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Richard Williams <Richard.A.Williams.firstname.lastname@example.org> asks why -ml- will not perform
a likelihood ratio test when constraints are specified:
> According to the documentation, the -ml- command will provide a Wald test
> (rather than an LR test) when you specify robust, cluster or
> pweights. However, I am finding that it also provides a Wald test when you
> use the -constraint- option. Why? This isn't mentioned in the
> documentation. Is there some mathematical reason for this, or is it a
> bug/limitation of the software, or what? The log likelihood is being
> reported for the constrained model (not a pseudo log likelihood) so I don't
> understand why it can't give me a LR chi-square instead of a Wald
> chi-square for the model.
This restriction was added when Stata 8.1 was released (01jul2003). It was
added to prevent -ml- from producing an invalid likelihood ratio test, given
its theoretical requirements and the possibility for boundary conditions
imposed by constraints (see the discussion of the likelihood ratio test for
alpha=0 in [R] nbreg).
We considered it safer to produce the Wald test when constraints are supplied
than try to recover from all the possible cases where the standard likelihood
ratio test is not applicable.
As Richard points out, you can still use the -lrtest- command to produce a
likelihood ratio test.
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