Title: Bayesian structured additive distribution regression with non-random sample selection
Authors: Paul Wiemann - University of Goettingen (Germany) [presenting]
Abstract: Neglecting the selection process may lead to erroneous results, e.g. biased estimates, when non-randomly selected data is analyzed. Sample selection models account for the selection process and attempt to correct the selection bias by assuming a hierarchical procedure, where the first level governs the availability of observations in the second level. Well-established sample selection models make strong distributional assumptions regarding the dependency structure between both levels and furthermore, regarding the marginal distribution of the outcome of interest. Both constraints make them unsuitable for many practical applications. The presented approach addresses the issues of sample selection as well as both limitations. A copula is employed to entangle the selection process and the outcome of interest into a multivariate distribution. Since the marginal distributions are separated from the dependency structure, Bayesian distributional regression can be used to model the marginal distribution of outcome of interest appropriately. In the resulting joint model, structured additive predictors describe each parameter and thus allow for various effect types. The proposed Bayesian inference scheme uses an efficient Markov chain Monte Carlo technique to estimate the posterior distribution. An application from psychological research, which motivated the development of this model, serves as an illustrative example.