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I am running a logistic regression with customer event data with multiple predictors. However, one variable is extremely important, alone predicting 60% of the customers for the event. When this main predictor is included in the model, other predictors add very little to prediction over and above this main predictor.

This main predictor is not a post event variable. The variable has full business support to be in the model.

  • Given this, is it still okay to retain this main predictor variable in the model?
  • Does this suggest that there is anything wrong with the model?
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  • $\begingroup$ @ayush Could you edit your question clarifying what you mean by "certain values" and "event rate"? Could you explain what is making the situation "not very comfortable"? $\endgroup$ – Jeromy Anglim May 5 '11 at 9:59
  • $\begingroup$ The values are the value that categorical variable is taking..Lets say when it takes value C most, 60% of the times, the event happened(in historical data)and when it took value A 50% of time event didnt happen. I am saying its not very comfortable situation to be in because generally a model is termed bad when only 1 variable is making it predict good %age of events. Any addition to this variable is improving the prediction power by decimal values. Hope that makes the question more clear $\endgroup$ – ayush biyani May 5 '11 at 10:14
  • $\begingroup$ @ayush Thanks. That does clarify things. I'll update your question to make this clear. $\endgroup$ – Jeromy Anglim May 5 '11 at 10:26
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I understand your gut feeling. But depending on the type of response and predictor, this has not to be unsual (example: response = "weight", predictors "height" and others with presumably less meaning like "state", "favorite movie" etc.).

However, you should check that for the creation of the predictor only information has been used which was available at that time.

Here is an example: Suppose you want to predict an event of the next day. You have raw data from day 1 to 10. Now you create one predictor by calculating a statistic over all 10 days and other predictors using only "local" information (i.e. directly extracted from a single event on a single day, i.e. "event start time"). Now you build a model from day 1 to 5 using this predictors to predict the events on day 6. The model is flawed because it contains information from day 6-10, information which is never available when building the model for real (i.e. not simulation) usage.

If this check has been succesful (I guess you mean that with "not a post-event variable"), then it shouldn't be a problem. In one of my projects, something similar occurred. Checking on the meaning of the variables indeed revealed, that the detected relationship (i.e. variable importance) was trivial, but true ;).

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  • $\begingroup$ @stefen -- thanks..Yes, I have done this check. This information is absolutely available in my model. So that gives me my answer. But there is something more which I wanted people to ponder upon..Removing this variable and keeping just others giving me a miserable prediction is indeed an indicator that when I dont keep this variable, all others fail in the combined way to give me anything fruitful..Going into detail..this itself means to business that if you want to recognize event guys just look for this indicator and you have got most of 'em. what say ?? $\endgroup$ – ayush biyani May 5 '11 at 10:44
  • $\begingroup$ @ayush Yes, as far as I see from here (if the predictor/predictor information is always available). Does the meaning of the predictor does not indicate this ? 1. As I said, I recommend to talk to someone with domain language, if it is not instantly clear. 2. Although you hit 60%, you still miss 40%. So your precision is solid, but not excellent. Depends if this is enough for your business. $\endgroup$ – steffen May 5 '11 at 12:07
  • $\begingroup$ @stefen..Thanks..Yes, I understand your point. Yes,I am hitting 60% with this and some more variables..As it seems right now, I would not be able to take it to more than 65 %. $\endgroup$ – ayush biyani May 5 '11 at 12:29

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