If examining the main effects of dichotomous categorical variables, the levels of which are binary and absolute (present/absent), must they be treated as factors rather than numerics?
Would the answer change if also including in one's regression model the interactions between those variables? Notably, when factorized the number of interaction predictors double (in light of additional contrasts, yes?). What gets lost when relying on the numeric * numeric interaction terms in such a model rather than various factor * factor versions of such terms?
I presume factorizing the variables is good form, regardless. However, I'm having difficult wrapping my head around what's differently captured in the interactions of dichotomous numerics vs. dichotomous factors.
I presume the response is a matter of the math, not the software, but if relevant, I am examining the above scenario in R.
Clarification: Note, I understand the mechanical process of factorizing a categorical variable and, in theory when to do it. My question relates more to the math involved when dealing with interactions between such dichotomous categorical variables. In a model containing both main effects and interactions, a model that treats the dichotomous predictors as factors includes additional predictor terms compared to a model in which the predictors are treated as numerics (as the interaction is then represented by multiple factor-level interaction terms and no longer simply a single numeric * numeric interaction term). When comparing these two models, why would the main effect values for these dichotomous predictors change?