Would there be any problem with using principal component analysis (e.g. for reduction of dimensionality) so that principal components scores could be used as predictors in a mixed-model? For non-mixed models this strategy is frequently applied (principal component regression) but I am not sure if it is applicable in the context of mixed-models?
Please see below a dummy example in R:
library(lme4) USArrests$score <- prcomp(USArrests[,-1], scale = TRUE)$x[,1] USArrests$group[1:25)] <- "A" USArrests$group[26:50] <- "B" m1 <- lmer(Murder~1+score+(1|group), data=USArrests) summary(m1)