Bayesian semiparametric analysis for latent variable models with mixed continuous and ordinal outcomes

Latent variable models with continuous and ordinal responses are a useful tool for interpreting the causal interrelationships among the latent variables and building relations between the latent variables and manifest variables. These models have been successfully applied to many different fields, including behavioral, educational, and social and psychological sciences. However, most developments are constrained within parametric families, of which particular distributions are specified for the parameters of interest. This leads to difficulty in dealing with outliers and/or distribution deviations. In this paper, we propose a Bayesian semiparametric modeling for latent variable model with continuous and ordinal variables. A finite dimensional truncated stick-breaking prior is used to model the distributions of the intercepts and/or covariance structural parameters. Within the Bayesian framework, blocked Gibbs sampler is implemented to deal with the posterior analysis. Moreover, the logarithm of pseudo-marginal likelihood is used to compare the competing models. Empirical results are presented to illustrate the methodology.