Weight of Evidence and Information Value

Calculation of Weight of Evidence(WOE)

Weight of evidence(WOE):

$$WOE_i=\log({{\% pos_i} \over {\% neg_i}})$$

where $i=1,2, ... k$, and $k$ is the number of bins.

Calculation of Information Value(IV)

Information Value(IV):

$$IV = \sum_{i=1}^k \{(\% pos_i - \% neg_i) \times WOE_i \}$$

WOE and IV work for both continuous and categorical variables.

CONTINUOUS/CATEGORICAL->CATEGORICAL(discrete numeric values)

Calculation

Step 1: binning(out of the scope of this post)

• CONTINUOUS: calculate pos and neg relative percentage of frequencies by intervals
• CATEGORICAL: calculate pos and neg relative percentage of frequencies by categories

Optionally there could be a MISSING bin.

Step 2: Calculate WOE for each bin

$$WOE_i = \ln({\%pos_i \over \%neg_i}) = \ln({pos_i / \sum_i pos_i \over neg_i / \sum_i neg_i})$$

Step 3: Calculate IV

$$IV_i = (\%pos_i - \%neg_i) * WOE_i$$

Step 4: Sum Up

$$IV = \sum_{i=1}^k IV_i$$

put everything together:

$$IV = \sum_{i=1}^k \{(\%pos_i - \%neg_i)\ln({\%pos_i \over \%neg_i}) \}$$

Example

(This data is made up and only for illustration of calculation)

bin	%pos	%neg	WOE	IV
MISSING	0.1	0.05	0.693	0.035
1	0.15	0.05	1.099	0.110
2	0.15	0.1	0.405	0.020
3	0.2	0.2	0.0	0.0
4	0.2	0.25	-0.223	0.011
5	0.2	0.35	-0.560	0.084
Sum	1.0	1.0		0.260

• WOE of (e.g.) MISSING: $WOE_{MISSING} = \ln(0.1/0.05) = 0.693$
• IV of (e.g.) MISSING: $IV_{MISSING} = (0.1-0.05) * 0.693 = 0.035$
• Total IV: $0.035 + 0.110 + 0.020 + 0.0 + 0.011 + 0.084 = 0.260$

Observations

• if %pos > %neg, WOE is positive
• if %pos < %neg, WOE is negative
• if %pos = %neg, WOE is 0
• IV is always positive