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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.

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thus my new formula is just XZ + YZ ?

No, the * operator in R expands into all lower-order terms.

terms(~(X * Z) + (Y * Z))

Simply adding a product term to a formula can be accomplished with the : operator (not that I assume you want to do this, but it can be useful to know).

terms(~ X:Z + Y:Z)

See the ?formula help page for details.

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