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

Yang Liu ()
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Yang Liu: University of Maryland

Psychometrika, 2020, vol. 85, issue 2, No 10, 439-468

Abstract: 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 theory; item factor analysis; high-dimensional data; matrix completion; maximum likelihood; Riemannian optimization; matrix manifold; constrained optimization; penalty method (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11336-020-09711-8

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