Re: random effects

[Spencer Graves <spencer.graves@pdf.com>]

     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
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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