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RE: st: Gologit, ologit and Akaike's Information Criterion


From   "Herve STOLOWY" <stolowy@hec.fr>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Gologit, ologit and Akaike's Information Criterion
Date   Mon, 20 Sep 2004 16:43:32 +0200

Dear Maarten:

Thank you for your detailed reply. I immediately ordered the book you mention.

However, I would like to reformulate my question. I do not want to compare the goodness of fit of ologit vs gologit. I would like to measure the goodness of fit for a single gologit model. So, I am looking for something equivalent to the Hosmer and Lemeshow test which I find easily readable because there is a threshold.

When I use 'fitstat', I get many figures but do not know what to choose. (I know how to use all the R2s and am looking for something else).

Should I take the 'Prob>LR' which is only probability appearing in these stats?

 Thanks again for your help.

Best regards

Hervé Stolowy
HEC Paris

***********************************************************
HEC Paris
Département Comptabilité-Contrôle de gestion / Dept of Accounting and Management Control
1, rue de la Liberation
78351 - Jouy-en-Josas
France
Tel: +33 1 39 67 94 42
Fax: +33 1 39 67 70 86
stolowy@hec.fr
http://campus.hec.fr/profs/stolowy/perso/home.htm
>>> M.Buis@fsw.vu.nl 09/20/04 1:46 PM >>>
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" <stolowy@hec.fr>
> 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
> 
> Hervé Stolowy
> HEC Paris
> 
> ***********************************************************
> HEC Paris
> Département Comptabilité-Contrôle de gestion / Dept of 
> Accounting and Management Control
> 1, rue de la Liberation
> 78351 - Jouy-en-Josas
> France
> Tel: +33 1 39 67 94 42
> Fax: +33 1 39 67 70 86
> stolowy@hec.fr
> http://campus.hec.fr/profs/stolowy/perso/home.htm
> 
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