Bayesian Variable Selection for Restricted Latent Class Model with an Application in Cognitive Diagnostic Models

• Activity Number: 394 - Recent Advances in Cognitive Diagnosis Modeling
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Mental Health Statistics Section
• Author(s): Steven Culpepper and Feng Liang and Yinyin Chen*
• Companies: University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign and University of Illinois at Urbana Champaign
• Keywords: Restricted Latent Class Models; Bayesian Variable Selection; Psychometrics; Identifiability

Abstract

Restricted latent class models (RLCMs) are latent variable models developed to infer latent skills, knowledge, or personalities that underlie responses to educational, psychological, and social science tests and measures. Recent research focused on theory and methods for using RLCMs in an exploratory fashion to infer the latent processes and structure underlying responses. We report new theoretical results about sufficient conditions for generic identifiability of RLCM model parameters. An important contribution for practice is that our new generic identifiability conditions are more likely to be satisfied in empirical applications than existing conditions that ensure strict identifiability. We develop a new Bayesian variable selection algorithm that explicitly enforces generic identifiability conditions and monotonicity of item response functions to ensure valid posterior inference. We present Monte Carlo simulation results to support accurate inferences and discuss the implications of our findings for future RLCM research and psychometric assesment.