|Title||Stata 6: Wald tests associated with the alpha parameter|
|Author||James Hardin, StataCorp|
The alpha parameter is a positive value that is parameterized using the natural log. The equivalent test of alpha=0 is thus log(alpha) = -infinity. In the maximization, the value of log(alpha) is limited to the range [-18, 18] such that we limit alpha to the range [1.523e-08, 65659969].
Note: the actual range that can be achieved is somewhat wide as the optimizer will take one final step after any correction is made in the calculation.
The limiting case is alpha=0 where the zero-inflated negative binomial estimator does not differ from the zero-inflated Poisson estimator or, when combined with testing that all of the inflation equation parameters are zero, where the zero-inflated negative binomial model does not differ from the Poisson estimator.
At the initial time of preparing the documentation of the manuals, we considered testing whether log(alpha)=-18 (since this was the limiting value). After the manuals were printed, we revisited this subject and discovered that we did not, in fact, want to include this test. The likelihood-ratio test is the only test that one should consider in these limiting cases.
So, a test involving the alpha parameter is only included if you specify the nbreg and/or zip options.