Morten Hesse wrote:
>>My question is probably more a general statistical question than a Stata
question (and maybe one for beginners). But I wonder: how do I estimate
the significance of random effects in multilevel models, such as
xtmixed? I suspect there is a reason why neither GLLAMM nor xtmixed
gives significance levels and standardized effect sizes, but just
coefficients and standard errors. Of course, I could calculate a Z
statistic from these, but since the program doesn't I assume that is wrong.<<
Just elaborating Maarten's point a bit. Because tau = 0 is on the boundary of the parameter space, the distribution under the null hypothesis is ugly. It ends up being a mixture of chi squares of different degrees of freedom. The standard reference on this topic is by Liang and Self, uh:
Self, S. G., and Liang, K. Y. (1987). Asymptotic properties of maximum likelihood estimators and
likelihood ratio tests under nonstandard conditions. J Am Stat Assoc 82, 605-610.
The safest thing is to fit the model you want to test vs. the reference model you want to test it against and then do the LR test. I believe Stata does the proper mixture of chi squares and then issues a dire warning as a footnote about the fact that the LR test is conservative (which is true).
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