Latent Variable Model Selection for Binary Response Data with Application in Educational and Psychiatric Data

• Activity Number: 252
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Social Statistics Section
• Author(s): Yunxiao Chen*
• Companies: Columbia University
• Keywords: Latent variable model ; Graphical model ; Model selection ; Convex optimization

Abstract

In this paper, we propose a family of models that is flexible and jointly models the latent and observed variables in a parsimonious way. This modeling framework combines latent factor model and graphical models (Pearl, 1988; Dawid and Lauritzen, 1993) to capture dependence structure not attributable to the latent variables. The rationale is that the latent variables globally drive the dependency among all the observed variables and a sparse graphical model locally characterizes the dependency between the observed variables unexplained by the latent variables. In addition, model estimation is obtained by maximizing a regularized pseudo-likelihood function via a convex optimization algorithm. Using this algorithm, we are able to handle large scale data sets that may contain millions of subjects and hundreds of items. Methods are developed to visualize the estimated sparse graphical model, which helps people understanding the dependency structure unexplained by the latent variables. Finally, the model is applied to several educational testing and psychiatric assessment data sets.