Correcting for sample selection bias in Bayesian distributional regression models

In the presence of non-randomly selected samples, many statistical models, including standard regression models, can fail. In particular, without accounting for the underlying selection process estimates might be biased. Sample selection models can correct this bias when an informative selection process governs the availability of the outcome of interest. A copula based approach is presented for correcting the sample selection bias in Bayesian structured additive distributional regression models. This framework relaxes the distributional assumption on the response of the linear or the generalized linear model and models all distributional parameters as functions of the covariates. Covariate effects are not limited to being purely linear and other effect types, such as smooth functional effects, are available. As a consequence, the approach presented provides increased flexibility with respect to the dependence structure, the available predictor specifications and the choice of the marginal distributions compared to Heckman's classic sample selection model. To facilitate estimation in such a complex model, a fully Bayesian approach based on Markov chain Monte Carlo simulations is developed and the presented methodology is empirically evaluated. Furthermore, the introduced approach is compared to a frequentist competitor and an application on a data set from psychological judge-advisor research is presented.