Summary Re: lme$apVar and PROC MIXED Std. Error of varcomp ests

[Sven.Knudsen@adeptscience.dk]

Thank you for all the answers

I know that estimation of dispersion is a
huge issue - and testing components is even bigger (if not impossible to
agree on).

Below I will make some comments to the replies


SPENCER GRAVES writes:
> Have you checked Pinhiero
and Bates (2000) Mixed-Effects Models in S 
>and S-Plus (Springer)?  This is the primary documentation for
"lme" and 
>includes, I believe, the answer to this question and many others.  Doug
>Bates is the primary developer of "lme" in conjunction with
several of 
>his graduate students including Jose Pinhiero.

Yes - I have the book (a good one too). It
does include most of the answer - but not deveations to SAS. The anser
came from Jose; see below. 

>Doug is also arguably the
leading figure in nonlinear regression, 
>having explained carefully the difference between intrinsic and 
>parameter effects nonlinearity.  Bates and Watts (1988) Nonlinear
>Regression Analysis and Its Applications (Wiley) include a table in
a 
>later chapter showing that for 30-60 published data sets they analyzed,
>the parameter effects were roughly 10 times the intrinsic curvature.
>This means that profiling produces much more accurate confidence regions
>than using any neg inverse Hessian, and within the latter, a smart
>selection of transformation like log(variances) will produce much more
>accurate confidence regions than without.

Estimating dispersion is always very difficult
- and wanting standard erros is even more difficult. I have no doupt that
profiling performs better than the neg inverse hessian - or the inverse
Fisher information; after all there is always little information in data
to obatin standard deveations of dispersion estimates, and estimators are
more likely to be mixtures of chi-squares rather than normally distributed
(this gives the reason why log(varianes) work, in part becuase the Gamma
distrubution is much like a log-normal distribution). The invers Fisher
is good for fixed effect estimates beacuse these estimates are usually
very "normal", even if the data is not. This is what actualy
saves fixed effect standard errors in the GEE methodology. That, and the
fact that regression parameters are insensitve to dispersion.
 
-----
Jose Pinheiro writes
>The apVar matrix in lme is
obtained via the Hessian matrix as you indicated, using numerical derivatives.
>However, unlike PROC MIXED in SAS, it refers to an unconstrained parameterization
of the random effects 
>variance-covariance matrix (as well as unconstrained parameterizations
of other var-cov parameters that may 
>be present in the fit). This is mentioned on page 93 of my book with
Doug Bates. As a result, the standard 
>deviations and covariances that you get in apVar refer to the unsconstrained
parameterization and are not 
>comparable to the ones you get from the SAS output. The intervals function,
when applied to an lme object, 
>constructs the appropriate confidence intervals in the constrained
scales (std. dev and correlations). 
>Hope this helps clarifying your question

This explains the deveation - thanks. And
now I can just extract the right result by retransforming intervals to
pseudo std.devs
-----
Gregory D. Rodd writes
I cannot speak directly to the
particulars of PROC MIXED.  (I have Bates & Pinheiro handy, but
not the SAS docs.  I don't know where they've got to.)  As you
indicate, one only >need to look to see what NLME is doing.  However,
there are numerous examples where SAS has standardized on non-standard
procedures and made default assumptions contrary >to common usage.  This
is not to say that what they produce is necessarily wrong, just that the
default assumptions are not explained carefully, I suspect for "ease
of use."  As an >example, the coefficients from proc logistic
are opposite the convention in the literature.  This may be part of
your discrepancy.  (I've had similar difficulty explaining how SAS
does >this to a party evaluating a competitor.)

What I don't understand is why
you need to rely on rumor about how SAS computes any sort of statistic.
 Why would they not explain it clearly?  So, isn't your question
really about what SAS is doing?  Are you putting the same question
before a SAS list, then, to compare differences in responsiveness?  :0)
 Is this consideration part of your evaluation? 

I dis not rely on the rumor. The rumor was
if SAS did compute the stat correctly (e.g. there is a bug).