Spencer Graves <spencer.graves@pdf.com> writes:
> Have you consulted Pinhiero and Bates (2000) Mixed-Effects
> Models in S and S-Plus (Springer)? On pp. 82-96, they discuss that
> very issue. In brief, they found from simulations that
> 2*log(likelihood ratio) in situations like this were well approximated
> by a mixtures of two chi-square distributions. My memory of that
> material is that one part is the naive chi-square that one would
> expect without the boundary constraint while other(s) has(have)
> reduced degrees of freedom. Pinhiero and Bates provide a insight into
> what occurs and why as well as a simulation methodology for evaluating
> the result in a particular context. I hope Doug or someone else will
> comment if I've missed or misunderstood something here. hope this
> helps. spencer graves
Thanks for the summary Spencer. I agree with what you wrote.
The test performed by the anova function should be conservative in the
sense that the p-value returned will be an upper bound on the true
p-value you would obtain via simulation of the null model.
More recent work on this issue is reported in
Crainiceanu, C. and Ruppert, D. (2004). Likelihood ratio tests in
linear mixed models with one variance component, JRSS-B, 66,
165-185.
and other references given on
http://www.orie.cornell.edu/~davidr/papers/index.html
>
>
> Frank Lawrence wrote:
>
> >When using lme to test if random effects are zero, I have used the anova
> >function to compare two models; one representing the null hypothesis the
> >other representing the alternative. I would like to know if use of anova is
> >appropriate in these circumstances because I understand that the null
> >hypothesis places the parameter of interest on the boundary of the parameter
> >space.
> >
> >Respectfully,
> >
> >Frank R. Lawrence
> >
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--
Douglas Bates bates@stat.wisc.edu
Statistics Department 608/262-2598
University of Wisconsin - Madison http://www.stat.wisc.edu/~bates/
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