I had a question regarding the composition of coefficents of a linear model in R.
Let's say my model is as follows, with three columns/independent variables: X, Y, and Z.
And my model is: (X * Z) + (Y * Z).
Is this comparable to performing the transformation X * Z, Y * Z before modeling ? I.e. mutate() creating new columns 'XZ' and 'YZ', thus my new formula is just XZ + YZ ?
In my intuition, I want to say 'no', because when you're running the model, it is holding all other variables constant.
I just ask because if it were possible, this would greatly simplify my analysis -- plus, having the multiplication in the equation makes it unbearably slow in R (like, days), and provided the limited computing resources I have access to, restricts me to processing incredibly small sample data sets.
However, I know this equation is the result I am after.
Any advice would be appreciated.