[R] Conservative "ANOVA tables" in lmer

[Manuel Morales]

On Mon, 2006-09-11 at 11:43 -0500, Douglas Bates wrote:
> On 9/10/06, Andrew Robinson <A.Robinson at ms.unimelb.edu.au> wrote:
> > On Thu, Sep 07, 2006 at 07:59:58AM -0500, Douglas Bates wrote:
> >
> > > I would be happy to re-institute p-values for fixed effects in the
> > > summary and anova methods for lmer objects using a denominator degrees
> > > of freedom based on the trace of the hat matrix or the rank of Z:X if
> > > others will volunteer to respond to the "these answers are obviously
> > > wrong because they don't agree with <whatever> and the idiot who wrote
> > > this software should be thrashed to within an inch of his life"
> > > messages.  I don't have the patience.
> >
> > This seems to be more than fair to me.  I'll volunteer to help explain
> > why the anova.lmer() output doesn't match SAS, etc.  Is it worth
> > putting a caveat in the output and the help files?  Is it even worth
> > writing a FAQ about this?
> 
> Having made that offer I think I will now withdraw it.  Peter's
> example has convinced me that this is the wrong thing to do.
> 
> I am encouraged by the fact that the results from mcmcsamp correspond
> closely to the correct theoretical results in the case that Peter
> described.  I appreciate that some users will find it difficult to
> work with a MCMC sample (or to convince editors to accept results
> based on such a sample) but I think that these results indicate that
> it is better to go after the marginal distribution of the fixed
> effects estimates (which is what is being approximated by the MCMC
> sample - up to Bayesian/frequentist philosophical differences) than to
> use the conditional distribution and somehow try to adjust the
> reference distribution.

Am I right that the MCMC sample can not be used, however, to evaluate
the significance of parameter groups. For example, to assess the
significance of a three-level factor? Are there better alternatives than
simply adjusting the CI for the number of factor levels
(1-alpha/levels).

Thanks!

Manuel

=
Manuel A. Morales
Asst. Prof., Biology
Williams College
http://mutualism.williams.edu