Bayesian modelling of statistical region- and family-level clustered ordinal outcome data from Turkey

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.