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st: xtmelogit nonsensical constant


From   William Hauser <whauseriii@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: xtmelogit nonsensical constant
Date   Fri, 16 Mar 2012 15:10:12 -0400

The constant I obtain in a random intercepts model is substantively
nonsensical and is highly inconsistent with what I get by
postestimating the intercept as "predict intercept, reffects" and then
averaging the prediction (summ intercept).  This is using Stata12.  My
variables are all group/cluster mean centered.

The "reffects" prediction is also consistent with what I get via
intercept estimation via MLE.  I used the linear term as an offset and
predicted the intercept using a series of logit models with the offset
option specified (as discussed in Rabe-Hesketh & Skrondal, 2nd ed.
p264).


The constant displayed the xtmelogit model without the "or" option is
-6.54063.  Converted to odds, that's .0014, and conversion to a
probability yields essentially the same value (odds/(1+odds)).  Within
the context of my model predicting incarceration, this would mean that
the average probability of incarceration across judges is .0014.  That
can't be right.

The Bayes estimates from reffects are about what you would expect, a
mean odds ratio for the intercept of 1.67 and a mean probability of
about .51.

So what explains this difference?  Is the constant term displayed in
xtmelogit results not the random intercept?  I can't find anything
about this in the documentation and there is an old thread on
statalist discussing the (woeful) lack of an intercept for the
xtmelogit command when the "or" option is specified.
(http://www.stata.com/statalist/archive/2008-01/msg00805.html)


Thanks,

Will Hauser
P.S. With the frequency of my posting here I believe I will have to
include statalist in my acknowledgments for my dissertation!
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