I'm doing a simple AIC-based backward elimination model where some variables are categorical variables with multiple levels. These variables are modeled as a set of dummy variables. When doing backward elimination, should I be removing all the levels of a variable together? Or should I treat each dummy variable separately? And why?
As a related question, step in R handles each dummy variable separately when doing backward elimination. If I wanted to remove an entire categorical variable at once, can I do that using step? Or are there alternatives to step which can handle this?