My analysis includes, among others, three independent variables: X (interest rate), Y (type of rate; it is a dummy), and Z (likelihood of bankruptcy). I have transformed the latter into a categorical variable ZZ. To do so, I have used deciles (i.e., ZZ is 1 if the value of Z is lower than the 10th percentile of Z, etc). In some specifications of the model, I use the interaction term X·ZZ, and in others, Y·ZZ and X·Y·ZZ.
However, I have now the following doubt. Leaving aside other considerations, is there a statistical reason to use ZZ instead of Z (i.e., the categorical version of a continuous variable instead of the variable itself) in interaction terms? Does it make any difference the fact that the other variable in the relevant interaction terms is a dummy (Y) or a continuous variable (X)?
Thanks in advance.