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Gauss-Hermite Quadrature Approximation for Estimation in Generalised Linear Mixed Models

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  • Jianxin Pan

    (Keele University)

  • Robin Thompson

    (IACR-Rothamsted)

Abstract

Summary This paper provides a unified algorithm to explicitly calculate the maximum likelihood estimates of parameters in a general setting of generalised linear mixed models (GLMMs) in terms of Gauss-Hermite quadrature approximation. The score function and observed information matrix are expressed explicitly as analytically closed forms so that Newton-Raphson algorithm can be applied straightforwardly. Compared with some existing methods, this approach can produce more accurate estimates of the fixed effects and variance components in GLMMs, and can serve as a basis of assessing existing approximations in GLMMs. A simulation study and practical example analysis are provided to illustrate this point.

Suggested Citation

  • Jianxin Pan & Robin Thompson, 2003. "Gauss-Hermite Quadrature Approximation for Estimation in Generalised Linear Mixed Models," Computational Statistics, Springer, vol. 18(1), pages 57-78, March.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:1:d:10.1007_s001800300132
    DOI: 10.1007/s001800300132
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    References listed on IDEAS

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    1. Martin J. Crowder, 1978. "Beta‐Binomial Anova for Proportions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(1), pages 34-37, March.
    2. J. C. Naylor & A. F. M. Smith, 1982. "Applications of a Method for the Efficient Computation of Posterior Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 214-225, November.
    3. Emmanuel Lesaffre & Bart Spiessens, 2001. "On the effect of the number of quadrature points in a logistic random effects model: an example," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(3), pages 325-335.
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    Cited by:

    1. Pan, Jianxin & Thompson, Robin, 2007. "Quasi-Monte Carlo estimation in generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5765-5775, August.
    2. Kuo-Chin Lin & Yi-Ju Chen, 2016. "Goodness-of-fit tests of generalized linear mixed models for repeated ordinal responses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 2053-2064, August.
    3. Tourani-Farani, Fahimeh & Kazemi, Iraj, 2022. "Transformed mixed-effects modeling of correlated bounded and positive data with a novel multivariate generalized Johnson distribution," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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