Semiparametric Bayes analysis of longitudinal data treatment models

Abstract

This paper is concerned with the problem of determining the e ect 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-speciÿc random e ects. 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 e ect 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 e ects 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 e ect, the treatment e ect on the treated, and matched treatment e ects are derived and illustrated.

Modeling and calculating the effect of treatment at baseline from panel outcomes

“…Because we operate under the framework of Chib (2004), these predictive treatment effects are based only on the marginal distribution of the potential outcomes. This is in contrast to the predictive effects in Chib and Hamilton (2002) and Li et al (2004) and other papers by these and many other authors, which need not be just the marginal, but also the unidentified joint distribution of the potential outcomes. Our final methodological contribution relates to the problem of model choice where we show how the approach of Chib (1995) can be used to find the model marginal likelihood and Bayes factors for competing model specifications.…”

“…The general modeling strategy is related to that of Chib and Hamilton (2002) except that they dealt with the situation of time varying treatments. Although our set-up is in some ways more restrictive, the single treatment intake at baseline leads to new estimation and inferential concerns.…”

Bayesian analysis of the two‐part model with endogeneity: application to health care expenditure

“…The average treatment effects reported in this paper involve an additional step in which we integrate out h i numerically with respect to the posterior distribution of the parameters in the model. One can also report the whole distribution of treatment effects for all individuals, as discussed by Chib and Hamilton (2002) and Poirier and Tobias (2003).…”

Risk, Return, and Volatility Feedback: A Bayesian Nonparametric Analysis

“…For example, see Chib and Hamilton (2002); Burda et al (2008); Conley et al (2008); Delatola and Griffin (2013); Griffin and Steel (2004);and Chib and Greenberg (2010); Jensen and Maheu (2010, 2013, 2014 for recent applications of the DPM model. feedback.…”