24 September 2023

Understanding R Formulas

by markolenik

Why is the formula x ~ (y + z)^2 equivalent to x ~ y*z? Here are the exact transformation steps:

• Step 1: Start with the formula x ~ (y + z)^2 and take the square, we get y^2 + z^2 + 2*y*z.
• Step 2: In R, the square of a term in a formula (like y^2 or z^2) just refers to the term itself. So, y^2 becomes y and z^2 becomes z. Now, the formula is x ~ y + z + 2*y*z.
• Step 4: The coefficient 2 in front of the interaction term y*z doesn’t change the nature of the interaction, so it is dropped. Now, the formula is x ~ y + z + y*z.
• Step 5: Since y*z is a shorthand for y+z+y:z, we get x ~ 2y + 2z+ y:z. Again we can get rid of the coefficients, which simplifies to x ~ y + z + y:z, i.e. x ~ y*z.