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Determining the number of factors in high-dimensional generalized latent factor models
[Eigenvalue ratio test for the number of factors]

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  • Y Chen
  • X Li

Abstract

SummaryAs 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

  • Y Chen & X Li, 2022. "Determining the number of factors in high-dimensional generalized latent factor models [Eigenvalue ratio test for the number of factors]," Biometrika, Biometrika Trust, vol. 109(3), pages 769-782.
    • Handle: RePEc:oup:biomet:v:109:y:2022:i:3:p:769-782.
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    File URL: http://hdl.handle.net/10.1093/biomet/asab044
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    References listed on IDEAS

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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. Chen, Yunxiao & Li, Chengcheng & Ouyang, Jing & Xu, Gongjun, 2023. "Statistical inference for noisy incomplete binary matrix," LSE Research Online Documents on Economics 118350, London School of Economics and Political Science, LSE Library.

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