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st: RE: Mixed question

From   "Verkuilen, Jay" <[email protected]>
To   "'[email protected]'" <[email protected]>
Subject   st: RE: Mixed question
Date   Wed, 13 Jan 2010 16:25:15 -0500

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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