I'm making a credit scoring model and I get that one variable has Information Value (IV) more than 1, is that possible?

Formulas are pretty simple for weight of evidence(WoE) and information value(IV)

$$WoE_i = \log \left( \dfrac{\dfrac{g_i}{g}}{\dfrac{b_i}{b}} \right)$$ where $g_i$ represents the number of goods (no default) in category $i$ of variable $x_i$, $b_i$ represents the number of bads (default) in category $i$ of variable $x_i$, $g$ represents the number of goods (no default) in the entire dataset, $b$ represents the number of bads (default) in the entire dataset, $N(x)$ is the number of levels in the variable $x$, that is number of categories $$IV = \sum_{i=1}^{N(x)}\left( \dfrac{g_i}{g} - \dfrac{b_i}{b} \right) \cdot WoE_i$$

Also, what is a perfect fit in the model?

By the perfect fit I understand that there is just two categories in x: the first includes all goods and the second includes all bads. In that case when computing $WoE_1$ I get 0 in $log$ denominator, because $b_1 = 0$. When computing $WoE_2$ I get 0 in $log$ numerator, because $g_2 = 0$. Does that make sense?


1 Answer 1


IV of greater than 1 is possible, and very common. Assume you are using the natural logarithm? You can deduce the limit by using two categories. Say the model/feature can separate the good and bad perfectly, and let $G_1, B_1, G_2, B_2$ be the proportion of goods and bads falling in the two categories. Then let $G_1 \to 1, B_1 \to 0, G_2 \to 0, B_2 \to 1$. So we are assuming a large pool and the Model is perfectly separating the goods/bads. Then easy to check that that the IV equals:

$\ln \left( \frac{G_1}{B_1}\right) -\ln \left( \frac{G_2}{B_2}\right) $

And minus sign in front of the second means you can invert the second ratio, and hence it is 2 times the log of a quantity that goes to infinity, so you can get infinity. But in practice you should be getting IV of less than 10 most of the time.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.