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Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Yunxiao Chen Open the ORCID record for Yunxiao Chen [Opens in a new window] ,
Xiaoou Li  and
Siliang Zhang
Yunxiao Chen*
Affiliation:
London School of Economics and Political Science
Xiaoou Li
Affiliation:
University of Minnesota
Siliang Zhang
Affiliation:
Fudan University
*
Correspondence should be made toYunxiao Chen, London School of Economics and Political Science, London, UK. Email: y.chen186@lse.ac.uk
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Abstract

Joint maximum likelihood (JML) estimation is one of the earliest approaches to fitting item response theory (IRT) models. This procedure treats both the item and person parameters as unknown but fixed model parameters and estimates them simultaneously by solving an optimization problem. However, the JML estimator is known to be asymptotically inconsistent for many IRT models, when the sample size goes to infinity and the number of items keeps fixed. Consequently, in the psychometrics literature, this estimator is less preferred to the marginal maximum likelihood (MML) estimator. In this paper, we re-investigate the JML estimator for high-dimensional exploratory item factor analysis, from both statistical and computational perspectives. In particular, we establish a notion of statistical consistency for a constrained JML estimator, under an asymptotic setting that both the numbers of items and people grow to infinity and that many responses may be missing. A parallel computing algorithm is proposed for this estimator that can scale to very large datasets. Via simulation studies, we show that when the dimensionality is high, the proposed estimator yields similar or even better results than those from the MML estimator, but can be obtained computationally much more efficiently. An illustrative real data example is provided based on the revised version of Eysenck’s Personality Questionnaire (EPQ-R).

Keywords

joint maximum likelihood estimatoritem response theoryIRThigh-dimensional dataalternating minimizationprojected gradient descentpersonality assessment

Information

Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 1 , 15 March 2019 , pp. 124 - 146
Copyright
Copyright © 2018 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-018-9646-5) contains supplementary material, which is available to authorized users.

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