The data include 3 equally sized subsets A, B and C, belonging to two classes:

  • A belongs to class 1.
  • B and C belong to class 2.

The prior probabilities of an observation coming from class 1 and class 2 are thus 0.33 and 0.67.

Next, a logistic regression model is fitted on all 3 subsets.
The predicted value of this model is the probability of an observation belonging to class 2 given his predictors values.

In reality I know for sure that I will never have observations belonging to subset C. So the observations will allways originate from either subset A or B and since both subsets are equally sized, I can assume that the prior probability of a new observation to be from class 1 or class 2 will changes to 0.5.

My questions are:

  1. Given the knowledge that all observations are from either A or B but not C, can you still interpret the predicted values as the probability of being in class 2 with the logistic regression model fitted on all 3 subsets?
  2. Are these probabilities biased because of the changed prior probability of being in class 1 and 2?
  3. If so, how to correct for this?
  • $\begingroup$ As long as you specify the outcome variable the same, where 1=belong to class 2, and 0=belong to class 1, for both models, I believe the interpretation will be the same. $\endgroup$ – robin.datadrivers Feb 22 '15 at 23:17
  • $\begingroup$ Linked: stats.stackexchange.com/questions/6067/… $\endgroup$ – Zhubarb Feb 23 '15 at 9:29
  • $\begingroup$ @Zhubarb Did I understand correctly from the link above, that the probabilities are indeed biased and a possible solution would be to perform weighted logistic regression? $\endgroup$ – statastic Feb 23 '15 at 10:22
  • $\begingroup$ It's not clear to me -- how did your priors arise? Please explain the second one in detail. $\endgroup$ – Glen_b Mar 5 '15 at 2:52
  • $\begingroup$ @Glen_b I hope it's more clear now :) $\endgroup$ – statastic Mar 5 '15 at 11:28

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