Low Predicted Probabilty Scores - Logistic Regression

[sachin01663]

Hello,

I have a logistic regression model which predicts likelihood of a customer to churn. The predicted probability scores range between .4299 to .00094.

Somebody confused me by saying 'The score of less than .5 means, less probability of churn as compared to 'average'. I think its incorrect because:

The average churn rate of my sample is 2%. This means 2/100 = .02 probability score.

Hence the highest probability score of .4299 means much higher chance to churn than average. Not necessarily the highest probability has to be above .5 score.

Is my interpretation correct?

[Reeza]

Depends on what event you modeled, assuming you modeled the event of a customer churning (which you should likely be using PROC PHREG/survival analysis) then 0.4299 means that's the probability of churning. I'm surprised your range is less than 0.5 the entire distribution you should verify your model first.

[sachin01663]

Yes, I modeled the event of churning but I used Proc Logistic. Is it surprising that the highest predicted probability score is .499 when average churn rate is 2% for the sample I am using i.e. the probability score should be .02 for average churn? Am I wrong saying this?

[sachin01663]

Sorry, I mean the highest score is .4299

[StatDave]

That statement about what .5 means is incorrect. A predicted probability of, say, 0.4 simply means that the probability of churning that was predicted by your model for that person (or any person with that same setting of the model predictors) is 0.4. The low range of predicted probabilities that you note is not inconsistent with the low average churn proportion of 2% that you observed. Of course, changing your model will change the predicted probabilities, and it is possible that a different model will be better and discriminating between churners and nonchurners.