6100RC3

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RES 610 Module 3 Assessing Models using Normal Regression and a SEM Tools

As of 6 Oct 2018

Critical Instructions

Make Notes Along the Way

At the end of this exercise – it is essential that you email me or upload questions for anything you do not understand to the Cyber CAFÉ

If you do not questions you MAY have a very difficult time in the future in both the qualifying exam or your own work.

Objective

To enable students to understand how to assess models

Make sure you skim over the following article

“Work Context And The Definition Of Self-How Organizational Care Influences Organization-Based Self-Esteem.pdf”

We are going to recreate the report from the above paper

Important:

If it has been long time since you used SPSS or you have never used SmartPLS, look up some You Tube Videos.

If you do not have a large or dual monitors on your computer, it is highly recommended that you print these slides or you will have challenges executing the assignment.

Goals

Understand what a measurement model is and how to assess it

Understand what a structural model is and how to assess it

Obtain experience with different tools

Note the above terms are generally used in Structural Equation Modeling but the concepts also fit regression modeling

Assignment Structure

After reviewing concepts, provided in a separate briefing, students will assess the same model using 2 tools and be able to explain why most of the answers are the same but not all.

SPSS – Scale Analysis, Factor Analysis, Regression Model Analysis

SmartPLS – Measurement Model, Structural Model

Successful completion is the uploading of the Outputs of the SPSS and SmartPLS Program!!! Make sure the file names are LAST Names-RES160

Upload per the instructions on the charts later on.

Notes: The following are simple analogies – don’t’ quote them

Scale Analysis and Factor Analysis can be considered the counterparts for methods related to the Measurement Model in SEM

Regression Analysis can be considered the counterpart for Structural Model Analysis in SEM

OBSE

ORG_CARE

FAIRNESS

AUTHORITY

REPUTATION

The Theoretical Model From the Paper

The Theoretical Model for the Paper Under Analysis

(with construct definitions and hypothesis

Used to Asses if it “makes SENSE?”)

Organization-based self-esteem (OBSE) reflects "an employee's evaluation of his or her personal adequacy and worthiness as an organizational member"

Organizational care is a "deep structure" (cf. Denison, 1996) of values and organizing principles centered on fulfilling employees' needs, promoting employees' best interests, and valuing employees' contributions (Derry, 1999; Liedtka, 1999, 1996; Tronto, 1998

Employees in organizations see themselves as fairly treated when they believe they have received, or will receive, what they are entitled to or deserve (Tyler, 1989)

Hypothesis 1. Perceived organizational fairness positively mediates the positive relationship between organizational care and organization-based self-esteem.

Job authority refers to the amount of discretion and influence employees believe they can exercise in decisions about the work they do (Van de Ven & Ferry, 1980).

Hypothesis 2. Perceived job authority positively mediates the positive relationship between organizational care and organization based self-esteem

Alternate Predictor. A peer assessment of reputational effectiveness was included in the study as an indicator of competence, which might represent an alternative predictor of self-esteem.

OBSE

ORG_CARE

FAIRNESS

AUTHORITY

REPUTATION

The Operationalized Model – All Reflective Indicators in this Study

OrgCare 1

OrgCare 2

OrgCare 3

OrgCare 4

OrgCare 5

Author 1

Author 2

Author 3

Author 4

Author 5

Fair 1

Fair 2

Fair 3

Fair 4

Fair 5

OBSE 1

OBSE 2

OBSE 3

OBSE 4

OBSE 5

REP 1

REP 2

REP 3

REP 4

REP 5

OBSE

ORG_CARE

FAIRNESS

AUTHORITY

OrgCare 1

OrgCare 2

OrgCare 3

OrgCare 4

OrgCare 5

Author 1

Author 2

Author 3

Author 4

Author 5

Fair 1

Fair 2

Fair 3

Fair 4

Fair 5

OBSE 1

OBSE 2

OBSE 3

OBSE 4

OBSE 5

REP 1

REP 2

REP 3

REP 4

REP 5

The Measurement Instrument/Measurement Model

(What is Indicator Reliability and Internal Consistency Reliability – What are the Differences?)

Indicator Reliability

The weight and p-value

of each individual indicator with the associated variable

Internal Consistency Reliability

A total measure of how well ALL the indictors support measuring the construct – 3 separate ways to measure

1. Composite Reliability (CR) > 0.7

2. Cronbach Alpha > 0.7

3. Average Variance Extracted (AVE> 0.5

REPUTATION

OBSE

ORG_CARE

FAIRNESS

AUTHORITY

REPUTATION

OrgCare 1

OrgCare 2

OrgCare 3

OrgCare 4

OrgCare 5

Author 1

Author 2

Author 3

Author 4

Author 5

Fair 1

Fair 2

Fair 3

Fair 4

Fair 5

OBSE 1

OBSE 2

OBSE 3

OBSE 4

OBSE 5

REP 1

REP 2

REP 3

REP 4

REP 5

Explained Variance

Measured by R2 AT THE VARIABLE itself. It is only calculated for Variable with predictors

In this example Org Care and Reputation have no predictors and there for would not have explained variance calculate

R2, the correlation coefficient (squared) and the path coefficient are THE SAME number

If there are only two variables – see last slide

Regression Wight, Path Coefficient with a p-value and f2

Measured ON the path between 2 variables

In this case there are 6 paths that this could be calculated for. Regression weights and Path Coefficients are accompanied by a p-value. The researcher determines if 0.1 or 0.05 are good enough as the thresholds for the p-value depending on their research objectives. For f2 not all tools calculate this. In the PLS example - the f2 is calculated by the tool. The SPSS example does not calculate f2

The p-value is the probability the NULL hypothesis is true. Example p=.05 is a 5% chance the relationship is NOT as tested or it is a 95% chance the relationship is as tested assuming all the conditions are accurate.

Regression/Beta Weight or Path Coefficient and p-value

The Regression, Path, or Structural Model

Coefficients, p-values, R2

SEM Answer from Original Article

Note that Reputational Effectives was NOT a predictor of OBSE

You will later see the test results indicate this

Analysis 1 – SPSS Assessment – 6 Total Steps

Step 1 – Assess Internal Consistency reliability of the the indicators, remove the bad indicators, report on Cronbach Alpha.

Step 1A - Assess Discriminative Validity using item correlations.

Step 1B–Convergent Validity using Factor Analysis

Step 2 – Create composite data for variables – SPSS Regression cannot use indicators!

Step 3 – Run the double mediation analysis using the mediation script. Paste answers into table. (Report Answers using Excel and fill out the diagram)

Step 3 A – Interpret the Results

Step 4 – Save the ENTIRE Output file as Excel or PDF and upload a copy with your name on it to MYTLC.

Step 1 – Assess the indicators, remove the bad indicators, report on Cronbach Alpha

Download and install SPSS (use the temporary license until you decide to buy). Recommend you buy a student version – you will need to master this tool.

Google SPSS and get an appropriate version

Open the following file in EXCEL – take a look a the data – note that there are 5 indicators and then the main variable. This exercise will show that all the indicators labeled with a “1” are not reliable and should be removed. Then the remaining 4 are use to calculate the composite values for use in regression.

Data for Module 3- Main Variables and Indicators-Import SPSS.xlsx

Take a look at the data – we will end up removing all items (i.e. indicators) that end in a “1”. These indicators reduce the reliability of the associated variable.

You can tell this is probable because for a given respondent (each row are the responses is from on respondent) many indicators (but not all) labeled 1 are much different than the average of its sister (2 – 5) indicators identified in the column with indicator names that do not have numbers (i.e. the composite average of each 2-5 indicator set.

Open SPSS, after importing the data, Select Analyze, Scale, Reliability. Load all the OBSE indicators 1 to 5 ONLY. Call the scale OBSESCALE. Then select Statistics and check the boxes below. Select Continue and O.K.

Note the internal consistency reliability (Cronbach Alpha) is .739 which is good but…

Below it says it can go to .939 if we get rid of OBSE 1.

This is because OBSE 1 does not correlate was well as the other do… take a look at the inter-item correlation.

Go back to Analyze, Scale, Reliability, Remove OBSE 1 and do it again

Asses Internal Consistency Reliability

Now the internal consistency reliability (Cronbach Alpha) is .930 and it says that if you delete more indicators (items), the reliability will actually go down.

- We will stay as is.

Asses Internal Consistency Reliability - Continued

Go back to Analyze, Scale, Reliability. Remove the OBSE indicators. Load the ORGCARE indicators, (All 5 of them). Call the scale ORGCARESCALE. Make sure the statistics are still selected. Select Continue and O.K.

You should get a similar result. The internal consistency reliability (Cronbach Alpha) is .810 but if we remove ORGCARE 1 it jumps to .955

Again this is because ORGCARE 1 does not correlate as well i.e. it does not demonstrate the same internal consistency as the others.

Asses Internal Consistency Reliability - Continued

Go back to Analyze, Scale, Reliability, Remove ORGCARE 1 and do it again

Asses Internal Consistency Reliability - Continued

Now internal consistency reliability (Cronbach Alpha) is .955 and it says that if you delete more indicators (items), the reliability will actually go down.

- We will stay as is.

Asses Internal Consistency Reliability - Continued

Accomplish the same procedure for all the other indicators.

I.e. Fairness, Authority, Reputation.

Asses Internal Consistency Reliability - Continued

Step 1 B – Perform Factor Analysis to Assess Discriminative Validity and Convergent Validity – Note – this is accomplished ONLY USING THE GOOD INDICATORS – WE NEVER USE THE ENTIRE DATA SET AGAIN!!!

In the following steps (follow-on charts), use only the items labeled 2 – 5

Load the 2 - 5 items into the factor analysis calculator

Select Principle Components Analysis,

Select Varimax Rotation.

Note that the purpose of the other “analysis methods and rotations” are beyond the scope of this class but…. Later on you want to learn about this. You may want to search for papers on this.

Open the factor analysis tool in SPSS

Only load the “2-5” items See how the “1” items and the computed variable are not used Select the descriptive shown Select the Factor Analysis shown Select the rotation shown

Configure data

Assess Discriminative Validity See how the items correlate the best with their own factor – and have acceptable p-values with other items within their variable/factor. I.e. They demonstrate Discriminative Validity

Assess Convergent Validity Now see how the items only extract (load high) on their own factors and yet factors DO NOT have Names – the Items are CONVERGING based on their relationship to their sister items as compared to the others

We finished the measurement model analysis

We looked at:

Internal consistency reliability – the indicator reliability was a given i.e. we removed the bad indicators

Discriminant validity

Convergent validity

Step 2 – Create composite values for variables

Overview of follow-on charts

Composite values for variables are required for use in regression – Unlike SEM tools - SPSS regression cannot use indicators

The final variables are already calculated but we want to make sure you know how to compute new ones in case you use SPSS regression in the future.

We will use the transform compute variable function to create new variables that are the average for the all the indicators labeled 2 – 5. Make sure you create the in the order provided.

We will give them unique names

We will compare them to the pre-computed variables.

Step 2 – Create composite variables

Start with OBSE, Select Transform, Compute Variable,

Use the Name OBSECOMPUTED

The expression is noted

Select O.K.

Do this for all the other variables. I am only showing 2 examples

Step 2 – Create composite values for variables

When your done, look at the data in data view

Go to the END (scroll right) and you will see 5 new variables

Compare the “computed variables” with the original calculated variable i.e. the ones that DO NOT HAVE the numbers at the end. These should be the same!!!

Again this is an exercise because the future steps do not use indicators (items) they used computed variables.

Step 3 – Running the Mediation Macro

Normally a mediation is accomplished in 3 STEPS for each Mediation group.

To save time, you will use a mediation macro!

First, open the date file for the mediation – the mediation macro will not work if the variables are not in a specific order and there cannot be extra varables.

The file name is:

Data for Mediation Analysis.sav

It should look like this

Step 3 – Running the Mediation Macro

The double click on the Macro file named:

59069MB mediation test macro.sps

It will open a window like this

Step 3 – Running the Mediation Macro

Go into the box, hit “Control A”

This will select all the text.

Then select the green arrow.

This will move all of the above into the “Data Output” file

Step 3 – Running the Mediation Macro

When the data output file opens go to the bottom. If you see some of the results on the next page, it already ran.

Otherwise Double click inside the box and the Macro will Run

Step 3 – Running the Mediation Macro

Go to the bottom of the Data output file

You will see all the coefficients

I have already transposed them on to the next chart

Make sure you know how to accomplish this. You may have to do this yourself in the future

OBSE

R2=.15

ORG_CARE

FAIRNESS

AUTHORITY

REPUTATION

a =.21*

a = 34**

b = .20**

b = .11***

c = .19**

c’ = .11***

c-c’ = 08***

b = -.03++

** = p < 0.00

* = p < 0.02

***= p < 0.10

++= n.s. =

F = 8.15, df = 4, p < 0.00

The Transposed Answers - take a look at the Interpretation

Take a look at the legend on the left

See if you can tell how I made these

From the previous chart

Note that this is insignificant

Explanatory Power

Predictive Ability

We have PARTIAL Mediation of Org-Care to OBSE via Fairness (0.21, p < 0.02) and Authority ( 0.34, p <.0.00) given that Direct Path between Org-Care and OBSE is significant (c-c” 0.08, p < 0.10).

Reputation is not a predictor of OBSE (-0.03, p = n.s.)

ORG_CARE explains 3% of the variance associated with FAIRNESS and 12% of the Variance associated with AUTHORITY. FAIRNESS and AUTHORTY explain 16% of the variance associate with OBSE

OBSE

R2=.15

ORG_CARE

FAIRNESS

AUTHORITY

REPUTATION

a =.21*

a = 34**

b = .20**

b = .11***

c = .19**

c’ = .11***

c-c’ = 08***

b = -.03++

** = p < 0.00

* = p < 0.02

***= p < 0.10

++= n.s. =

F = 8.15, df = 4, p < 0.00

The Transposed Answers - take a look at the Interpretation

Note that this is insignificant

Explanatory Power

Predictive Ability

We have PARTIAL Mediation of Org-Care to OBSE via Fairness (0.21, p < 0.02) and Authority ( 0.34, p <.0.00) given that Direct Path between Org-Care and OBSE is significant (c-c” 0.08, p < 0.10).

Reputation is not a predictor of OBSE (-0.03, p = n.s.)

ORG_CARE explains 3% of the variance associated with FAIRNESS and 12% of the Variance associated with AUTHORITY. FAIRNESS and AUTHORTY explain 16% of the variance associate with OBSE

We now completed the structural model analysis

We have the explanatory power and predictive behavior

Questions - How many steps did the above take?

P.S. It would have take more steps if we didn’t have the mediation macro

Summary of structural/regression model analysis

Compare the original article to the newly calculated ones.

Note that the path between ORG_CARE and OBSE is NOT significant

Note that the path between ORG_CARE and OBSE is SIGNFICANT at p < 0.10 but it would NOT be significant at p < 0.05

Use the later p-value the interpretations are the same

Original Paper

SPSS Analysis

Step 4 – Save the SPSS OUTPUT file as – Last Name, RES 610.spv and as SPSS web Report (Htm)

Upload both later along with all other files to assignment.

Now for Smart PLS.

Go to http://www.smartpls.de/

The professional version will run the full data set. You can download it for 30 day free trial.

If you use the student version, you will have to use the reduced data set to make it run because the student version only supports 100 rows

Also the student version may not save files – you can PRINT SCREEN the answers to a PowerPoint or Word File

The following example with a data set for 99 rows. (the file ends with 99).

At the end I ran it with all 184 rows so you can see the differences.

See below - find this on the web site.

Once the software is loaded, open it

Create a New Project called Homework Assignment

Right Click on Homework Assignment page and Import the data

Use either the full file labeled SmartPLS or the version with only 99 sample if you chose not to download the 30 day trial version

Select Latent Variables – Add 5 circles

Select the “Select” button, right click on each variable and re-label them. Then use the Connect feature to create paths.

Finally add the indicators

Select the indicators and drag them to their variables – USE ONLY the indicators(i.e. the ones that have numbers at the end) DO NOT use the full composite value variable, then right click on the variable and align them

When your done it should l like this.

Now Use the Calculate button and run PLS

The output should look like this. These are the path coefficients. On the bottom are many other reports.

Before you forget – select the Excel File and Save the output. Then select the “model” tab and go to the next screen

Look at other data

This is chart is currently displaying the Effect Size (f – square). Take a look at the numbers.

Then go down and change the display to the path coefficients for the inner model

The Path Coefficients Display

For the outer model it is displaying the indicator weights - Notice how all the “indicators labeled 1 are the worst”

For the inner model we are looking at path coefficients –

We can also see the construct R2

Delete all the “1’ indicators – see that they all have LOW weights compared to the others

Select Calculate again.

What we effectively accomplished was removing the bad indicators without all the steps in SPSS reliability calculations

Go to the bottom right and Select the Report Button

Take a look at the R2 - Inside the Variables – See analysis at the bottom we will use this later

Remove un-reliable indicators

ORG_CARE explains 2% of the variance associated with FAIRNESS and 15% of the Variance associated with AUTHORITY. FAIRNESS and AUTHORTY explain 19% of the variance associate with OBSE

See the Path Coeficients

Select the Construct Reliability and Validity report

Path Coefficient Table

Select the Construct reliability and validity report

Take a look at the Internal Consistency Reliability and Construct Validity statistics calculated

The select the Discriminant Validity report

Internal Consistency Reliability Options

See the first tab

This is the Fornell-Lacker criterion which says the SQRT of the AVE (ie. the diagonal) should be greater than the correlations of the other variables

Then select the cross loading tab

Discriminative Validity

Notice how the items mostly load on their associated variables.

This is similar to the factor analysis, rotated extraction.

Go back to the main model by selecting the diagram tab on the top right

Other Discriminative Validity Options

You just completed the measurement model analysis

This time select calculate, bootstrapping

Structural Model Assessment

Then select the model again. The path coefficients now have p-values.

If this is not what you see change the display by selecting one of the buttons below

For the full data set, we NO Mediation of Org-Care to OBSE via Fairness (0.15, p < 0.13) and Partial Mediation of Authority ( 0.39, p <.0.00) given that Direct Path between Org-Care and OBSE is significant (0.08, p > 0.40).

Reputation is not a predictor of OBSE (-0.10, p = 363)

FROM THE PREVIOUS CHART:

ORG_CARE explains 3% of the variance associated with FAIRNESS and 12% of the Variance associated with AUTHORITY. FAIRNESS and AUTHORTY explain 16% of the variance associate with OBSE

Structural Model – Path Coefficients and P-Values

You just completed the structural model analysis

Now lets Interpret the Results

For the 99 Sample Set - How does this compare to the one created with SPSS that used the Full SAMPLE?

Remember this is the reduced sample version – go to the next page

Note that the path between ORG_CARE and OBSE is SIGNFICANT at p < 0.10 but it would NOT be significant at p < 0.05

Use the later p-value the interpretations are the same

SPSS Analysis

Reputation is not a predictor of OBSE (-0.10, p = 363)

Smart PLS Analysis

This is the full sample version. The data is better!

How does this compare to the one created with SPSS.

Note that the path between ORG_CARE and OBSE is SIGNFICANT at p < 0.10 but it would NOT be significant at p < 0.05

Use the later p-value the interpretations are the same

SPSS Analysis

For the full data set, we Partial Mediation of Org-Care to OBSE via Fairness (0.18, p < 0.07) and Partial Mediation of Authority ( 0.30, p <.0.00) given that Direct Path between Org-Care and OBSE is significant (0.08, p > 0.40).

Reputation is not a predictor of OBSE (-0.15, p = 12)

THIS DEMONSTRATE THAT THE ’99’ SAMPLE DATA SET WAS TOO SMALL FOR THIS MANY VARIALES AND INDICATORS

Smart PLS Analysis

Now the full sample on the right and the reduced sample on the left.

Reputation is not a predictor of OBSE (-0.15, p = 12)

THIS DEMONSTRATE THAT THE ’99’ SAMPLE DATA SET WAS TOO SMALL FOR THIS MANY VARIALES AND INDICATORS

Smart PLS Analysis – FULL Sample

Reputation is not a predictor of OBSE (-0.10, p = 363)

Smart PLS Analysis – 99 Sample Size

We are DONE with Smart PLS

If you have the full version, please make sure you output 2 files, One file is for the PLS main algorithm and one for the Bootstrapping. You can upload to the assignments either the EXCEL or HTML versions of EACH.

If you used the free version, PRINT Screen all the diagrams and outputs into Word or PowerPoint.

Answer these questions and load as comments when you upload the files 1. Which tool was easier to use? Why 2. Does the sample size matter? Why 3. Does establishing a p-value matter? Why?