Explain concordance with example.

It is a process of measuring quality of fit for a binary outcome in a model. It is a proportion of pairs in which the predicted event probability is higher for the actual event than non-event.

Let us take the following example to explain the concept.

In the following table, both actual and predicted values are shown with a sample of seven rows. Let us calculate the concordance.

Now we will apply the Cartesian product of each row from both tables to form pairs by splitting the table into two (each table with actual values as 1 and 0)

The complete Cartesian product has been calculated classification is done based on the condition

1. A concordant pair whenever the predicted probability for 1 category is higher than the predicted probability for 0 category.
2. A discordant pair whenever the predicted probability for 0 category is higher than the predicted probability for 1 category.
3. if both probabilities are the same, those pairs will be classified as tied instead.

Now Percentage of concordant pair is calculated as follows:

Now Percentage of discordant pair is calculated as follows:

Now C-statistic is determined in order to know the fate of the model

This is 83.315 percent, and any value greater than 0.7 percent or 70 percent is considered a good model to use for practical purposes.