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

 From "Joseph Coveney" To 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.
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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