[R] Getting "Information matrix" in mixed models
Douglas Bates
bates at stat.wisc.edu
Thu Feb 3 15:36:59 CET 2005
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.
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