A Bayesian semiparametric latent variable model for mixed responses

In this article we introduce a latent variable model (LVM) for
mixed ordinal and continuous responses, where covariate effects on
the continuous latent variables are modelled through a flexible
semiparametric predictor. We extend existing LVM with simple linear
covariate effects by including nonparametric components for
nonlinear effects of continuous covariates and interactions with
other covariates as well as spatial effects. Full Bayesian
modelling is based on penalized spline and Markov random field
priors and is performed by computationally efficient Markov chain
Monte Carlo (MCMC) methods. We apply our approach to a large German
social science survey which motivated our methodological
development.