Bayesian analysis for confirmatory factor model with finite-dimensional Dirichlet prior mixing

ABSTRACT

Confirmatory factor analysis (CFA) model is a useful multivariate statistical tool for interpreting relationships between latent variables and manifest variables. Often statistical results based on a single CFA are seriously distorted when data set takes on heterogeneity. To address the heterogeneity resulting from the multivariate responses, we propose a Bayesian semiparametric modeling for CFA. The approach relies on using a prior over the space of mixing distributions with finite components. Blocked Gibbs sampler is implemented to cope with the posterior analysis. Results obtained from a simulation study and a real data set are presented to illustrate the methodology.

KEYWORDS:

• Blocked Gibbs sampler
• confirmatory factor model
• model comparison
• truncated Dirichlet prior

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H25; 62G07

Acknowledgments

The authors are thankful to Prof. J. C. N. Chan for using their kidney data and would like to thank the editors and referees for their valuable comments and suggestions.

Funding

The work described in this paper was supported by the National Nature Science Foundation (11471161), Nanjing Forestry University Fund (163101004), and Technological Innovation Item of Personnel Division (013101001).