I am working on a census-related project where I am interested in assigning to everyone a score that estimates the probability they will have a demographic characteristic of interest. In this case, the demographic characteristic of interest (say, having red hair) is quite rare. (Roughly 15,000 out of 1,000,000 people have red hair.)
Though it is easy for me to gather all of the data, due to computational efficiency I am down-sampling my 0s and applying corrections from King & Zeng, 2001, Logistic Regression in Rare Events Data.
In an attempt to predict this rare event, I have a couple of questions:
When conducting logistic regression with rare events, how might you suggest executing feature selection?
Is PCA acceptable to use when dealing with logistic regression? With rare-event-corrected logistic regression? Do you suggest other methods of ensuring independent variables are orthogonal for this type of model?