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.