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

Tom Van Dooren t.j.m.van.dooren at biology.leidenuniv.nl
Tue Nov 17 21:41:47 CET 2009

With REML=FALSE RLRsim seems to work fine in R 2.10, if I use the design 
matrix and Zt as arguments in LRTSim().
Otherwise I didn't get useful results out.

That's not too much of a problem.
It is not difficult to simulate the null model without random effect, 
extract logLikelihoods from the (generalized) mixed model and the 
(generalized) linear model fitted to those pseudo-data, to calculate a 
distribution of likelihood ratios,
which are then maybe off by a constant.
What I was mainly uncertain about, is whether the log-likelihood of a 
mixed model (also fitted to data simulated from the null model without 
random effect),
can be used as a statistic itself?
The answer might be a simple NO! of course, or something more involved...


Douglas Bates wrote:
> On Tue, Nov 17, 2009 at 3:49 AM, Matthias Gralle
> <matthias_gralle at eva.mpg.de> wrote:
>> I had basically the same problem a short time ago, and resorted to lme
>> instead of lmer, because one can directly compare lme and lm objects using
>> anova(). Is that OK, or is this feature of lme depreciated ?
> Is that not possible for linear mixed-effects models fit by lmer using
> REML = FALSE? (Occasionally I lose track of what can be done in
> different versions of lme4.)  You don't want to compare an lmer model
> fit by REML with the log-likelihood of an lm model but you should be
> able to compare likelihoods (subject to the caveat that the p-value
> for the likelihood ratio test on the boundary of the parameter space
> is conservative).
>> Ben Bolker wrote:
>>>  Have you tried the RLRsim package??
>>> Tom Van Dooren wrote:
>>>> 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))
>>>> _______________________________________________
>>>> R-sig-mixed-models at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>> --
>> Matthias Gralle, PhD
>> Dept. Evolutionary Genetics
>> Max Planck Institute for Evolutionary Anthropology
>> Deutscher Platz 6
>> 04103 Leipzig, Germany
>> Tel +49 341 3550 519
>> Fax +49 341 3550 555
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

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