Alan H. Feiveson <[email protected]> writes:
> Are there any results (published or unofficial) that suggest that computing
> P-values using a t-distribution with pseudo degrees of freedom consistently
> gives more correct inference with -xtmixed- than simple Wald tests? Or is
> this not what you guys are talking about?
Alan asks a very good question. In cases where you have completely balanced
data (same number of observations in each group, same number of subgroups
within each group, etc.) and you are performing REML estimation, then
test-statistics for fixed effects are normally distributed and in small
samples you can go after the degrees of freedom for the corresponding
t-distribution.
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."
--Bobby
[email protected]
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