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 variancesof 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.
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 here.