I'm trying to model the data (not make predictions) and am NOT using lasso for this, just want to know if my plan is somewhat reasonable here:
I'm modelling for a "yes/no" response variable, so I used logistic regression and stepwiseAIC for variable selection. The results gives me 13 parameters: 8 covariates with 5 interaction terms (several parameters are not significant on their own but have a significant interaction).
When I instead used stepwise based on BIC criteria, I only got two covariates and their interaction. Much simpler of course, but the deviance increased quite a bit. Since all the parameters in the small model were also in the large one, I considered the small one to be nested, so I did the deviance test (likelihood ratio test) and it gave me a p-value of nearly 0, indicating that the larger model is better.
Am I doing it right?