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From |
"Newson, Roger B" <r.newson@imperial.ac.uk> |

To |
"'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: RE: st: C-statistic with -gologit2- |

Date |
Wed, 7 Oct 2009 21:22:20 +0100 |

Yes, you would have to calculate separate c-statistics with -mlogit-, as you describe. And these would have to be restricted to the 2 groups being compared, in order to make sense. In the case of mlogit, you could also calculate multiple c-statistics, one for each partition of the outcome values. Alternatively, you could presumably define one stratum for each partition of the outcome variable, expand each subject into a cluster of observations (1 observation per subject per partition), define X for each subject-partition as a binary indicator of that subject's membership of the higher group in that partition, define Y for each subject-partition as the linear predictor for that subject of membership of the upper group in that partition, and define the summary c-statistic as the Harrell's c of Y with respect to X, stratified by partition. As in: somersd X Y, cluster(subject) wstrata(partition) transf(c) tdist where -subject- is the subject ID for each subject-partition, -partition- is the partition variable for each subject-partition, and Y and Y are as defined above. The c-statistic would then summarize the general ability of the linear predictors (as stored in Y) to predict the membership of upper groups of partitions (as stored in X), restricted to comparisons involving the same linear predictor for the same partition. I hope this helps. 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: r.newson@imperial.ac.uk 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: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Richard Williams Sent: 07 October 2009 20:59 To: statalist@hsphsun2.harvard.edu; 'statalist@hsphsun2.harvard.edu' Subject: Re: st: RE: st: C-statistic with -gologit2- 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? ------------------------------------------- Richard Williams, Notre Dame Dept of Sociology OFFICE: (574)631-6668, (574)631-6463 HOME: (574)289-5227 EMAIL: Richard.A.Williams.5@ND.Edu WWW: http://www.nd.edu/~rwilliam * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: st: C-statistic with -gologit2-***From:*Sara Muller <s.muller@cphc.keele.ac.uk>

**References**:**st: C-statistic with -gologit2-***From:*s.muller@cphc.keele.ac.uk

**Re: st: C-statistic with -gologit2-***From:*Jeph Herrin <junk@spandrel.net>

**Re: st: C-statistic with -gologit2-***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

**st: RE: st: C-statistic with -gologit2-***From:*"Newson, Roger B" <r.newson@imperial.ac.uk>

**Re: st: RE: st: C-statistic with -gologit2-***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

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