
From  Richard Williams <Richard.A.Williams.5@ND.edu> 
To  statalist@hsphsun2.harvard.edu 
Subject  Re: st: Fixing an ml model syntax problem 
Date  Tue, 20 Feb 2007 17:29:13 0500 
At 04:42 PM 2/20/2007, Clive Nicholas wrote:
The model parameters and standard errors are exactly the same, but the model fit is better under oglm. TheNot really. The hypotheses being tested are different. There are 2 equations in the model (typically called choice and variance, or else location and scale). oglm is doing a likelihood ratio chisquare test of whether the coefficients in both equations all equal zero. complogit is only testing the coefficients in the first equation and is using a Wald test. (Note that the d.f. reported by the two programs are different.) With oglm, it is easy enough to do other Wald or LR tests if you don't happen to like the one that is reported.
key issue, however, is the value of the $\{delta}$ parameter. under gplogit, $\{delta} < 0$, implying that residual variation is larger amongst blacks than amongst nonblacks. Under oglm, $\{delta} > 0$, which implies exactly the opposite. This throws up two followup questions:Not so. As noted in one of my other followup messages, a little bit of algebra can switch you back and forth between Allison's delta and oglm's lnsigma, but they are not exactly the same thing. Further, whatever tests you look at (z values, Wald or LR chisquare tests) you conclude that the residual variances do not significantly differ by race.
(1) If both of these achieved significance here, how on Earth do you decide whether or not to include an interactive term in the model?None of the analyses presented so far have said anything about interaction terms; they've only addressed whether residual variation differs across groups, and the answer seems to be no. If you now want to test interaction terms involving race, go ahead; and plain old logit will probably be adequate for your needs.
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