Semiparametric Bayes analysis of longitudinal data treatment models

Abstract

This paper is concerned with the problem of determining the effect of a binary treatment variable on a continuous outcome given longitudinal observational data and non-randomly assigned treatments. A general semiparametric Bayesian model (based on Dirichlet process mixing) is developed which contains potential outcomes and subject level outcome-specific random effects. The model is subjected to a fully Bayesian analysis based on Markov chain Monte Carlo simulation methods. The methods are used to compute the posterior distribution of the parameters and potential outcomes. The sampled posterior output from the simulation is also used to construct treatment effect distributions at the unit level (and at other levels of aggregation), marginalized over all unknowns of the model, including the unknown distribution of responses and treatments, and treatment effects matched by treatment probability. A real data example, dealing with the wage premium associated with union membership, is considered in detail where quantities such as the average treatment effect, the treatment effect on the treated, and matched treatment effects are derived and illustrated.