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A Sparse Latent Class Model for Cognitive Diagnosis

  • Yinyin Chen
  • Steven CulpepperEmail author
  • Feng Liang
Theory and Methods
  • 33 Downloads
Part of the following topical collections:
  1. Theory and Methods

Abstract

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.

Keywords

sparse latent class models Bayesian variable selection identifiability 

Notes

Supplementary material

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Copyright information

© The Psychometric Society 2020

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of Illinois at Urbana-ChampaignChampaignUSA
  2. 2.Beckman Institute for Advanced Science and TechnologyUniversity of Illinois at Urbana–ChampaignChampaignUSA

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