A Joint MLE Approach to Large-Scale Structured Latent Attribute Analysis
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Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology. A SLAM postulates that multiple discrete latent attributes explain the dependence of observed variables in a highly structured fashion. Usually, the maximum marginal likelihood estimation approach is adopted for SLAMs, treating the latent attributes as random effects. The increasing scope of modern measurement data involves large numbers of observed variables and high-dimensional latent attributes. This poses challenges to classical estimation methods and requires new methodology and understanding of latent variable modeling. Motivated by this, we consider the joint maximum likelihood estimation (MLE) approach to SLAMs, treating latent attributes as fixed unknown parameters. We investigate estimability, consistency, and computation in the regime where sample size, number of variables, and number of latent attributes can all diverge. We establish consistency of the joint MLE and propose an efficient algorithm that scales well to large-scale data. Additionally, we provide theoretically valid and effective methods for misspecification scenarios when a more general SLAM is misspecified to a submodel. Simulations demonstrate the superior empirical performance of the proposed methods. An application to real data from an international educational assessment gives interpretable findings of cognitive diagnosis.
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