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Base SAS Procedures Guide: High-Performance Procedures
 

The HPBIN Procedure

Computing the Weight of Evidence and Information Value

PROC HPBIN can compute the weight of evidence and the information value.

Weight of evidence (WOE) is a measure of how much the evidence supports or undermines a hypothesis. WOE measures the relative risk of an attribute of binning level. The value depends on whether the value of the target variable is a non-event or an event. An attribute’s WOE is defined as follows:

upper W upper O upper E Subscript a t t r i b u t e Baseline equals l n StartFraction p Subscript a t t r i b u t e Superscript n o n minus e v e n t Baseline Over p Subscript a t t r i b u t e Superscript e v e n t Baseline EndFraction equals l n StartStartFraction StartFraction upper N Subscript n o n minus e v e n t Superscript a t t r i b u t e Baseline Over upper N Subscript n o n minus e v e n t Superscript t o t a l Baseline EndFraction OverOver StartFraction upper N Subscript e v e n t Superscript a t t r i b u t e Baseline Over upper N Subscript e v e n t Superscript t o t a l Baseline EndFraction EndEndFraction

The definitions of the quantities in the preceding formula are as follows:

  • upper N Subscript n o n minus e v e n t Superscript a t t r i b u t e: the number of non-event records that exhibit the attribute

  • upper N Subscript n o n minus e v e n t Superscript t o t a l: the total number of non-event records

  • upper N Subscript e v e n t Superscript a t t r i b u t e: the number of event records that exhibit the attribute

  • upper N Subscript e v e n t Superscript t o t a l: the total number of event records

To avoid an undefined WOE, an adjustment factor, x, is used:

upper W upper O upper E Subscript a t t r i b u t e Baseline equals l n StartStartFraction StartFraction upper N Subscript n o n minus e v e n t Superscript a t t r i b u t e Baseline plus x Over upper N Subscript n o n minus e v e n t Superscript t o t a l Baseline EndFraction OverOver StartFraction upper N Subscript e v e n t Superscript a t t r i b u t e Baseline plus x Over upper N Subscript e v e n t Superscript t o t a l Baseline EndFraction EndEndFraction

You can use the WOEADJUST= option to specify a value between [0, 1] for x. By default, x is 0.5.

The information value (IV) is a weighted sum of the WOE of the characteristic’s attributes. The weight is the difference between the conditional probability of an attribute given an event and the conditional probability of that attribute given a non-event. In the following formula of IV, m is the number of bins of a variable:

upper I upper V equals sigma-summation Underscript i equals 1 Overscript m Endscripts left-parenthesis StartFraction upper N Subscript n o n minus e v e n t Superscript a t t r i b u t e Baseline Over upper N Subscript n o n minus e v e n t Superscript t o t a l Baseline EndFraction minus StartFraction upper N Subscript e v e n t Superscript a t t r i b u t e Baseline Over upper N Subscript e v e n t Superscript t o t a l Baseline EndFraction right-parenthesis asterisk upper W upper O upper E Subscript i

An information value can be any real number. Generally speaking, the higher the information value, the more predictive a characteristic is likely to be.

Last updated: March 06, 2023