Dear all,

I am interested in testing the correlation between two random effects 
while controlling for a number of fixed effects, something similar to 
the sleepstudy data. So, I have two models (continuous variables were 
centred using scale(x, center=TRUE, scale=FALSE):

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)

The correlation is very high:

  Data: ndf
   AIC  BIC logLik deviance REMLdev
  2165 2231  -1068     2135    2173
Random effects:
  Groups   Name        Variance  Std.Dev. Corr
  id       (Intercept)    2.1979797 1.482558
            mtempc        0.0045812 0.067685 0.904
  Residual                1.5495789 1.244821
Number of obs: 590, groups: id, 83

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?

Thanks,

Gustavo S. Betini
PhD Candidate
Dept. of Integrative Biology
University of Guelph, Canada


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