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On generalized latent factor modeling and inference for high‐dimensional binomial data

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  • Ting Fung Ma
  • Fangfang Wang
  • Jun Zhu

Abstract

We explore a hierarchical generalized latent factor model for discrete and bounded response variables and in particular, binomial responses. Specifically, we develop a novel two‐step estimation procedure and the corresponding statistical inference that is computationally efficient and scalable for the high dimension in terms of both the number of subjects and the number of features per subject. We also establish the validity of the estimation procedure, particularly the asymptotic properties of the estimated effect size and the latent structure, as well as the estimated number of latent factors. The results are corroborated by a simulation study and for illustration, the proposed methodology is applied to analyze a dataset in a gene–environment association study.

Suggested Citation

  • Ting Fung Ma & Fangfang Wang & Jun Zhu, 2023. "On generalized latent factor modeling and inference for high‐dimensional binomial data," Biometrics, The International Biometric Society, vol. 79(3), pages 2311-2320, September.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:3:p:2311-2320
    DOI: 10.1111/biom.13768
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    1. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    2. Bai, Jushan & Ng, Serena, 2013. "Principal components estimation and identification of static factors," Journal of Econometrics, Elsevier, vol. 176(1), pages 18-29.
    3. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    4. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    5. repec:taf:jnlasa:v:108:y:2013:i:502:p:656-665 is not listed on IDEAS
    6. Jenni Niku & Wesley Brooks & Riki Herliansyah & Francis K C Hui & Sara Taskinen & David I Warton, 2019. "Efficient estimation of generalized linear latent variable models," PLOS ONE, Public Library of Science, vol. 14(5), pages 1-20, May.
    7. Francis K. C. Hui & Emi Tanaka & David I. Warton, 2018. "Order selection and sparsity in latent variable models via the ordered factor LASSO," Biometrics, The International Biometric Society, vol. 74(4), pages 1311-1319, December.
    8. Chen, Mingli & Fernández-Val, Iván & Weidner, Martin, 2021. "Nonlinear factor models for network and panel data," Journal of Econometrics, Elsevier, vol. 220(2), pages 296-324.
    9. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    10. Noah A Rosenberg & Saurabh Mahajan & Sohini Ramachandran & Chengfeng Zhao & Jonathan K Pritchard & Marcus W Feldman, 2005. "Clines, Clusters, and the Effect of Study Design on the Inference of Human Population Structure," PLOS Genetics, Public Library of Science, vol. 1(6), pages 1-12, December.
    11. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    12. Pavel Krupskii & Raphaël Huser & Marc G. Genton, 2018. "Factor Copula Models for Replicated Spatial Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 467-479, January.
    13. Irini Moustaki & Martin Knott, 2000. "Generalized latent trait models," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 391-411, September.
    14. S. Kundu & D. B. Dunson, 2014. "Latent factor models for density estimation," Biometrika, Biometrika Trust, vol. 101(3), pages 641-654.
    15. Richard A. Davis & Rongning Wu, 2009. "A negative binomial model for time series of counts," Biometrika, Biometrika Trust, vol. 96(3), pages 735-749.
    16. 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.
    17. Antoniadis A. & Fan J., 2001. "Regularization of Wavelet Approximations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 939-967, September.
    18. Carvalho, Carlos M. & Chang, Jeffrey & Lucas, Joseph E. & Nevins, Joseph R. & Wang, Quanli & West, Mike, 2008. "High-Dimensional Sparse Factor Modeling: Applications in Gene Expression Genomics," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1438-1456.
    19. Jenni Niku & David I. Warton & Francis K. C. Hui & Sara Taskinen, 2017. "Generalized Linear Latent Variable Models for Multivariate Count and Biomass Data in Ecology," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 498-522, December.
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