Encoding with the Weight of Evidence

The Weight of Evidence (WoE) was developed primarily for credit and financial industries to facilitate variable screening and exploratory analysis and to build more predictive linear models to evaluate the risk of loan default; that is, to predict how likely money lent to a person or institution is to be lost.

The WoE is computed from the basic odds ratio:

Here, p(Y=1) is the probability of an event occurring. Therefore, the WoE takes the following values:

• WoE = 0 if p(1) / p(0) = 1, that is, if the outcome is random
• WoE > 0 if p(1) > p(0)
• WoE < 0 if p(0) > p(1)

This allows for a direct visualization of the predictive power of the category in the variable: the higher the WoE, the more likely the event will occur, and in fact, if the W0E is positive, the event is likely to occur.

Logistic regression models a binary response...