I am sorry if this is very trivial and a repetition. I could not find a direct question on the website that addresses my question
I am studying the relationship between X1 (independent variable) and Y (outcome) variable. X2 is my moderating variable
What is the difference between these two following regression equations :
Y = b1 + b2X1 + b3X2 +b4 X1X2 ... (1)
Y = b1 + b2X1 +b3 X1X2 ....... (2)
X1 and X2 are not correlated and Since X2 is my moderating variable , I am not interested in the main effects of the moderating variable..in that case would equation 2 be okay where I take only the interaction effects? Is equation 2 okay to use? If not, what are the problems. Any inputs will help. Mainly I am trying to understand if dropping main effects estimation of the moderating variable will be of any issue?
I did read this - The regression analysis that tests for an X1 by X2 interaction must also include the X1 and X2 variables as predictors. In fact, the X1 × X2 product term represents an interaction only in the context of a model that also includes X1 and X2 as predictors (Cohen, 1978).
However I have seen models that do not include the moderating variable as a predictor. When does one do this. How do I interpret this?