[R-sig-ME] extractor function for coefficient table fromsummary.mer ?

[Douglas Bates]

On Tue, Jun 2, 2009 at 10:05 PM, David Duffy<David.Duffy at qimr.edu.au> wrote:
> On Tue, 2 Jun 2009, Ben Bolker wrote:

>>  Request for comment: would it be reasonable to have the
>> "coef" method for "summary.mer" objects return the table
>> of parameter values, standard errors etc.?

> Yes please, oh and a profile likelihood based confint.lmer() too,
> thanks ;).

I have been thinking about this recently and I have a way of
constructing a profile likelihood for the variance component
parameters.  Are those the parameters that are of interest or are you
more interested in the fixed-effects parameters?

The enclosed plots are from the simple random-effects model fit to the
Dyestuff data in the lme4 package.

Part of my purpose in producing such plots is to show why quoting an
estimate of a variance and a standard error for the estimate is not a
very reasonable summary.  In introductory courses we teach that a
confidence interval on the population variance based on the mythical
i.i.d. sample from a Gaussian population would be constructed from the
chi-squared distribution and would be quite asymmetric in most cases.
Yet somehow the variability in estimates of variance components in
much more complicated models can be expressed by quoting a standard
error.  As shown here, the variability is not at all symmetric.  For
the residual variance term the profiled likelihood is approximately
symmetric when considering the logarithm of the variance (or,
equivalently, the logarithm of the standard error) but even that is
inadequate for other variance components that could feasibly be zero.
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