[R] Getting "Information matrix" in mixed models

[Douglas Bates]

Chandra H. wrote:
> Hello,
> I am Hukum Chandra and I'm a statistician. I am using R. I have gone
> through R but I could not get the way how to find "Information matrix"
> in R. In particular,  var-Cov matrix of components of variances in
> linear mixed model. Could you please help me in getting the way to
> produce it using R?

They are not given for linear mixed models fit by lme (either from the 
nlme package or from the lme4 package) or by lmer (the lme4 package). 
This is intentional.  I don't think they are meaningful and I prefer not 
to give an answer than to give a misleading answer.

The reason I don't think they are meaningful is because an information 
matrix (or, equivalently, standard errors and correlations) are useful 
summaries when we can expect the distribution of the parameter estimates 
to be roughly symmetric.  In the case of a variance component the 
parameter estimate has a distribution that is like a Chi-squared 
distribution and not at all symmetric.

Think of the simple case of obtaining a confidence interval on the 
variance of a sample that is assumed to be i.i.d. normal.  We use a 
Chi-squared reference distribution and expect to obtain an interval that 
is quite asymmetric.  We do not use estimate +/- some multiple of a 
standard error to form an interval.

Many packages that fit mixed models report estimates of variance 
components, their approximate standard errors, a 'z' statistic and a 
p-value for the test of the variance component being greater than zero. 
  The approximations are so bad in this test that I think it is better 
not to have a p-value than to have one that is extremely doubtful.