Deal with categorical variables in regression with overlapping classes I want to perform a OLS regression analysis on some venue hire data (to get cost of venue hire). I have many categorical variables and some of them have correlated / duplicated information e.g. An example is one category called 'External_Hire' that defines whether you can hire external caterers for the venue. It has the following values:

*

*'From Approved List Only'

*'Any External Hire'

*'Not allowed'

Then I have another variable called 'External Hire Fee' which defines whether a fee is required for the 'Any External Hire' option, it has values:

*

*'Fee Required'

*'No Fee Required'

*'No External Hire Allowed'

Whenever the 'External Hire' category has value 'Any External Hire' then the variable 'External Hire Fee' must have values 'Fee Required' or 'No Fee Required'. Otherwise, it will have 'No External Hire Allowed'.
I could therefore combine these 2 categorical variables into a combined category with values:

*

*'From Approved List Only'

*'Not Allowed'

*'Any External Hire (Hire Fee Required)'

*'Any External Hire (No Hire Fee Required)'

My question is, should I keep these variables as separate categorical variables, and then dummy encode them separately or should I combine them into a single variable as above and then dummy encode that? Does that even make a difference?
Is it wasteful computationally to do it one way or another? Are there further considerations for different models e.g. Decision trees?
Should I review the relationship between these categories and the response variable?

My gut feeling, which is often wrong, is that combining the two variables into a single, non-redundant one is preferable.
In the extreme case, you could have two variables that are completely overlapping. I.e. one is just a renaming of the other. If you keep them separate you are going to have issues with collinearity but if you combine them you just have more verbose names.
Also, if you keep variables separate you allow the model to consider parts of the parameter space that you know beforehand are not allowed. This means you spread the available information more thinly than necessary (apologies for sloppy phrasing).
On the other hand, by combining variables you lose information about their individual contribution. You may or may not be concerned about this.
