In: Statistics and Probability
Econometrics question - Can you include multiple two-way interaction terms in a regression model? Will doing this have any consequences on the estimates or the interpretation of the coefficients?
i. e. Y=X1+X2+X3+X4+(X1*X2)+(X1*X3)+(X1*X4)
Yes, multiple two-way interaction terms can be included in a regression model to find out whether there is significant interaction effect on the dependent variable or not. There will be consequences on the interpretation of the coeffiients in the following manner:
Earlier, if there were no interaction terms, the regression equation is:
Y = B0 + B1*X1 + B2*X2 + B3*X3
Ynew = B0 + B1*(X1+1) + B2*X2 + B3*X3
Yold = B0 + B1*X1 + B2*X2 + B3*X3
Difference = B1
The effect of variable X1 on Y is such that with one unit increase in X1, Y increase by B1 units which does not depend on any other independent variables or there is no interaction.
If there are interaction terms present in the regression model:
Y = B0 + B1*X1 + B2*X2 + B3*X3 + B4*X4 + B5*(X1*X2) + B6*(X1*X3) + B7*(X1*X4)
The effect of one unit increase in X1 from let's say X1 to (X1+1) will be:
Ynew = B0 + B1*(X1+1) + B2*X2 + B3*X3 + B4*X4 + B5*(X1+1 * X2) +
B6*(X1+1 * X3) + B7*(X1+1 * X4)
Yold = B0 + B1*X1 + B2*X2 + B3*X3 + B4*X4 + B5*(X1*X2) + B6*(X1*X3)
+ B7*(X1*X4)
Difference = B1 + B5*X2 + B6*X3 + B7*X4
Hence, now the interpretation of coefficients change in such a manner that if there is a one unit incraese in the X1 variable with other variables constant, the variable Y increases by an amount which is dependent on the current levels of the other variables. Hence, this means that there is an interaction effect.