  This study is concerned with the analysis of three-level ordinal outcome data
with polytomous logistic regression in the presence of random-effects. It is
assumed that the random-effects follow a Bridge distribution for the logit
link, which allows one to obtain marginal interpretations of the regression
coefficients. The data are obtained from the Turkish Income and Living
Conditions Study, where the outcome variable is self-rated health (SRH), which
is ordinal in nature. The analysis of these data is to compare covariate
sub-groups and draw region- and family-level inferences in terms of SRH.
Parameters and random-effects are sampled from the joint posterior densities
following a Bayesian paradigm. Three criteria are used for model selection:
Watenable information criterion, log pseudo marginal likelihood, and deviance
information criterion. All three suggest that we need to account for both
region- and family-level variabilities in order to model SRH. The extent to
which the models replicate the observed data is examined by posterior
predictive checks. Differences in SRH are found between levels of economic and
demographic variables, regions of Turkey, and families who participated in the
survey. Some of the interesting findings are that unemployed people are 19%
more likely to report poorer health than employed people, and rural Aegean is
the region that has the least probability of reporting poorer health.
