A Tensor-EM Method for Large-Scale Latent Class Analysis with Binary Responses

• Published in: Psychometrika Vol. 88; no. 2; pp. 580 - 612
• Main Authors: Zeng, Zhenghao, Gu, Yuqi, Xu, Gongjun
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2023; Springer Nature B.V
• Subjects: Algorithms; Assessment; Behavioral Science and Psychology; Computer Simulation; Educational Assessment; Humanities; Humans; Latent Class Analysis; Law; Likelihood Functions; Mathematical models; Mathematics; Maximum Likelihood Statistics; Models, Statistical; Psychology; Psychometrics; Statistical analysis; Statistical Theory and Methods; Statistics for Social Sciences; Testing and Evaluation; Theory and Methods; clustering consistency; large-scale latent class analysis; tensor power method; EM algorithm; tensor decomposition
• DOI: 10.1007/s11336-022-09887-1
• ISSN: 0033-3123; 1860-0980

Latent class models are powerful statistical modeling tools widely used in psychological, behavioral, and social sciences. In the modern era of data science, researchers often have access to response data collected from large-scale surveys or assessments, featuring many items (large J ) and many subjects (large N ). This is in contrary to the traditional regime with fixed J and large N . To analyze such large-scale data, it is important to develop methods that are both computationally efficient and theoretically valid. In terms of computation, the conventional EM algorithm for latent class models tends to have a slow algorithmic convergence rate for large-scale data and may converge to some local optima instead of the maximum likelihood estimator (MLE). Motivated by this, we introduce the tensor decomposition perspective into latent class analysis with binary responses. Methodologically, we propose to use a moment-based tensor power method in the first step and then use the obtained estimates as initialization for the EM algorithm in the second step. Theoretically, we establish the clustering consistency of the MLE in assigning subjects into latent classes when N and J both go to infinity. Simulation studies suggest that the proposed tensor-EM pipeline enjoys both good accuracy and computational efficiency for large-scale data with binary responses. We also apply the proposed method to an educational assessment dataset as an illustration.