These are models for grouped data in which datapoints may be correlated, and there is a need to treat variance differently among the groups. They are variously called multilevel, mixed, or heirarchical/ models.
Suitable for longitudinal data in which one is interested in estimating coefficients for groups or individuals within the population, rather than for the population at large.
There is a chapter (10) in Ben Bolker's book about them.
A few resources:
- Pinheiro and Bates, Mixed-Effects Models in S and S-PLUS. 2000, Springer
- Gelman and Hill, Data Analysis Using Regression and Multilevel/Hierarchichal Models. (website)
- West, Welsch, and Galecki, Linear Mixed Models: A Practical Guide Using Statistical Software. (website)
- Mixed effects modelsappendix to John Fox's book "An R and S-PLUS Companion to Applied Regression".