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Efficient estimation of generalized linear latent variable models

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  • Jenni Niku
  • Wesley Brooks
  • Riki Herliansyah
  • Francis K C Hui
  • Sara Taskinen
  • David I Warton

Abstract

Generalized linear latent variable models (GLLVM) are popular tools for modeling multivariate, correlated responses. Such data are often encountered, for instance, in ecological studies, where presence-absences, counts, or biomass of interacting species are collected from a set of sites. Until very recently, the main challenge in fitting GLLVMs has been the lack of computationally efficient estimation methods. For likelihood based estimation, several closed form approximations for the marginal likelihood of GLLVMs have been proposed, but their efficient implementations have been lacking in the literature. To fill this gap, we show in this paper how to obtain computationally convenient estimation algorithms based on a combination of either the Laplace approximation method or variational approximation method, and automatic optimization techniques implemented in R software. An extensive set of simulation studies is used to assess the performances of different methods, from which it is shown that the variational approximation method used in conjunction with automatic optimization offers a powerful tool for estimation.

Suggested Citation

  • 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.
    • Handle: RePEc:plo:pone00:0216129
    DOI: 10.1371/journal.pone.0216129
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    Cited by:

    1. Riki Herliansyah & Ruth King & Stuart King, 2022. "Laplace Approximations for Capture–Recapture Models in the Presence of Individual Heterogeneity," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(3), pages 401-418, September.
    2. Robin Fuchs & Denys Pommeret & Cinzia Viroli, 2022. "Mixed Deep Gaussian Mixture Model: a clustering model for mixed datasets," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(1), pages 31-53, March.
    3. Jenni Niku & Francis K. C. Hui & Sara Taskinen & David I. Warton, 2021. "Analyzing environmental‐trait interactions in ecological communities with fourth‐corner latent variable models," Environmetrics, John Wiley & Sons, Ltd., vol. 32(6), September.
    4. Francis K.C. Hui & Nicole A. Hill & A.H. Welsh, 2022. "Assuming independence in spatial latent variable models: Consequences and implications of misspecification," Biometrics, The International Biometric Society, vol. 78(1), pages 85-99, March.
    5. 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.
    6. Andersson, Björn & Jin, Shaobo & Zhang, Maoxin, 2023. "Fast estimation of multiple group generalized linear latent variable models for categorical observed variables," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).

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