[R] random effects correlation in lmer

[Kurt Smith]

I am having an issue with lmer that I wonder if someone could explain.

I am trying to fit a mixed effects model to a set of longitudinal data
over a set of individual subjects:
(fm1 <- lmer(x ~ time + (time|ID),aa))


I quite often find that the correlation between the random effects is 1.0:
Linear mixed model fit by REML
Formula: x ~ time + (time | ID)
   Data: aa
   AIC   BIC logLik deviance REMLdev
 28574 28611 -14281    28561   28562
Random effects:
 Groups   Name        Variance Std.Dev. Corr
 ID       (Intercept)  77.035   8.7770
          time         10.817   3.2889  1.000
 Residual             112.151  10.5901
Number of obs: 3539, groups: ID, 1000

Fixed effects:
            Estimate Std. Error t value
(Intercept)  98.7601     0.3894  253.64
time          1.3671     0.2001    6.83

Correlation of Fixed Effects:
     (Intr)
time -0.045


All other parameters seem to converge as I increase the size of the
data set, or have a reasonable distribution over several bootstrap
samples. This suggests to me there is a singularity or something in
solving for the random effects correlation. Does anyone have any
insight?
Thanks,
Kurt Smith