Latent Variable Models in Heterogeneous Spaces for Observations of Mixed Types

Abstract

The maximum likelihood approach to the estimation of factor analytic model parameters most commonly deals with outcomes that are assumed to be multivariate Gaussian random variables in a homogeneous input space. In many practical settings, however, many studies needing factor analytic modeling involve data that, not only are not multivariate Gaussian variables, but also come from a partitioned input space. This article introduces an extension of the maximum likelihood factor analysis that handles multivariate outcomes made up of attributes with different probability distributions, and originating from a partitioned input space. An EM Algorithm combined with Fisher Scoring is used to estimate the parameters of the derived model.

Keywords:

• Conditional independence
• EM algorithm
• Factor analysis
• Finite mixtures
• Fisher score
• Generalized linear model
• Latent variable models
• Monte Carlo
• Non Gaussian observations

Mathematics Subject Classification:

• Primary 62H25
• Secondary 62H30, 62H20