I want to choose variables for building a logistic regression model by comparing the GOF of different types. The problem is, that some of the candidatecandidates have some missing values so I can´t use the likelihood ratio test for comparing models, given that when I want to compare models with those variables they are not nested anymore.
So after exploring some options, I found that AIC or even BIC might be an option for that purpose. Is either of those a valid option?
I am not familiar with the use of BIC, is it the same as AIC, where the smaller the value is, the better?