[R-sig-ME] test significance of single random effect

[Tom Van Dooren]

I tried to find an easy way to test whether the random effect would be 
significant in a (generalized) mixed model with a single random effect.
It annoyed me that log-likelihoods of lm or glm and lmer are not 
necesarily directly comparable -> trouble with calculating likelihood 
ratios.
What do members of this list think of the following simulation approach?
It basically amounts to simulating a distribution for the log 
likelihood, given the null hypothesis that there is no random effect 
variance and that the fixed effect model is correct.


library(lme4)
mm1 <- lmer(Reaction ~ Days + (1|Subject), sleepstudy)
lm1<- lm(Reaction ~ Days, sleepstudy)


LL<-numeric(500)
for(i in 1:500){
resp<-simulate(lm1)
LL[i]<-logLik(lmer(resp[,1] ~ Days + (1|Subject), sleepstudy))
}

hist(LL)
logLik(mm1)
mean(LL>logLik(mm1))