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

[David Henderson]

Hi Doug:

> Perhaps I should clarify.  The summary of a fitted lmer model does not
> provide p-values because I don't know how to calculate them in an
> acceptable way, not because I am philosophically opposed to them.  The
> estimates and the approximate standard errors can be readily
> calculated as can their ratio.  The problem is determining the
> appropriate reference distribution for that ratio from which to
> calculate a p-value.  In fixed-effects models (under the "usual"
> assumptions) that ratio is distributed as a T with a certain number of
> degrees of freedom.  For mixed models it is not clear exactly what
> distribution it has - except in certain cases of completely balanced
> data sets (i.e. the sort of data sets that occur in text books).  At
> one time I used a T distribution and an upper bound on the degrees of
> freedom but I was persuaded that providing p-values that could be
> strongly "anti-conservative" is worse than not providing any.

Now I understand the situation better and am in agreement that this is  
clearly the right solution at this point.

> The approach that I feel is most likely to be successful in
> summarizing these models is first to obtain the REML or ML estimates
> of the parameters then to run a Markov chain Monte Carlo sampler to
> assess the variability in the parameters (or, if you prefer, the
> variability in the parameter estimators).  (Note: I am not advocating
> using MCMC to obtain the estimates, I suggest MCMC for assessing the
> variability.)

I'm a little confused as to what is the Monte Carlo part of this  
scenario?  If you perform REML or ML, theoretically it should always  
converge to the REML/ML estimates (unless you have a flat or  
multimodal likelihood which each produce other problems).  I  
understand you are fixing the parameter estimates of something at the  
REML/ML estimates, but what is the random component?

Of course, I could always stop being lazy and just look at the  
source... ;^)

> The current version of the mcmcsamp function suffers from the
> practical problem that it gets stuck at near-zero values of variance
> components.  There are some approaches to dealing with that.  Over the
> weekend I thought that I had a devastatingly simple way of dealing
> with such cases until I reflected on it a bit more and realized that
> it would require a division by zero.  Other than that, it was a good
> idea.

At least the variance estimates were not negative... ;^)

Thanks!!

Dave H
--
David Henderson, Ph.D.
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