Description of concordant and discordant in SAS PROC LOGISTIC
Part of the default output from PROC LOGISTIC is a table that has entries including`percent concordant’ and `percent discordant’. To me, this implies the percent that would correctly be assigned, based on the results of the logistic regression. But that is not what it is. It looks at all possible pairs of observations. A pair is concordant if the observation with the larger value of X also has the larger value of Y. A pair is discordant if the observation with the larger value of X has the smaller value of Y; here, X and Y are the predicted value and the actual value.
Example concordant and discordant
For our first example from these data, the output looks like this:
Association of Predicted Probabilities and Observed Responses
|Percent Concordant||25.0||Somers’ D||0.000|
Evidence of concordant and discordant in PROC LOGISTIC
It is hard to find documentation of this.
I couldn’t find it explained in the LOGISTIC documentation. I found a mention of `concordant’ and `discordant’ in the FREQ documentation, but it was not clear what X and Y were, until I
searched SAS-L and found an explanation from David Cassell.
Solution to the problem of concordant and discordant in PROC LOGISTIC
For what I was thinking of, you need the CTABLE option on the MODEL statement, which gives the proportion correctly classified, the sensitivity, the specificity, and other
measures for each of a number of cutpoints of the predicted probability level. By default, it gives probability levels from 0 to 1 at intervals of .02, but if you just want a few, you can get them:
proc logistic data = today3; class race sex/param = ref;
model disease(event = '1') = race sex/ctable pprob = (.25 .5 .75);
which yields sensitivity. specificity, false positive and false negative rates at various probability levels.
[learn_more caption="Author Bio"] I specialize in helping graduate students and researchers in psychology, education, economics and the social sciences with all aspects of statistical analysis. Many new and relatively uncommon statistical techniques are available, and these may widen the field of hypotheses you can investigate. Graphical techniques are often misapplied, but, done correctly, they can summarize a great deal of information in a single figure. I can help with writing papers, writing grant applications, and doing analysis for grants and research.
Specialties: Regression, logistic regression, cluster analysis, statistical graphics, quantile regression.