Dear list, I have written functions to perform simulation-based tests of HO: Var(Random Effects)=0, beta_foo=0 in linear mixed models based on the exact distribution of the LR- and Restricted LR-test statistic (see research presented in Crainiceanu, Ruppert: "LRT in LMM with 1 variance component", J. R. Statist. Soc. B (2004), 66, Part 1, pp. 165-185 ) -they are about 15-20 times faster than the parametric bootstrap.
At the moment, the exact distributions are only easily simulated for the case of 1 single variance component/random effect and i.i.d. errors; feasible approximations for the "multivariate" case are currently being investigated and will be implemented soon. the syntax looks something like this: #begin code: data(sleepstudy) summary(sleepstudy) #Effect of sleep deprivation on reaction time xyplot(Reaction~Days|Subject, data=sleepstudy) m<-lmer(Reaction~Days+(Days-1|Subject),data=sleepstudy) #random slopes, but no random intercept #doesna make sense, but it's just an example summary(m) #test for individual heterogeneity based on RLRT #(No restrictions on fixed effects under H0) #HO: lambda=Var(RandomSlopes)/Var(error)==0 <==> Var(RandomSlopes)==0 t3<-RLRT1SimTest(m, lambda0=0, seed=5, nsim=10000) #will produce output: #HO: lambda = 0 ; p-value = 0 # observed lambda = 0.06259639 #test for influence of Days based on LRT #(restriction on fixed efects: beta_Days==0) m0<-lm(Reaction~1,data=sleepstudy) t4<-LRT1SimTest(m, m0, seed=10, nsim=10000) #will produce output: #Model under HO: Reaction ~ 1 ; #Model under HA: Reaction ~ Days + (Days - 1 | Subject) ; # p-value = 0 # observed lambda = 0.06259639 #end code If you are interested in using these functions i'll be glad to send them to you- be aware, however, that you can only use them for testing "1 Random Effect" vs. "no Random Effect" in a model with i.i.d. errors!! The plan is to put them in a package beginning next year and use them as a basis for an (exact) anova.lmer() method. Greetings, Fabian Scheipl -- -- ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.