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In answer to a previous question factor pooling in model selection was discussed.
If a factor or categorical variable is to be dropped in model selection, should all levels be dropped simultaneously? If so, why?
The motivation for dropping factors is to aid model interpretation. For example, I might be interested in explaining the factors that influence customer behaviour when visiting a store and have a categorical variable "travel mode" with factors "walking, bus, private car, taxi, etc." In this context, I can remove all the dummy variables except "private car" because they have an insubstantial estimated magnitude and are not significant predictors of behaviour. I then end up with a "travelled in private car" vs "didn't travel in private car" variable and don't have to worry about troubling the reader with interpreting the other largely uninteresting variables.