Analysis of Latent Structures with Outcomes of Different types

• Activity Number: 333
• Type: Contributed
• Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Ernest Fokoue*+
• Companies: The Ohio State University
• Keywords: mixtures ; latent variable ; generalized linear models ; EM algorithm ; Monte Carlo ; conditional independence

Abstract

A finite Mixture of Factor Analyzers (MFA) model is a globally nonlinear extension of the traditional Factor Analysis (FA) model. By allowing a local factor analyzer in each subspace of the heterogeneous input space, the MFA model is inherently globally nonlinear. In studies and applications of the MFA model, the manifest variable X is treated in the pure spirit of traditional factor analysis, which assumes X to be a vector of continuous attributes. While there are many practical applications for which this is the case, fields such as social science, psychology and psychometrics are full of applications where the manifest variable is made up of attributes of various types (continuous, categorical, counts). We introduce and study such an extension of the MFA model, and in particular, we examine such issues as parameter estimation and prediction from a likelihood-based perspective via the EM algorithm. Although the resulting model does not allow the derivation of closed-form expressions for both the E-step and the M-step of the corresponding EM algorithm, it turns out that simple Monte Carlo approximations make it possible to compute parameter estimates.