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

[Richard Williams <Richard.A.Williams.5@ND.edu>]

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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