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.
j 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.
