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Re: st: Stumped...xtmixed and ANOVA F-stats not agreeing for balanced design


From   "Joseph Coveney" <jcoveney@bigplanet.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Stumped...xtmixed and ANOVA F-stats not agreeing for balanced design
Date   Sun, 8 May 2011 18:01:45 +0900

Jared Saletin wrote:

Is that model considered invalid then, with negative components? Should the
xtmixed output not be used? Or just accept that its a slightly different model
from the one ANOVA is able to fit?

--------------------------------------------------------------------------------

google will bring you up a ton of stuff on this.  The question of what to do
about negative variance components has been around for a long time, and opinions
among the experts seem to vary.

I'll gladly defer to the experts for the official take on it, but my simplistic
view is:  it depends upon how you see the phenomenon behind the data.

If you consider your data to represent a hierarchy, then you shouldn't have a
negative variance for the s factor in your hierarchical/multilevel model.
Negative values aren't "admissible" for variances.  In this case, your model
doesn't fit the data well.

On the other hand, if you consider your data to represent the outcome of a
repeated-measures experiment, then there's nothing wrong at all with a negative
value for s's variance component.  It merely reflects a negative association
(negative intraclass correlation coefficient) between residuals of repeated
measurements on s.  In this case, you'd even be remiss to drop s or constrain
its variance component to zero.

In this latter case, you're probably better off setting things up in -xtmixed-
as a repeated-measures model, that is, something like:

generate int ab = 10 * a + b
xtmixed y i.a##i.b || s: , noconstant residuals(unstructured, t(ab))

Because you have balanced data (and a small number of observations), your even
better off modeling it as doubly multivariate repeated measures using -manova-.
As David Airey mentioned earlier in the thread, you'll probably want to avoid
the compound symmetry assumption of ANOVA if you can (although the -repeated(a
b)- option of -anova- could be used here), and either of these approaches
(-xtmixed . . . residuals()- or -manova-) would allow you to do just that.

Joseph Coveney


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