# Binning with Weights

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After working on the MOB package, I received requests from multiple users if I can write a binning function that takes the weighting scheme into consideration. It is a legitimate request from the practical standpoint. For instance, in the development of fraud detection models, we often would sample down non-fraud cases given an extremely low frequency of fraud instances. After the sample down, a weight value > 1 should be assigned to all non-fraud cases to reflect the fraud rate in the pre-sample data.

While accommodating the request for weighting cases is trivial, I’d like to do a simple experitment showing what the impact might be with the consideration of weighting.

– First of all, let’s apply the monotonic binning to a variable named “tot_derog”. In this unweighted binning output, KS = 18.94, IV = 0.21, and WoE values range from -0.38 to 0.64.

– In the first trial, a weight value = 5 is assigned to cases with Y = 0 and a weight value = 1 assigned to cases with Y = 1. As expected, frequency, distribution, bad_frequency, and bad_rate changed. However, KS, IV, and WoE remain identical.

– In the second trial, a weight value = 1 is assigned to cases with Y = 0 and a weight value = 5 assigned to cases with Y = 1. Once again, KS, IV, and WoE are still the same as the unweighted output.

The conclusion from this demonstrate is very clear. In cases of two-value weights assigned to the binary Y, the variable importance reflected by IV / KS and WoE values should remain identical with or without weights. However, if you are concerned about the binning distribution and the bad rate in each bin, the function wts_bin() should do the correction and is available in the project repository (https://github.com/statcompute/MonotonicBinning).

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