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Re: st: LogL of null model in zinb and zip


From   rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: LogL of null model in zinb and zip
Date   Thu, 20 Dec 2007 10:40:45 -0600

Garry Anderson <g.anderson@unimelb.edu.au> asks about the log-likelihood for
the null model, called "ll(null)" by -lrtest-.  In particular, he is curious
as to why, in -zinb- and -zip-, the null log-likelihood is calculated as that
for a model with no variables in the main equation rather than for a model
with both empty main and "inflate" equations.

-lrtest- obtains the null log-likelihoods from the e-result e(ll_0).  By rule,
for all models e(ll_0) is the the log-likelihood of the model with the
variables deleting from the first equation only.  This is designed so that the
omnibus LR test that all coefficients are zero, as shown in heading of standard
regression output, will ignore any estimated ancillary parameters.

-lrtest- picks up this value of e(ll_0) to use for an additional test that the
models you are comparing are indeed nested.  In most cases, a difference in
null log-likelihoods would indicate that you have done something wrong, say,
changed the dependent variable or some other model characteristic that would
result in your models no longer being nested.

In the case Garry is describing, however, there is nothing wrong and his two
models are indeed nested.  Since -lrtest- was written to work will all
estimation commands, we designed it to err on the conservative side.  That is,
we would rather issue an error than give an invalid statistical result.
-lrtest- has a -force- option, giving you a way to assure -lrtest- that
everything is okay and that your two models are nested, but Garry knows this
already.  I can only add that Stata is working as it should.

--Bobby
rgutierrez@stata.com
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