[R-sig-ME] verbose output / high correlation

[Ben Pelzer]

Dear list,


My question is about the verbose output of a model for longitudinal 
data: testscores of children measured at different ages. At some point 
in time each child has been given hormone which is continued until the 
end of the observation period.

Age has a high and positive effect on the dependent "Testscore". The 
intake of hormone also positively affects the testcore (main effect of 
hormone) as well as the effect of age (interaction effect age:hormone): 
the age effect typically increases once the hormone has been prescibed. 
Further, variable Baseline is a child specific timeconstant variable; it 
interacts with the age-effect as well.

The effects of age, hormone and the interaction of both are taken to be 
random across children. The random intercept was dropped from the models 
below, because of -1 correlation with the random age effect.

We estimated the following model:

Model1 <- lmer (Testscore ~
             (0 + age + hormone + age:hormone|child) +
             age + baseline + age:hormone + age:baseline +
             hormone + age:hormone,
             family=gaussian, REML=FALSE, verbose=TRUE)
summary(Model1)

The random effect estimates for this Model1 were:

Random effects:
  Groups   Name        Variance   Std.Dev. Corr
  child    age         7.3158e-04 0.027048
           hormone     2.0429e+01 4.519843  0.774
           age:hormone 1.9936e-02 0.141195 -0.680 -0.951
  Residual             2.9791e+00 1.726011
Number of obs: 184, groups: child, 22

The high negative correlation of -0.951 worried me in first instance, 
but the final line in the verbose output read:

47: 784.78858: 0.0156707 1.65796 0.0243669 129.347 -3.55052 -0.0330499

As no of the figures in this verbose-line seems to be close to zero
(however: what is "close" here?) does this mean that the correlation of
-0.951 is actually causing no problem at all in terms of unreliability
of the random effect estimates?

To deal with this extremely strong correlation, we then estimated an
equivalent Model2, differing from Model1 only in the random interaction 
term for age and hormone. Instead of "age:hormone", we now specified 
"agecent:hormone", with "agecent" referring to the age variable centered 
around its (grand) sample mean of age. This led to the following results,

Random effects:
  Groups   Name            Variance  Std.Dev. Corr
  child    age             0.0007315 0.027046
           hormone         2.4904299 1.578110  0.676
           hormone:agecent 0.0199369 0.141198 -0.680 -0.457
  Residual                 2.9791486 1.726021
Number of obs: 184, groups: child, 22

and the final verbose-line being

46: 784.78858: 0.0156698 0.673363 0.0599532 39.4706 -3.55184 0.000506984

The correlation of has dropped substantially, from -0.951 to -0.457, 
however the rightmost figure in the verbose-line is much closer to zero!

No my central question is: which of the two sets of random-effect 
estimates should I trust more, those of Model1 or those of Model2?
Or: which criterion counts more, the correlation or the verbose figures

As to the verbose figure: I don't understand how these are related to
the random effect estimates. I noticed that these figures are available
in the ST slot of the models, but was not able to relate them to the
random effects estimates. Could you give a clue to this relation or 
point me to literature (or even better, to a R example) in which this is 
worked out for correlated random effects? Thanks a lot for any help!!!

Ben.