testing the significance of the variance components using lme

Hi,
you should say a little more about the data you have.
I guess you refer to longitudinal data. I say so
because if you deal with spatial smoothing splines in
form of mixed models, the answer to your question
would be different. Anyway, a good starting point is
given by the commands

fit.lme <- lme(...) # fitted model
fit.lme$apVar # approx. covariace matrix for the
variance-covariance coefficients (see ?lmeObject)
intervals(fit.lme) # confidence intervals for the
parameter(s)

I believe that Pinhiero and Bates (2000) Mixed-Effects
Models in S and S-Plus (Springer) includes some
answers to your questions. I don't really know what
happens when you use 'intervals' and the caveats of
this command. When it comes to making inference about
the variance components I tend to be suspicious. I
hope some R users can give you a more complete answer
than mine.

Testing whether or not a variance component is zero is
a delicate issue. Check:
- Self and Liang (1987), Asymptotic properties of
maximum likelihood estimators and likelihood ratio
tests under nonstandard conditions. Journal of the
American Statistical Association, 82, 605-610
- Zhang and Lin (2003), Hypothesis testing in
semiparametric additive mixed models. Biometrika, 4,
57-74
- Bottai (2003), Confidence regions when the Fisher
information is zero. Biometrika, 90, 73-84.

hope this helps a little

Marco

testing the significance of the variance components using lme

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