General introductory references

Books

• Littell et al 2006 [7] : good general intro to mixed models (including GLMMs), very hands-on, very SAS-specific (not unreasonable considering the title), does not go very deep into the underlying theory
• McCulloch et al 2008 [8] : I (BMB) haven't read it, but the title suggests it should be useful …
• Gelman and Hill 2006 [6] : very good on multi-level data analysis in general. Focuses on R/WinBUGS, although appendices cover SAS, STATA, and SPSS as well. Not an enormous amount on GLMMs, but the Bayesian framework they use extends naturally to GLMMs. Given the Bayesian framework, there is little about hypothesis testing here …
• Pinheiro and Bates 2000 [9] : good general introduction to mixed models, but nothing on GLMMs. R (nlme) focused.

Books (details needed)

• Zuur et al (Springer): Mixed Effects Models and Extensions in Ecology with R. Zuur, A.F., Ieno, E.N., Walker, N.J., Saveliev, A.A., Smith, G.M. 2009, XXII, 574 p. ISBN: 978-0-387-87457-9
• Jiang (Springer): very good technical intro to LMMs and GLMMs. In general I found the first few sections of each chapter useful, the later parts of the chapters get very technical and rather specific to the author's research interests …

Papers

(Not examples, but more general references)

• Qian and Shen 2007 [10]: a short note illustrating the advantages of (simple) multilevel Bayesian modeling in ecology, including a GLMM. Has WinBUGS/R example appendices, which I haven't looked at yet //should list this on the MCMC page as well //
• Aukema et al 2005 [1]: compares SAS and lmer examples — interesting, but mostly a cautionary tale illustrating that degrees of freedom (in particular) can be very different. Uses an old version of lmer.
• Venables and Dichmont 2004 [12]: not a huge amount on GLMMs, but a nice applied perspective
• Browne and Draper 2006, Breslow 2004, Raudenbush 2000, Diaz 2006: evaluations of PQL, or comparisons of PQL and Laplace

Bibliography

1. Aukema, Brian, Richard Werner, Kirsten Haberkern, et al. 2005. Quantifying sources of variation in the frequency of fungi associated with spruce beetles: Implications for hypothesis testing and sampling methodology in bark beetle-symbiont relationships. Forest Ecology and Management 217, no. 2-3 (October 10): 187-202.

2. Browne, William, and David Draper. “A comparison of Bayesian and likelihood-based methods for fitting multilevel models.” Bayesian Analysis 1, no. 3 (2006): 473-514.

3. Breslow, N. E. “Whither PQL?.” In Proceedings of the second Seattle symposium in biostatistics: Analysis of correlated data, edited by Danyu Y. Lin and P. J. Heagerty, 1–22. Springer, 2004.

4. Breslow, Norm. “Whither PQL?.” UW Biostatistics Working Paper Series, #192, 2003. http://www.bepress.com/uwbiostat/paper192.

5. Diaz, Rafael E. “Comparison of PQL and Laplace 6 estimates of hierarchical linear models when comparing groups of small incident rates in cluster randomised trials.” Computational Statistics & Data Analysis 51, no. 6 (March 1, 2007): 2871-2888.

6. Andrew Gelman and Jennifer Hill, Data Analysis Using Regression and Multilevel/Hierarchical Models, 1st ed. (Cambridge University Press, 2006).

7. Ramon C. Littell et al., SAS for Mixed Models, Second Edition, 2nd ed. (SAS Publishing, 2006).

8. Charles E. McCulloch, Shayle R. Searle, and John M. Neuhaus, Generalized, Linear, and Mixed Models, 2nd ed. (Wiley-Interscience, 2008).

9. Jose C. Pinheiro and Douglas M. Bates, Mixed Effects Models in S and S-Plus (Springer, 2002).

10. Qian, Song S., and Zehao Shen. 2007. Ecological Applications of Multilevel Analysis of Variance. Ecology 88, no. 10 (October 1): 2489-2495 . doi:10.1890/06-2041.1.

11. Raudenbush, S. W., M. L. Yang, and M. Yosef. “Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation.” Journal of Computational and Graphical Statistics 9 (2000): 141-57.

12. Venables, W., and C. Dichmont. 2004. GLMs, GAMs and GLMMs: an overview of theory for applications in fisheries research. Fisheries Research 70, no. 2-3: 319-337.