[R-sig-ME] Correlation of random effects

[Douglas Bates]

On Wed, Aug 4, 2010 at 2:23 AM, David Duffy <davidD at qimr.edu.au> wrote:
> On Tue, 3 Aug 2010, Gustavo Betini wrote:
>
>> m1<-lmer(pc1 ~ year + datejc + stage + rept + age + tarsusc + mtempc +
>> windsc + rhc + (1|id), data=ndf, REML=0)
>> m2<-lmer(pc1 ~ year + datejc + stage + rept + age + tarsusc + mtempc +
>> windsc + rhc + (1+mtempc|id), data=ndf, REML=0)
>>
>> In order to compare these two models I would use a LRT test:
>>
>> anova(m1,m2)
>>
>> However, LRT test is not recommended when Corr is near the extremes
>> (+1,-1). So, how I compare the fit of two models in lme4 when the
>> correlation between two random effects are near the extremes?
>>
>
> You can always look at the likelihood ratio, the question is whether it
> follows a simple chi-square distribution under the null or not.
> If the LR is large enough, then it probably won't matter anyway. You can
> obtain percentiles by an appropriate simulation based on your data setup,
> especially since m1 only has id as a random effect.  I don't think the
> RLRsim package can be used here, but its author may clarify on that.

I agree with David that you can always look at the likelihood ratio
and if its value is very large then whether or not the chi-square
approximation to the change in the deviance is accurate you will still
have strong evidence that the random effects correlation is
non-negligible.

However, I think you are comparing the wrong models.  You should
compare m2 to the same model but with random effects of the form

(1|id) + (0+mtempc|id)

if you want to isolate the correlation parameter.