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I'm fitting a generalized linear mixed model in R using the Laplace approximation. I'm looking for a reference for the Laplace approximation used for that, or a reference regarding the comparison between the PQL and Laplace methods for fitting generalized linear mixed models.

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Here are some papers:

Breslow and Clayton, 1993: Approximate Inference in Generalized Linear Mixed Models.

Tierney and Kadane, 1986: Accurate Approximations for Posterior Moments and Marginal Densities.

Breslow, 2003: Whither PQL?.

Tuerlinckx, et al. 2006: Statistical Inference in generalized linear mixed models: A review.

Wolfinger, 1993: Laplace's approximation for nonlinear mixed models.

Vonesh, 1996: A Note on the Use of Laplace's Approximation for Nonlinear Mixed-Effects Models.

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    $\begingroup$ See also the INLA package and papers by Havard Rue. $\endgroup$
    – guest
    Dec 1, 2011 at 8:19
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    $\begingroup$ Is there any literature on Laplace approximation for discrete distribution? $\endgroup$ Apr 30, 2012 at 15:14

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