[R-sig-ME] Fwd: same old question - lme4 and p-values

[Andrew Robinson]

On Sat, Apr 05, 2008 at 03:13:02PM +0200, Martin Maechler wrote:
> >>>>> "Jon" == Jonathan Baron <baron at psych.upenn.edu>
> >>>>>     on Sat, 5 Apr 2008 07:21:19 -0400 writes:
> 
>     Jon> On 04/05/08 12:10, Reinhold Kliegl wrote:
> 
> [...]
> 
>     >> In perspective, I think the p-value problem will simply
>     >> go away.
>
> [...]
> 
>     Jon> I'm afraid we do need significance tests, or confidence
>     Jon> intervals, or something.
> 
> I agree even though I'm very deeply inside the camp of statisticians
> who know that all models are wrong but some are useful, and
> hence I do not "believe" any P-values (or exact confidence /
> credibility intervals).
> 
> For those who need ``something like a P-value'' I've heard
> yesterday Lorenz Gygax (also subscriber here) proposing
> to report the "credibility of 0", possibly "2-sided", as a
> pseudo-P value;, i.e. basically that would be
> 2 * k/n, for an MCMC sample b_1,b_2, ..., b_n 
> k := {min k'; b_k' > 0}.
> The reasoning would be the following:
> Use the 1-to-1 correspondence between confidence intervals and
> testing pretending that the credibility intervals are confidence
> intervals, and consequently you just need to look at which
> confidence level 0 will be at the exact border of the
> credibility interval.
> 
> Yesterday after the talk, I found that a good idea.
> Just now, it seems a bit doubtful, since under the null
> hypothesis, I don't think such a pseudo P-value would be uniform
> in [0,1].

Is that because the credible intervals are not confidence intervals,
or for some other reason?  

Andrew
 
> Martin

-- 
Andrew Robinson  
Department of Mathematics and Statistics            Tel: +61-3-8344-6410
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
http://www.ms.unimelb.edu.au/~andrewpr
http://blogs.mbs.edu/fishing-in-the-bay/