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A Riemannian Optimization Algorithm for Joint Maximum Likelihood Estimation of High-Dimensional Exploratory Item Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Yang Liu Open the ORCID record for Yang Liu [Opens in a new window]
Yang Liu*
Affiliation:
University of Maryland
*
Correspondence should be made to Yang Liu, Department of Human Development and Quantitative Methodology, University of Maryland, College Park, USA. Email: [email protected]
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Abstract

There has been regained interest in joint maximum likelihood (JML) estimation of item factor analysis (IFA) recently, primarily due to its efficiency in handling high-dimensional data and numerous latent factors. It has been established under mild assumptions that the JML estimator is consistent as both the numbers of respondents and items tend to infinity. The current work presents an efficient Riemannian optimization algorithm for JML estimation of exploratory IFA with dichotomous response data, which takes advantage of the differential geometry of the fixed-rank matrix manifold. The proposed algorithm takes substantially less time to converge than a benchmark method that alternates between gradient ascent steps for person and item parameters. The performance of the proposed algorithm in the recovery of latent dimensionality, response probabilities, item parameters, and factor scores is evaluated via simulations.

Keywords

item response theoryitem factor analysishigh-dimensional datamatrix completionmaximum likelihoodRiemannian optimizationmatrix manifoldconstrained optimizationpenalty method
Type
Theory and Methods
Information
Psychometrika , Volume 85 , Issue 2 , June 2020 , pp. 439 - 468
Copyright
Copyright © 2020 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-020-09711-8) contains supplementary material, which is available to authorized users.

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