Trying to use PROC OPTMODEL for monotonic supervised optimal binning of a continuous predictor

[Top_Katz]

Hi @Ksharp !

A hockey stick is not necessarily non-monotonic.  I think the idea is that you have a flat stretch and then a sudden increase, rather than constant proportional increases.  For example, suppose you're offering discounts on a product.  Perhaps very few people buy at 5% or 10% or 15% or 20%, but something about a 25% discount grabs them and you get a sudden uptick, 40% even more, 50% way more, 60% through the roof.  I'm sure you could imagine such scenarios.  Also, not every effect is monotonic.  For example, if you're selling Buicks (a General Motors brand of automobile), low income people probably don't buy very many.  Middle income you start to see more interest, and it likely peaks in the very high middle income range.  But wealthier people buy more luxury brands, like Cadillac and Lexus and Mercedes.  If you wanted to model likelihood to purchase Buicks using income level as a linear predictor, you could use binning (or some other non-linear transformation) to transform the raw income levels.

[Ksharp]

Top , Maybe I misunderstood the point of Siddi. Hockey stick is still monotonic. And I understand the example in reality you refer to. But stand on the statistic point , woe should be monotonic, if you can't make woe monotonic,should not include this variable in logistic model.

[Top_Katz]

Hi @Ksharp !

If you have a predictor variable with a measurable effect on your outcome and you don't include it in your model, then your model likely will be mis-specified.  Of course, if the effect is non-monotonic  and you're building a regression model, then you have to transform the predictor first to linearize the relationship.  You can do that with bins or splines or other functions.  The transformed variable will have the proper WoE relationship by design.  I don't think I'm telling you anything you don't already know.  I also understand that for credit scorecards, people will be suspicious of non-monotonic relationships and won't want to try to transform them; luckily there don't seem to be many meaningful non-monotonic relationships in credit scorecarding.  But marketing is a different beast.

[Ksharp]

Hi Top,

"If you have a predictor variable with a measurable effect on your outcome and you don't include it in your model, then your model likely will be mis-specified. "

I don't think so. If not include that non-monotonic variable ,only make the power of prediction model lower ,doesn't affect the use of scorecard.

Or you can bin it into just two groups, that must be monotonic .

"I also understand that for credit scorecards, people will be suspicious of non-monotonic relationships and won't want to try to transform them"

If need fit non-monotonic relationships, that need include interaction effect in model ,but that is uneasy to explain,so in score card only include main effect for the better explanation . .

[Ksharp]

Hi Top,

Just let you know. I send a private a message to Naeem Siddiqi via LinkedIn.com just a minute before .

Hope he could explain all these for you .

Actually I have another question for Naeem, Do all parameter coefficient must be positive/negative ?

I opinion is should be both positive and negative . But in his book didn't mention it yet .