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Determining the number of factors in high-dimensional generalized latent factor models

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  • Chen, Yunxiao
  • Li, Xiaoou

Abstract

As a generalization of the classical linear factor model, generalized latent factor models are useful for analysing multivariate data of different types, including binary choices and counts. This paper proposes an information criterion to determine the number of factors in generalized latent factor models. The consistency of the proposed information criterion is established under a high-dimensional setting, where both the sample size and the number of manifest variables grow to infinity, and data may have many missing values. An error bound is established for the parameter estimates, which plays an important role in establishing the consistency of the proposed information criterion. This error bound improves several existing results and may be of independent theoretical interest. We evaluate the proposed method by a simulation study and an application to Eysenck’s personality questionnaire.

Suggested Citation

  • Chen, Yunxiao & Li, Xiaoou, 2022. "Determining the number of factors in high-dimensional generalized latent factor models," LSE Research Online Documents on Economics 111574, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:111574
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    File URL: http://eprints.lse.ac.uk/111574/
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    References listed on IDEAS

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    5. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    6. Philippe Huber & Elvezio Ronchetti & Maria‐Pia Victoria‐Feser, 2004. "Estimation of generalized linear latent variable models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 893-908, November.
    7. Robin, Geneviève & Josse, Julie & Moulines, Éric & Sardy, Sylvain, 2019. "Low-rank model with covariates for count data with missing values," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 416-434.
    8. Yunzhang Zhu & Xiaotong Shen & Changqing Ye, 2016. "Personalized Prediction and Sparsity Pursuit in Latent Factor Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 241-252, March.
    9. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    10. Geneviève Robin & Olga Klopp & Julie Josse & Éric Moulines & Robert Tibshirani, 2020. "Main Effects and Interactions in Mixed and Incomplete Data Frames," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1292-1303, July.
    11. 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.
    12. Wedel, Michel & Böckenholt, Ulf & Kamakura, Wagner A., 2003. "Factor models for multivariate count data," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 356-369, November.
    13. Yunxiao Chen & Xiaoou Li & Siliang Zhang, 2020. "Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1756-1770, December.
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    Cited by:

    1. 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.
    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.

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    More about this item

    Keywords

    generalized latent factor model; joint maximum likelihood estimator; high-dimensional data; information criteria; selection consistency;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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