[R] AUC values from LRM and ROCR

Frank E Harrell Jr f.harrell at vanderbilt.edu
Sat Jan 5 17:01:54 CET 2008

Colin Robertson wrote:
> Dear List,
> I am trying to assess the prediction accuracy of an ordinal model fit with
> LRM in the Design package. I used predict.lrm to predict on an independent
> dataset and am now attempting to assess the accuracy of these predictions.
>>From what I have read, the AUC is good for this because it is threshold
> independent. I obtained the AUC for the fit model output from the c score (c
> = 0.78). For the predicted values and independent data, for each level of
> the response I used the ROCR functions to get the AUC (i.e., probability y
>> = class1, y >= class2, y >= class3 etc) and plotted the ROC curves for
> each. The AUC values are all higher (AUC = 0.80 - 0.93) for the predicted
> values than what I got from the fit model in lrm. 
> I am not sure whether I have misinterpreted the use of the AUC for ordinal
> models or whether the prediction results are actually better than the model
> results.
> Any help / clarification appreciated,
> Colin
> Colin Robertson
> University of Victoria

Cliff - several points:

Unless the independent dataset and the training dataset are both huge, 
splitting the data is inefficient and gives a low-precision estimate of 
predictive accuracy (when compared to bootstrapping or 50-fold repeats 
of 10-fold cross-validation).

lrm computes a quick approximate AUC which you can confirm by running 
rcorr.cens(predict(fit)< Y) and using Dxy=2(C-.5).  The C index printed 
by lrm is for predicting all categories of Y; it is easier to predict 
whether Y>=j for a given j than to predict an ordinal Y over the whole 
set of categories.  Somers' D and the AUC (C) do not penalize for ties in Y.

For independent model validation you can use the val.prob function for 
each Y-cutoff j.

Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University

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