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A Note on Exploratory Item Factor Analysis by Singular Value Decomposition

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  • Haoran Zhang

    (Fudan University)

  • Yunxiao Chen

    (London School of Economics and Political Science)

  • Xiaoou Li

    (University of Minnesota)

Abstract

We revisit a singular value decomposition (SVD) algorithm given in Chen et al. (Psychometrika 84:124–146, 2019b) for exploratory item factor analysis (IFA). This algorithm estimates a multidimensional IFA model by SVD and was used to obtain a starting point for joint maximum likelihood estimation in Chen et al. (2019b). Thanks to the analytic and computational properties of SVD, this algorithm guarantees a unique solution and has computational advantage over other exploratory IFA methods. Its computational advantage becomes significant when the numbers of respondents, items, and factors are all large. This algorithm can be viewed as a generalization of principal component analysis to binary data. In this note, we provide the statistical underpinning of the algorithm. In particular, we show its statistical consistency under the same double asymptotic setting as in Chen et al. (2019b). We also demonstrate how this algorithm provides a scree plot for investigating the number of factors and provide its asymptotic theory. Further extensions of the algorithm are discussed. Finally, simulation studies suggest that the algorithm has good finite sample performance.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:85:y:2020:i:2:d:10.1007_s11336-020-09704-7
    DOI: 10.1007/s11336-020-09704-7
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    References listed on IDEAS

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    Cited by:

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    2. 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.
    3. Liu, Xinyi Lin & Wallin, Gabriel & Chen, Yunxiao & Moustaki, Irini, 2023. "Rotation to sparse loadings using Lp losses and related inference problems," LSE Research Online Documents on Economics 118349, London School of Economics and Political Science, LSE Library.
    4. Christopher J. Urban & Daniel J. Bauer, 2021. "A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 1-29, March.
    5. 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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