[R] mixed model hypothesis testing

[Daniel Ezra Johnson]

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