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Standard error estimates in hierarchical generalized linear models

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  • Jin, Shaobo
  • Lee, Youngjo

Abstract

Hierarchical generalized linear models are often used to fit random effects models. However, attention is mostly paid to the estimation of fixed unknown parameters and inference for latent random effects. In contrast, standard error estimators receive less attention than they should be. Currently, the standard error estimators are based on various approximations, even when the mean parameters may be estimated from a higher-order approximation of the likelihood and the dispersion parameters are estimated by restricted maximum likelihood. Existing standard error estimation procedures are reviewed. A numerical illustration shows that the current standard errors are not necessarily accurate. Alternative standard errors are also proposed. In particular, a sandwich estimator that accounts for the dependence between the mean parameters and the dispersion parameters greatly improve the current standard errors.

Suggested Citation

  • Jin, Shaobo & Lee, Youngjo, 2024. "Standard error estimates in hierarchical generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:csdana:v:189:y:2024:i:c:s0167947323001639
    DOI: 10.1016/j.csda.2023.107852
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    References listed on IDEAS

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    1. Wu, Jianmin & Bentler, Peter M., 2012. "Application of H-likelihood to factor analysis models with binary response data," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 72-79.
    2. Youngjo Lee & John A. Nelder, 2006. "Double hierarchical generalized linear models (with discussion)," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 139-185, April.
    3. Noh, Maengseok & Lee, Youngjo, 2007. "REML estimation for binary data in GLMMs," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 896-915, May.
    4. Yun, Sungcheol & Lee, Youngjo, 2004. "Comparison of hierarchical and marginal likelihood estimators for binary outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 639-650, April.
    5. Flores-Agreda, Daniel & Cantoni, Eva, 2019. "Bootstrap estimation of uncertainty in prediction for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 1-17.
    6. Youngjo Lee & Jan F. Bjørnstad, 2013. "Extended likelihood approach to large-scale multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 553-575, June.
    7. Youngjo Lee & Gwangsu Kim, 2016. "H-likelihood Predictive Intervals for Unobservables," International Statistical Review, International Statistical Institute, vol. 84(3), pages 487-505, December.
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