a plethora of measures

and metrics at different levels, such that one level can be linked to the next. This resulted

in an architecture for the measures and metrics comparable to neural networks (Zelinka et

al., 2011). The difference was that with this approach of extending the data model, the

analysts would have control of the types of transformations within each layer. Although,

this may prevent erroneous transformations, it also limited the transformations applied to

those that are interpretable in business terms. As such, in situations where unconstrained

transformations were allowed, different analytic outcomes and recommendations could

result. Experience with unconstrained transformation was that they sometimes included

transformation that do not have management analytics and decision support value

(Zelinka et al., 2011).

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Apart from the limitations of the study discussed above, there were no other

limitation of the study that arose from the study. The acceptance of the management

programs that resulted from the analysis process indicated that that the limitations

discussed above did not materially impact the quality of the analytic recommendation

derived from the data model constructed from the data available for analytic processing.

Recommendations

The use of analytic extensions addressed the different levels of information

expression (measured, estimated, inferred, and forecasted) necessary for management

analytic and decision-support problem-solving. This analytic extension of data models

provided avenues to incorporate complex data elements of higher order logic into analytic

processing and programming framework. The derived data was made available to the end

user through the traditional analytic application user interfaces. The analytic extension of

the data model led to an information representation scheme that aligned with the

cognitive model of the domain of interest. It supported identification and classification of

objects of interest within the domain. It also supported the abstraction of these

information artifacts to the level needed for analytics and decision-support in

management. The study identified three levels of data model transformation or analytic

continuity concepts: semantic, symbolic, and dimensional extensions

The methods applied to the transformations at each level were also driven by

specific theories. The theories of measurements (metrology) which advocated the

formulation of measurement scales and instruments in all scientific disciplines drove

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semantic extensions. These theoretical formulations enabled scales developed for

quantitative expression of non-physical quantities in nature, for example, key

performance indicators (KPIs), balanced scorecard (BSC) metrics, customer lifetime

value, customer churn, intelligent quotient, to name a few. The symbolic form addressed

issues related to the optimal specification of the objects in a specific analytic context. At

this level, accurate statistical and heuristic abstraction of data was necessary. The

dimensional form addressed characteristics of subjects of interest mapped to abstract

geometric forms.

The goal was to answer complex management decision questions directly from

available data. For example, these transformations integrated the determinants and

coefficients of expression within the domain of interest. Analytic extensions allowed

reasoning about problems using the data model, rather than analytic algorithms.

Therefore, in data analytics with big data where there would be many attributes, attribute

levels, and analytic models, the use of data model extensions to persist these artifacts is

recommended. The output of the analytic algorithm should also be captured in the data

model and within the analytic application to enable real time comparison of analytic

expectations to actual.

Implications

As mentioned in the previous section, as much as 50% of efforts to develop

decision-support systems for management fail. The implication of such failures was the

misalignment of fundamentals and market value of organizations. The situations of

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undervaluation or overvaluation had a long-term impact on organizations, as has been

demonstrated by the technology industry burst of 2002 and financial industry failure and

subsequent global market turmoil beginning in 2008.

Market economies depend on the accurate valuation of companies, which in turn

depends on the predictability of the management activities of public and private

companies. Since capitalism has become the dominant national economic philosophy in

the world, the private sector plays an important role in national economic productivity,

market efficiency, and overall societal prosperity. The productivity of organizations are

important to the economic and social well-being of the society.

This study contains a schema-based approach to analytic problem-solving in

management. That is, the solution to management analytics and decision-support

problems lies in building a good data model to support analytic processing at all levels of

the organization. In recent years, the focus on algorithms which are black-box solutions

created the cognitive gap between empirical situation and analytic solutions. This

schema-based solution provided a new layer of solutions that ensured proper application

of analytical and numerical solution techniques.

About the contribution to social change, the company in the case illustration was a

major distributor of medical equipment and a supplier to health care organizations.

Discovering the causes of profitability issues, such as wasteful manufacturing processes,

low value products, pricing discrepancies, product development partnership opportunities

and so on brought the company closer to its customer base and the communities they

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served. The partnerships with Non-profit Community Hospitals and Health Centers in

urban inner-city communities in Chicago, Detroit, Memphis, Atlanta, and many others

opened up avenues for involvement in Community wellness and disease management

programs. The company established incentives for the sale agents to participate in social

programs within the communities they covered. The company established a foundation to

support Health care facilities whose primary patients were Medicaid recipients to help

cover losses from under-reimbursement for services from the U. S. government. The

company also reached out to medical missions to South America, Africa, and Middle

East to provide medical equipment and medical supply donations that these missions

depended on for the free services they offered to very needy patients. The social change

that could be realized through all these activities was improvement in health conditions of

many communities, improvement in the daily activities of patients and residents of health

care institutions served by the company, and support for non-profit organizations that

were active in improving conditions of patients around the world.

Conclusions

The need for data-driven decision-making in organizations will only increase as

data gathering, storage, and retrieval techniques improve. Significant work has been done

in the construction of statistical databases for very large databases as well as in

knowledge discovery from databases. While statistical databases lack the scalability of

relational databases, relational databases based on classical data models were not able to

provide the level of knowledge representation made possible by statistical databases. This

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study’s goal was to evolve data-modeling beyond an organizing framework for data. The

goal was device tools and method to model data for higher levels of information

representation necessary for business knowledge and intelligence discovery.

The discussion above showed that further extensions of the relational data model

allowed a fundamental redefinition of the concept of the dimension from one popularized

by OLAP community to one that was much more aligned to the mathematical

interpretation (Hart, 2005). While the classical multidimensional model had attributes

like dimensions, the dimensional extension approach provided a higher-order logic for

constrained optimization and simulation problem-solving in management. The approach

avoided the issue of the use of theoretical statistical distributions since comparison to

chance was not valuable for management analytics and decision making.

In this study, I examined the use of analytic extensions to the data model to

improve the discovery of management scenarios, insights, and complex business rules

and constraints from big data. I established that the use of these analytic extensions was

not just necessary but important to align available data to the intuitive concepts within the

domain of interest. By using a combination of ontology learning, data engineering, and

analytic formulation techniques in the derivation of these analytic extensions, the

resulting data model was the concise and compact representation of the management

scenarios, insights, and the rules that the management analyst and executive would

optimize to achieve predictable outcome states. The use of analytic extensions closed the

gap between analytic solutions and intuitive cognitive models of the business problems.

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