A Sparse Latent Class Model for Cognitive Diagnosis

Yinyin Chen (), Steven Culpepper () and Feng Liang ()
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Yinyin Chen: University of Illinois at Urbana-Champaign
Steven Culpepper: University of Illinois at Urbana-Champaign
Feng Liang: University of Illinois at Urbana-Champaign

Psychometrika, 2020, vol. 85, issue 1, No 8, 153 pages

Abstract: 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 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (16)

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DOI: 10.1007/s11336-019-09693-2

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