A geoadditive Bayesian latent variable model for Poisson indicators

We introduce a new latent variable model with count variable indicators, where usual linear parametric effects of covariates, nonparametric effects of continuous covariates and spatial effects on the continuous latent variables are modelled through a geoadditive predictor. Bayesian modelling of nonparametric functions and spatial effects is based on penalized spline and Markov random field priors. Full Bayesian inference is performed via an auxiliary variable Gibbs sampling technique, using a recent suggestion of Fr¨uhwirth-Schnatter and Wagner (2006). As an advantage, our Poisson indicator latent variable model can be combined with semiparametric latent variable models for mixed binary, ordinal and continuous indicator variables within an unified and coherent framework for modelling and inference. A simulation study investigates performance, and an application to post war human security in Cambodia illustrates the approach.