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

 From Richard Williams To "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:
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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.
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Thanks Roger. This won't work with gologit2, because there are multiple equations and hence multiple XBs. gologit2 is like mlogit in that respect.
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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.
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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).
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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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