Bayesian Semiparametric Analysis and Model Comparison for Confirmatory Factor Model

A Bayesian semiparametric procedure for confirmatory factor analysis model is proposed to address the heterogeneity of the multivariate responses. The approach relies on the use of a prior over the space of mixing distributions with finite components. Blocked Gibbs sampler is implemented to cope with the posterior analysis. For model comparison, the measure and Bayes factor are developed. A generalized weighted Chinese restaurant algorithm is suggested to compute the likelihood of data. Empirical results are presented to illustrate the effectiveness of the methodologies.