Bayesian structured additive distributional regression for multivariate responses - Nadja Klein; Thomas Kneib; Stephan Klasen; Stefan Lang (University of Innsbruck, Research Platform Empirical and Experimental Economics (eeecon), 2013)
In this paper, we propose a unified Bayesian approach for multivariate structured additive distributional regression analysis where inference is applicable to a huge class of multivariate response distributions, comprising continuous, discrete and latent models, and 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. nonlinear effects of continuous variables, random effects, spatial variations, or interaction effects. Inference is realised by a generic, 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. Examples will be given by illustrations on analysing the joint model of risk factors for chronic and acute childhood malnutrition in India and on ecological regression for German election results.
Keywords: 330; correlated responses; iteratively weighted least squares proposal; Markov chain Monte Carlo simulation; penalised splines; semiparametric regression; Dirichlet regression; seemingly unrelated regression