A Spectral Method for Identifiable Grade of Membership Analysis with Binary Responses

Grade of membership (GoM) models are popular individual-level mixture models for multivariate categorical data. GoM allows each subject to have mixed memberships in multiple extreme latent profiles. Therefore, GoM models have a richer modeling capacity than latent class models that restrict each sub...

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Vydáno v:	Psychometrika Ročník 89; číslo 2; s. 626 - 657
Hlavní autoři:	Chen, Ling, Gu, Yuqi
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.06.2024 Springer Nature B.V
Témata:	Algorithms Assessment Bayes Theorem Bayesian analysis Behavioral Science and Psychology Computer Simulation Decomposition Efficiency Expectation Humanities Humans Law Mathematical models Memberships Models, Statistical Personality Measures Psychology Psychometrics Psychometrics - methods Quantitative psychology Simulation Statistical Theory and Methods Statistics for Social Sciences Testing and Evaluation Theory & Methods Variables spectral method successive projection algorithm grade of membership model identifiability latent variable model singular value decomposition mixed membership model
ISSN:	0033-3123, 1860-0980, 1860-0980
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Shrnutí:	Grade of membership (GoM) models are popular individual-level mixture models for multivariate categorical data. GoM allows each subject to have mixed memberships in multiple extreme latent profiles. Therefore, GoM models have a richer modeling capacity than latent class models that restrict each subject to belong to a single profile. The flexibility of GoM comes at the cost of more challenging identifiability and estimation problems. In this work, we propose a singular value decomposition (SVD)-based spectral approach to GoM analysis with multivariate binary responses. Our approach hinges on the observation that the expectation of the data matrix has a low-rank decomposition under a GoM model. For identifiability , we develop sufficient and almost necessary conditions for a notion of expectation identifiability. For estimation , we extract only a few leading singular vectors of the observed data matrix and exploit the simplex geometry of these vectors to estimate the mixed membership scores and other parameters. We also establish the consistency of our estimator in the double-asymptotic regime where both the number of subjects and the number of items grow to infinity. Our spectral method has a huge computational advantage over Bayesian or likelihood-based methods and is scalable to large-scale and high-dimensional data. Extensive simulation studies demonstrate the superior efficiency and accuracy of our method. We also illustrate our method by applying it to a personality test dataset.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
ISSN:	0033-3123 1860-0980 1860-0980
DOI:	10.1007/s11336-024-09951-y