Partial identifiability of restricted latent class models

Yuqi Gu · Gongjun Xu

72 citations0/0 files storedThe Annals of Statistics

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Psychometric Methodologies and Testing Statistical Methods and Bayesian Inference Bayesian Methods and Mixture Models

Abstract

Latent class models have wide applications in social and biological sciences. In many applications, prespecified restrictions are imposed on the parameter space of latent class models, through a design matrix, to reflect practitioners’ assumptions about how the observed responses depend on subjects’ latent traits. Though widely used in various fields, such restricted latent class models suffer from nonidentifiability due to their discreteness nature and complex structure of restrictions. This work addresses the fundamental identifiability issue of restricted latent class models by developing a general framework for strict and partial identifiability of the model parameters. Under correct model specification, the developed identifiability conditions only depend on the design matrix and are easily checkable, which provide useful practical guidelines for designing statistically valid diagnostic tests. Furthermore, the new theoretical framework is applied to establish, for the first time, identifiability of several designs from cognitive diagnosis applications.

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References

1974Exploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models 2001Cognitive Assessment Models with Few Assumptions, and Connections with Nonparametric Item Response Theory 1983RULE SPACE: AN APPROACH FOR DEALING WITH MISCONCEPTIONS BASED ON ITEM RESPONSE THEORY 2011The Generalized DINA Model Framework 2006Measurement of psychological disorders using cognitive diagnosis models.2004Higher-Order Latent Trait Models for Cognitive Diagnosis 2008Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables 2007A general diagnostic model applied to language testing data

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2019Sufficient and Necessary Conditions for the Identifiability of the Q-matrix 2020Learning Attribute Hierarchies From Data: Two Exploratory Approaches 2022Diagnostic Classification Analysis of Problem-Solving Competence using Process Data: An Item Expansion Method 2025Item Response Theory—A Statistical Framework for Educational and Psychological Measurement 2021A Gibbs Sampling Algorithm with Monotonicity Constraints for Diagnostic Classification Models

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