Journal Article

A Sparse Latent Class Model for Cognitive Diagnosis

Culpepper, Steven, Chen, Yinyin, Liang, Feng

2020

Overview

Cognitive diagnostic models (CDMs) 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 sparse latent class models (SLCMs) 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 SLCM 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. Learning the underlying latent structure can be formulated as a variable selection problem. 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 SLCM research and educational testing.

• Publisher: Springer US,Springer Nature B.V
• Subject: Algorithms / Assessment / Bayes Theorem / Bayesian analysis / Behavioral Science and Psychology / Cognition - classification / Cognition - physiology / Cognitive ability / Computer Simulation - statistics & numerical data / Educational Testing / Feature selection / Humanities / Humans / Identification, Psychological / Inferences / Latent Class Analysis / Law / Mathematical models / Models, Theoretical / Monte Carlo Method / Monte Carlo Methods / Monte Carlo simulation / Psychology / Psychometrics / Psychometrics - instrumentation / Science Tests / Social Skills / Statistical Theory and Methods / Statistics for Social Sciences / Testing and Evaluation / Theory and Methods