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

Jianxin Pan and Robin Thompson
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Jianxin Pan: Keele University
Robin Thompson: IACR-Rothamsted

Computational Statistics, 2003, vol. 18, issue 1, No 4, 57-78

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.

Keywords: Gauss-Hermite quadrature; Generalised linear mixed models; Maximum likelihood estimates; Newton-Raphson algorithm; Random effects (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s001800300132

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