Bayesian Finite Mixture Factor Analyzer with Mixed Continuous and Ordinal Responses

• Activity Number: 300
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Xinming An *+ and Peter M. Bentler
• Companies: University of California at Los Angeles and University of California at Los Angeles
• Keywords: factor analysis ; finite mixture ; mixed responses

Abstract

Researches in the social and biomedical sciences often encounter high dimensional responses from a heterogeneous population. Finite mixture factor analyzer provides an efficient modeling technique to explore the unobserved group structures of high dimensional data. Because of its remarkable modeling ability, finite mixture factor analyzer has been widely used in many fields, such as image analysis, cluster analysis and high dimensional data visualization. However, this modeling technique cannot be applied to categorical responses. The purpose of the present research is to solve this problem by developing a Bayesian finite mixture factor analyzer with mixed continuous and ordinal responses. In our modeling process, natural conjugate priors will be used for model parameters, and the Gibbs sampler will be used to draw parameter samples from their posterior distributions. Based on these samples, point estimates and corresponding standard errors for model parameters will be developed. Finally, simulation studies will be used to investigate the properties of this modeling technique.