I have commonly heard that LME models are more sound in the analysis of accuracy data (i.e., in psychology experiments), in that they can work with binomial and other non-normal distributions that traditional approaches (e.g., ANOVA) can’t.
What is the mathematical basis of LME models that allow them to incorporate these other distributions, and what are some not-overly-technical papers describing this?
One major benefit of mixed-effects models is that they don’t assume independence amongst observations, and there can be a correlated observations within a unit or cluster.
This is covered concisely in “Modern Applied Statistics with S” (MASS) in the first section of chapter 10 on “Random and Mixed Effects”. V&R walk through an example with gasoline data comparing ANOVA and lme in that section, so it’s a good overview. The R function to be used in
lme in the
The model formulation is based on Laird and Ware (1982), so you can refer to that as a primary source although it’s certainly not good for an introduction.
- Laird, N.M. and Ware, J.H. (1982) “Random-Effects Models for Longitudinal Data”, Biometrics, 38, 963–974.
- Venables, W.N. and Ripley, B.D. (2002) “Modern Applied Statistics with S“, 4th Edition, Springer-Verlag.
You can also have a look at the “Linear Mixed Models” (PDF) appendix to John Fox’s “An R and S-PLUS Companion to Applied Regression”. And this lecture by Roger Levy (PDF) discusses mixed effects models w.r.t. a multivariate normal distribution.