The following is a summary of what I have gathered about hypothesis testing with mixed-effects models. I would appreciate it if someone can clarify or correct this, or make any further comments on the topic. To test a single fixed effect: 1) Likelihood-ratio test (anova) using ML (not REML) is appropriate but can be anti-conservative. 2) Monte Carlo methods (mcmcsamp) provide a better p-value estimate, but this is not yet implemented for GLMM (e.g. binomial). To test a single random effect: 1) Likelihood-ratio test (anova) is a) appropriate without modification (Pinheiro & Bates 2000); b) appropriate, but double the p-value (Spencer Bates, R-help); c) appropriate, but halve the p-value (Agresti 2006, Lee Nelder & Pawitan 2006). 2) Monte Carlo methods, here too, can provide an accurate p-value estimate. Thanks for your help, Daniel