Bayesian analysis of cross-section and clustered data treatment models

This paper is concerned with the problem of determining the effect of a categorical treatment variable on a response given that the treatment is non-randomly assigned and the response (on any given subject) is observed for one setting of the treatment. We consider classes of models that are designed for such problems. These models are subjected to a fully Bayesian analysis based on Markov chain Monte Carlo methods. The analysis of the treatment effect is then based on, amongst other things, the posterior distribution of the potential outcomes (counter-factuals) at the subject level, which is obtained as a by-product of the MCMC simulation procedure. The analysis is extended to models with categorical treatments and binary and clustered outcomes. The problem of model comparisons is also considered. Different aspects of the methodology are illustrated through two data examples.