Gauss-Hermite quadrature approximation for estimation in generalised linear mixed models

A - Papers appearing in refereed journals

Pan, J. and Thompson, R. 2003. Gauss-Hermite quadrature approximation for estimation in generalised linear mixed models. Computational Statistics. 18 (1), pp. 57-78.

AuthorsPan, J. and Thompson, R.

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 quadration 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.

KeywordsGauss-Hermite quadrature; Generalised linear mixed models; Maximum likelihood estimates; Newton-Raphson algorithm; Random effects
Year of Publication2003
JournalComputational Statistics
Journal citation18 (1), pp. 57-78
Digital Object Identifier (DOI)doi:10.1007/s001800300132
Open accessPublished as non-open access
Funder project or code445
Research in statistics relevant to biological processes
Output statusPublished
Publication dates
Print01 Mar 2003
Copyright licensePublisher copyright
PublisherSpringer Heidelberg

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