Gologit is a generalization of ologit. In ologit the change in odds of choosing one outcome versus all `lower' outcomes due to a change in the explanatory variable are constraint to be the same for all outcomes. Gologit relaxes this constraint and estimates different odds ratios for different outcomes (acutually the number of possible outcomes minus one). So ologit is nested in Gologit and testing the difference between these models can be tested with a likelihood ratio test. So -2*(log likelihood(ologit)-log likelihood(gologit)) is distributed chi-square with degrees of freedom of (# oucomes-2)*# variables, or use -lrtest-.
You can't test anything with the AIC. All you can say is less is better.
I find `Regression models for categorical dependent variables using stata' from Scot Long and Jeremy Freese a very helpfull text for questions like these.
Maarten
Ps. An obvious extension of the gologit is to relax the proportional odds assumption for some variables while keeping this assumption for others. I tried to do that some time ago and found out that the -gologit- command can not handle restrictions. At the time I wrote a quick and dirty solution for that. If you are interested I can look that sollution up for you, and clean it up a little (but not before wednesday, I got a deadline...).
> Date: Sat, 18 Sep 2004 19:15:15 +0200
> From: "Herve STOLOWY" <[email protected]>
> Subject: st: Gologit, ologit and Akaike's Information Criterion
>
> Dear All:
>
> 1 - I would like to evaluate the goodness of fit of a gologit
> model (in general and versus an ologit). With fitstat, I get
> several statistics. Which statistics would you suggest to
> take and how would you use (= read) it?
>
> 2 - Following my first question, I read in a working paper
> that the author used the Akaike Information Criterion (AIC)
> to compare the goodness of fit of two models: gologit and
> ologit. But I still don't understand how to use the AIC. Is
> there a threshold? Should I simply compare the two AIC got
> with fitstat? If so, what is the "best" model? With the
> highest or lowest level? (Sorry, but my level in statistics
> is not good enough to find the answer from the computation of
> the AIC).
>
> Additionally, would you have a good reference which explains
> how to evaluate the goodness of fit of gologit and ologit models?
>
> Best regards
>
> Herv� Stolowy
> HEC Paris
>
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