--- On Wed, 13/1/10, Morten Hesse wrote:
> how do I estimate the significance of random effects
> in multilevel models, such as xtmixed?
The problem is that the significance presumes a null-hypothesis:
it is the probability of observing the data, or data that deviates
stronger from the null hypothesis, given that the null-hypothesis
is true in the population (if this probability is small, then it
is so unlikely that we have drawn such a "weird" sample by accident,
that there must be something wrong with the null hypothesis, so
we reject the null hypothesis.) The standard null hypothesis is that
a coefficient is 0, so in the case of random effects that would mean
that the coefficient doesn't differ across your higher level units.
However, this coefficient is a variance or standard deviation, and
these can only take values of 0 or larger, so this null hypothesis
is "on the edge of the parameter space", and things get weird there.
One way you can see that, is to see that usually variances are
transformed during estimation to ln(variance) to ensure that variance
cannot be negative. So in that case the null hypothesis would
correspond to ln(variance) = - infinity, you can imagine that that
can cause trouble.
Hope this helps,
Maarten
--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany
http://www.maartenbuis.nl
--------------------------
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