I already have used visualizations in my data prep process, and the
more in-depth data analysis will require additional visualizations,
moving from the largely univariate analysis-focused visualizations
that informed data cleansing and other preparation decisions, to
using visualizations to perform multivariate analysis. Scatterplots
will be used to look for visual clues about the relationships between
the variables of interest (the sets of variables that describe:
Medicaid expansion status, health insurance coverage, and Medicaid
enrollment) and the outcome variables (health outcomes, education
outcomes, and employment/income outcomes. R offers a relatively
simple function for creating a scatterplot matrix, called pairs, that
can operate on the entire dataframe to generate pairwise
scatterplots. These visualizations may offer additional insight into
either variables that can be removed (to cut down on
dimensionality) or to at least prioritize the relationships to test in
the models.
The initial set of predictive models that will be used are association
analysis (using the Apriori algorithm in R), the conditional inference
tree algorithm (also in R), and Ensemble models in SAS Enterprise
Miner. In all cases, the models will be run on a randomly generated
subset of the data (training data) and then validated on a separate
subset (test/validation data set).
The Apriori method will require discretization of nearly all of the
variables, which are generally continuous, numeric variables. These
variables will be divided into groups using the “discretize” function
in R, primarily with equal interval or cluster methods, given the
skewness of the data, the size of the dataset, and the difficulty of
identifying breakpoints manually. The Apriori method for generating
association rules is applicable to this project because it does not
comprehensively model every combination of every level of the
discretized variables to identify strong associations. The method
identifies only evaluates those relationships that meet the user-
determined minimum support level to then output a confidence
level, that again must meet a user-determined threshold. The
strength of the correlation is captured in the lift value: greater than
or less than 1 means that there is some dependency (positive or
negative, respectively) between the two items, while a lift value of 1
means the two events are independent. Using lift helps mitigate the
potentially misleading/overstating of relationships that are simply
frequent, but not statistically correlated. These models should offer
further insight (building on the scatterplots) to identify relationships
that not only appear visually, but those which may be hidden by
relatively fewer cases or those which may be overstated with a
simple one-to-one mapping.
Supervised classification models using conditional inference
decision trees should refine class memberships that may show up
less clearly in Apriori results. The conditional inference approach
operates in a strict if/then structure that resolves the limitations of
Apriori models, which allow for overlapping class memberships that
can muddy insights and create ambiguity in predictions of future
case outcomes. This model will not require discretization of the
variables, because conditional inference trees can take both discrete
and continuous variables. This type of approach has the added
benefit of being agnostic to skewed or normal distributions, which
is relevant given the skewness of several of the posited outcomes
of interest, and of participation in Medicaid expansion itself. This
approach is also valuable because it does not require the
explanatory variables to be independent. For example, this project
does not evaluate whether the decision to expand Medicaid or not
is predicated on a particular income level or set of health
outcomes—in other words, the causality of the relationship may be
the reverse of what is being tested. This issue makes conditional
inference particularly useful. Because conditional inference trees
can handle collinear models and select the best predictor, they also
offer the benefit of being able to take all or most of the variables
identified the previous section has having some degree of
collinearity, rather than requiring the researcher to make the choice
or test multiple combinations.
h h h Finally, Ensemble Models generated in SAS Enterprise
Miner will also be used. The decision trees and boosted trees in the
random forest, gradient boosting, and bagging models are, like
conditional inference trees, typically robust to asymmetric or
unbalanced datasets. SAS Enterprise Miner offers the advantage
over R of being able to relatively quickly generate model results,
which allows the user to try different mechanisms to tweak (and
improve) the results. For example, the models can be tuned with
adjusted cutoff thresholds or cost adjustments to improve
predictive strength. The power of the SAS Enterprise Miner
application is that it enables the identification of optimal thresholds
that, in turn, increase the robustness of the model’s predictive
strength across multiple evaluative dimensions: recall, specificity,
and precision (in addition to general accuracy). The application also
enables comparisons of more and less complex models, to
ultimately arrive at a predictive model that is as simple as possible
with as robust an outcome as possible. The benefits of this tool are
directly relevant to the project at hand because of the size and
complexity of the dataset, as described previously; the apparent
collinearity among the variables of interest; and the need to be able
to tell as clear an analytic story as possible to inform health care
policy.
This last item is particularly important and particularly well-served
by the ability available through SAS EM to iterate through dozens
of versions of models if necessary, to arrive at the most
understandable, explainable, and actionable implications. the
ultimate goal of this project is to determine what, if any,
relationship exists between the policy decision and implementation
of Medicaid expansion and positive societal results, in order to
inform future policy choices on health care.
