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Re: st: RE: st: C-statistic with -gologit2-


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>, "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: RE: st: C-statistic with -gologit2-
Date   Wed, 07 Oct 2009 14:58:42 -0500

At 01:30 PM 10/7/2009, Newson, Roger B wrote:
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.

Thanks Roger. This won't work with gologit2, because there are multiple equations and hence multiple XBs. gologit2 is like mlogit in that respect.

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.

So, does that mean you would compute separate C statistics only using groups 1 and 2, then 1 and 3, then 1 and 4 (assuming group 1 is the baseline and there are 4 groups).

gologit2 doesn't quite fit into this scheme either. gologit2 is like a series of binary logistic regressions with different dichotomizations of the original ordinal variable. First, it is group 1 versus groups 2, 3, 4; then groups 1 and 2 versus groups 3 and 4; then groups 1, 2 and 3 versus 4. If proportional odds holds each dichotomization produces the same coefficients except for the intercepts. I am not sure how the C statistic fits in with such a scheme; perhaps, in the above you would have 3 different C statistics?


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Richard Williams, Notre Dame Dept of Sociology
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