# Using principal component scores as predictors in mixed-model

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)

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I don't see why using this strategy in a mixed model would be any different, especially if you are treating the PCA score as a fixed effect, which it seems like you are in your example? –  Marc in the box May 5 '12 at 19:02