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

Author

Listed:
  • Yunxiao Chen

    (London School of Economics and Political Science)

  • Xiaoou Li

    (University of Minnesota)

  • Siliang Zhang

    (Fudan University)

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).

Suggested Citation

  • Yunxiao Chen & Xiaoou Li & Siliang Zhang, 2019. "Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 124-146, March.
    • Handle: RePEc:spr:psycho:v:84:y:2019:i:1:d:10.1007_s11336-018-9646-5
    DOI: 10.1007/s11336-018-9646-5
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    References listed on IDEAS

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    Cited by:

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    7. Zhang, Siliang & Chen, Yunxiao, 2022. "Computation for latent variable model estimation: a unified stochastic proximal framework," LSE Research Online Documents on Economics 114489, London School of Economics and Political Science, LSE Library.
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    14. Xinyi Liu & Gabriel Wallin & Yunxiao Chen & Irini Moustaki, 2023. "Rotation to Sparse Loadings Using $$L^p$$ L p Losses and Related Inference Problems," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 527-553, June.
    15. Haoran Zhang & Yunxiao Chen & Xiaoou Li, 2020. "A Note on Exploratory Item Factor Analysis by Singular Value Decomposition," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 358-372, June.
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