Computational Statistics

, Volume 18, Issue 1, pp 57–78 | Cite as

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

  • Jianxin Pan
  • Robin Thompson


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.


Gauss-Hermite quadrature Generalised linear mixed models Maximum likelihood estimates Newton-Raphson algorithm Random effects 


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Copyright information

© Physica-Verlag 2003

Authors and Affiliations

  • Jianxin Pan
    • 1
  • Robin Thompson
    • 2
  1. 1.The Centre of Medical Statistics, Department of MathematicsKeele UniversityKeeleUK
  2. 2.Statistics DepartmentIACR-RothamstedHarpendenUK

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