Bayesian Structured Additive Distributional Regression for Multivariate Responses

Abstract

Summary We propose a unified Bayesian approach for multivariate structured additive distributional regression analysis comprising a huge class of continuous, discrete and latent multivariate response distributions, where each parameter of these potentially complex distributions is modelled by a structured additive predictor. The latter is an additive composition of different types of covariate effects, e.g. non-linear effects of continuous covariates, random effects, spatial effects or interaction effects. Inference is realized by a generic, computationally efficient Markov chain Monte Carlo algorithm based on iteratively weighted least squares approximations and with multivariate Gaussian priors to enforce specific properties of functional effects. Applications to illustrate our approach include a joint model of risk factors for chronic and acute childhood undernutrition in India and ecological regressions studying the drivers of election results in Germany.