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Generalized linear model based on latent factors and supervised components

Author

Listed:
  • Julien Gibaud

    (Université de Montpellier)

  • Xavier Bry

    (Université de Montpellier)

  • Catherine Trottier

    (Université de Montpellier
    Université Paul-Valéry Montpellier 3)

Abstract

In a context of component-based multivariate modeling we propose to model the residual dependence of the responses. Each response of a response vector is assumed to depend, through a Generalized Linear Model, on a set of explanatory variables. The vast majority of explanatory variables are partitioned into conceptually homogeneous variable groups, viewed as explanatory themes. Variables in themes are supposed many and some of them are highly correlated or even collinear. Thus, generalized linear regression demands dimension reduction and regularization with respect to each theme. Besides them, we consider a small set of “additional” covariates not conceptually linked to the themes, and demanding no regularization. Supervised Component Generalized Linear Regression proposed to both regularize and reduce the dimension of the explanatory space by searching each theme for an appropriate number of orthogonal components, which both contribute to predict the responses and capture relevant structural information in themes. In this paper, we introduce random latent variables (a.k.a. factors) so as to model the covariance matrix of the linear predictors of the responses conditional on the components. To estimate the model, we present an algorithm combining supervised component-based model estimation with factor model estimation. This methodology is tested on simulated data and then applied to an agricultural ecology dataset.

Suggested Citation

  • Julien Gibaud & Xavier Bry & Catherine Trottier, 2025. "Generalized linear model based on latent factors and supervised components," Computational Statistics, Springer, vol. 40(3), pages 1475-1516, March.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:3:d:10.1007_s00180-024-01544-8
    DOI: 10.1007/s00180-024-01544-8
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    References listed on IDEAS

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    1. Xavier Bry & Théo Simac & Salah Eddine El Ghachi & Philippe Antoine, 2020. "Bridging data exploration and modeling in event-history analysis: the supervised-component Cox regression," Mathematical Population Studies, Taylor & Francis Journals, vol. 27(3), pages 139-174, July.
    2. Bry, X. & Trottier, C. & Verron, T. & Mortier, F., 2013. "Supervised component generalized linear regression using a PLS-extension of the Fisher scoring algorithm," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 47-60.
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. 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.
    5. 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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