[R-lang] how to test corr of random-effects levels?

[René Mayer]

Dear R-users,
I have a binomial outcome variable t (1 = correct, 0=incorrect) with a  
factor d (3 levels  "s" "c" "n").
If I run
lmer(t ~ d + (0+d|subjects), m, binomial).
I got a correlation between levels ?c? and ?n? of -.61

Random effects:
  Groups   	Name Variance Std.Dev. Corr
  subjects 	ds   0.288402 	0.53703
           		dc   0.389222 0.62388  -0.017
           		dn   0.038638 0.19657  -0.036 -0.616

seems that subjects who are more correct at level ?c? are less at level ?n?.


lm.s 	= lmer(t ~ d + (1|subjects), m, binomial) # var(d) = 0,  
cov(intercept, d) = 0
lm.d 	= lmer(t ~ d + (0+d|subjects), m, binomial) # d-adjustments per  
subject only
anova(lm.s, lm.d) # p < .000 ?

does this show that corr(c,n) is reliable or only that different  
sigmas for d are justified?


The second thing what confuses me is that a parametrization which  
assumes that all d-levels have the same variance is in the LRT not  
different from the one that assumes d to have different sigmas.

lm2.d = lmer(t ~ d +(1|subjects)+(1|subjects:d), m, binomial)
anova(lm.d, lm2.d) # p > .3

does this show that different sigmas for every level of d are not  
justified, and the correlation (c,n) is unreliable?


Thanks a lot for any help!
Rene