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Re: st: LR-tests and Xtnbreg

From (Roberto G. Gutierrez, StataCorp.)
Subject   Re: st: LR-tests and Xtnbreg
Date   Mon, 02 Jun 2003 09:43:42 -0500

Jon Heron <> asks: 

> I have a question about the LR-test given at the end of xtnbreg output.

> Is this a test of the variance of the beta random effect being equal to
> zero?

Yes it is.

> If so, why, when I compare the likelihoods of an xtnbreg model with it's
> equivalent nbreg model does (2 x) the difference not agree with the
> chi-square value quoted in this test?  The discrepancy is slight, but I do
> obtain an exact agreement when comparing the likelihoods of poisson and
> xtpois in the same way.

Note that there are two parameterizations of the negative binomial that 
are available under -nbreg-, the mean dispersion (default) and the constant
dispersion (option -dispersion(constant)-).

The model associated with -xtnbreg- is a generalization of the constant
dispersion parameterization of the negative binomial.  Thus, if you are going
to calculate likelihood ratio tests manually, you need to specify
-dispersion(constant)- with -nbreg-.

> Furthermore, since these 4 models appear to be nested, why can't I use the
> 'lrtest' command to assess their relative worth?

-lrtest- will complain if your models, even though nested, are fitted using
different estimation commands.  A little too cautious perhaps, yet we feel
this is a necessary safeguard against calculating likelihood ratios for
non-nested models.

When you are sure that the models are nested, you can turn off this safeguard
by specifying option -force- to -lrtest-.

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