Bayesian semiparametric latent variable model with DP prior for joint analysis: Implementation with nimble

Abstract

Multiple responses of mixed types are naturally encountered in a variety of data analysis problems, which should be jointly analysed to achieve higher efficiency gains. As an efficient approach for joint modelling, the latent variable model induces dependence among the mixed outcomes through a shared latent variable. Generally, the latent variable is assumed to be normal, which is not that flexible and realistic in practice. This tutorial article demonstrates how to jointly analyse mixed continuous and ordinal responses using a semiparametric latent variable model by allowing the latent variable to follow a Dirichlet process (DP) prior, and illustrates how to implement Bayesian inference through a powerful R package nimble. Two model comparison criteria, deviance information criterion (DIC) and logarithm of the pseudo-marginal likelihood (LPML), are employed for model selection. Simulated data and data from a social survey study are used for illustrating the proposed method with nimble. An extension of DP prior to DP mixtures prior is introduced as well.