Where can I find out about using random effects models in R including obtaining proportion of variance attributable to a variable?

Paul Bleise has written an [attachment:nlmeR.pdf introductory guide ] to fitting random effects models in R using the nlme software with some case studies and general tips on using R objects.

The guide mentions, in particular, the function VarCorr() which computes residual variances of models specified to VarCorr. Comparisons of VarCorrs() related to nested models enables the computation of percentage of variance explained by variable sets. For example if VarCorr(y~a+b) gives residual variance A and VarCorr(y~a) gives residual variance B (<=A) the proportion of variance explained by variable B = 1 - B/A.

You can also fit random effects models in R using the lme4 program which computes percentiles of Monte- Carlo Markov Chain (mcmc) for regression estimates and variance components derived from simulations using the random effects model. The usual REML estimates are also produced. The median (50 percentile) of the mcmc estimates should approximately equal the analogous REML ones.

There is also a R guide on multilevel modelling by R. H. Baayen in pdf format [attachment:Baayenlmer.pdf here.] SPSS have a 28 page [attachment:spssmixed.pdf document] giving case studies using GLM and MIXED procedures. Data input, syntax and interpretation of output are all considered. This document is also available on-line from [http://www.spss.ch/upload/1126184451_Linear%20Mixed%20Effects%20Modeling%20in%20SPSS.pdf here].

There are some excellent comprehensive descriptions in these selected slides (in pdf format) for fitting Mixed models in R using the lme4 package (Bates and Rahway, 2010) using lmer and glmer procedures:

[attachment:3simple.pdf Part 3: Linear mixed models with simple, scalar random effects]

[attachment:4longitudinal.pdf Part 4: Longitudinal data, modeling interactions]

[attachment:7GLMM.pdf Part 7: Generalized linear mixed models]