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High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm

Published online by Cambridge University Press:  01 January 2025

Li Cai
Li Cai*
Affiliation:
University of California, Los Angeles
*
Requests for reprints should be sent to Li Cai, GSE & IS, UCLA, Los Angeles, CA, USA 90095-1521. E-mail: lcai@ucla.edu
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Abstract

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A Metropolis–Hastings Robbins–Monro (MH-RM) algorithm for high-dimensional maximum marginal likelihood exploratory item factor analysis is proposed. The sequence of estimates from the MH-RM algorithm converges with probability one to the maximum likelihood solution. Details on the computer implementation of this algorithm are provided. The accuracy of the proposed algorithm is demonstrated with simulations. As an illustration, the proposed algorithm is applied to explore the factor structure underlying a new quality of life scale for children. It is shown that when the dimensionality is high, MH-RM has advantages over existing methods such as numerical quadrature based EM algorithm. Extensions of the algorithm to other modeling frameworks are discussed.

Keywords

stochastic approximationSAitem response theoryIRTMarkov chain Monte CarloMCMCnumerical integrationcategorical factor analysislatent variable modelingstructural equation modeling
Type
Theory and Methods
Information
Psychometrika , Volume 75 , Issue 1 , March 2010 , pp. 33 - 57
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NC
This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Copyright
Copyright © 2009 The Psychometric Society

Footnotes

I thank the editor, the AE, and the reviewers for helpful suggestions. I am indebted to Drs. Chuanshu Ji, Robert MacCallum, and Zhengyuan Zhu for helpful discussions. I would also like to thank Drs. Mike Edwards and David Thissen for supplying the data sets used in the numerical demonstrations. The author gratefully acknowledges financial support from Educational Testing Service (the Gulliksen Psychometric Research Fellowship program), National Science Foundation (SES-0717941), National Center for Research on Evaluation, Standards and Student Testing (CRESST) through award R305A050004 from the US Department of Education’s Institute of Education Sciences (IES), and a predoctoral advanced quantitative methods training grant awarded to the UCLA Departments of Education and Psychology from IES. The views expressed in this paper are of the author’s alone and do not reflect the views or policies of the funding agencies.

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