How to interpret Concordance in logistic regression?
This article was originally published on Quora in 2015.
To understand concordance, we should first understand the concept of cutoff value.
CUTOFF VALUE: For instance, students are classified as pass (1) or fail (0) depending upon the cutoff passing marks in the examination. The cutoff marks varies depending upon the requirements of the different examination. Let us consider the cutoff passing marks as 60 out of 100; therefore, all the students getting marks greater than 60 will be considered pass(1) else fail(0).
CUTOFF VALUE : LOGISTIC REGRESSION: Now, let us consider a binary logistic model in which an event and a non events are classified as (1) and (0) respectively. We get the probability values as an output of the logistic model . We classify the output as event (1) or non event (0), depending upon the cutoff probability value (Popular choice of the cutoff probability is 0.5*). Thus, if the cutoff probability is chosen as 0.5, then all the observations with probability value greater than 0.5 will be classified as event (1) else nonevent (0).
NOTE: It should be noted that in case of classification we may fix our cutoff value; however , for the calculation of the Concordance we do not fix the cutoff value.
