Let's imagine I build a scorecard with a single binned variable that can only take two values. In the weight of reference framework I would replace the two possible values by their weight of evidence and run a logistic regression that would return the regression coefficient for each of the two possible values and the intercept. Then the score for each of those categories would simply be the product of the regression coefficient for the category times its weight of evidence (+ the intercept).

My question is simply, should the regression coefficient be the same for all bins of the same variable or can it be different? I'm asking because, if the weight of evidence is monotonic and the regression coefficient does not change across bins of the same variable, this would guarantee that the score is also monotonic. However, while using scorecard packages in the past, I have sometimes seen that, for a variable with a monotonic weight of evidence, bins with a different weight of evidence end up having the same score. Which to me indicates that their regression coefficient is not the same. I would appreciate some references as well.

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    $\begingroup$ Which scorecard package are you using and in what program? Can you provide an example with reproducible code? $\endgroup$ – André.B Oct 24 '19 at 21:36
  • $\begingroup$ I am talking about proprietary software (Model Builder from FICO). It is there where I see bins with very different weights of evidence with the same score after the CONSTRAINED minimization. That is why I assume that the regression coefficients are difference for each bin, but the constrained minimization does not allow that the WoE ordering is changed (but it does not prevent that two bins are virtually merged into the same one -- by assigning the same score) $\endgroup$ – edd Oct 25 '19 at 13:40

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