In the case of ordinal regression, instead of using the predicted probability, you should use the linear predictor, computed using -predict- with the -xb- option. This linear predictor is an ordinal predictor of the outcome. It then makes sense to use the c-statistic, although the confidence intervals should only be taken seriously if calculated (using out-of-sample prediction) in a different dataset from the dataset in which the ordinal model was fitted.
In the case of mlogit, there are multiple linear predictors, interpreted as the log odds ratios (per X-unit) of the various non-baseline outcomes compared to the baseline outcome. In that case, the c-statistic for the linear predictor for each non-baseline outcome only makes sense if restricted to observations with either that non-baseline outcome or the baseline outcome.
Best wishes
Roger
Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: [email protected]
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/
Opinions expressed are those of the author, not of the institution.
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Richard Williams
Sent: 07 October 2009 19:56
To: [email protected]; [email protected]
Subject: Re: st: C-statistic with -gologit2-
At 07:18 AM 10/7/2009, Jeph Herrin wrote:
>I posted some code for getting the C-stat a few days ago
>
>http://www.stata.com/statalist/archive/2009-10/msg00267.html
>
>I'm not familiar with -gologit-, but as long as you can produce
>a predicted probability, the method should apply.
>
>hth,
>Jeph
How about when there are multiple outcomes and hence multiple
predicted probabilities? e.g. with gologit2, ologit, oprobit,
mlogit, and others, you get predicted probabilities for outcome 1,
outcome 2, outcome 3, etc. Does the C-stat even apply in such
cases? (I'm glad the original question was sent to the list rather
than to me as the author of gologit2, because I have no idea what the
answer is!)
-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME: (574)289-5227
EMAIL: [email protected]
WWW: http://www.nd.edu/~rwilliam
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