# Reference for generalized linear mixed models using Laplace approximation

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.

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.

• See also the INLA package and papers by Havard Rue. – guest Dec 1 '11 at 8:19
• Is there any literature on Laplace approximation for discrete distribution? – user1061210 Apr 30 '12 at 15:14