Roberto G. Gutierrez wrote (excerpted):
. . .
For unbalanced data, test-statistics for fixed effects, whether derived from
ML or REML, are only asymptotically normal. In such cases, you can try to
go after approximating the distribution with a t with some approximate
degrees of freedom, yet in small samples you aren't even normal to begin
with. If you increase the sample size so that the t (normal) begins to make
sense, it is also likely that the difference between t and Z is no longer
important.
Asymptotic normality can be a funny and unpredictable thing. If you make a
small-sample correction on something only asymptotically normal, I don't
think you can even guarantee that your correction is in the right direction.
Now consider cases where the data are _nearly_ balanced. In these
situations it would make sense to assume that test-statistics are nearly
normal, even in small samples. As such, a d.f. correction would make sense.
In summary, the answer to Alan's question is "It depends."
--------------------------------------------------------------------------------
Thank you for pointing this out.
After running across a couple of posts from Douglas Bates last year on the
R-help list (
http://finzi.psych.upenn.edu/R/Rhelp02a/archive/76742.html
http://tolstoy.newcastle.edu.au/R/help/06/07/31792.html ) and now Bobby
Gutierrez's post, it's beginning to dawn on me that inserting
DDFM=KENWARDROGER in a SAS PROC MIXED control stream might not be quite the
charm that it was intimated by some to be.
The realization leaves some practical questions in its wake, however: it
would be good if there were some rules of thumb to gauge when a given-sized
dataset is sufficiently nearly balanced to be able to use degrees-of-freedom
approximations, and what to do otherwise.
Joseph Coveney
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
