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I have four logistic regression model that predicts likelihood that customer make a purchase in 4 product categories(purchase event is rare and oversampled 50-50 for each model). Is there way to normalize so the scores comparable across product ?

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What you want to do is called probability calibration. See wikipedia article. There are two common approaches, one is called Platt scaling or Platt calibration, another is called isotonic calibration, as well as some less common approaches. As a rule of thumb, if you allocated up to 200 observations for calibraton, Platt calibration is better, while if you use more than 5000 examples for calibration, the isotonic calibration is better. If there are 200-5000 observations, it depends on the dataset.

Whatever you do, don't use same observations for training and for calibration. You should allocate part of your training set for calibration, and use it for this purpose only.

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  • $\begingroup$ thank this is helpful . Does this work for multiple models and after calibration multiple models can be compared? $\endgroup$ – Naveenan Apr 22 '16 at 3:33
  • $\begingroup$ As far as I understand you have 4 models, and you may calibrate each model independently. I believe that they can be compared after calibration. $\endgroup$ – user31264 Apr 22 '16 at 8:39

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