[R] Conservative "ANOVA tables" in lmer

[Douglas Bates]

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.