Interpreting coefficients with two interaction terms

[Magnus Jensen]

Hello,

I have a general question about how to interpret regression coefficients, when you have more than one interaction term.

I am aware that with one interaction term (between the independent variables X and Z), the coefficient of X should be interpreted as the effect of X on Y, when Z=0. To find the effect of X on Y when Z=1, I would add the coefficients of X and X#Z.

I suppose that if if I have two interaction terms (X#Z and X#W), the coefficient of X should be interpreted as the effect of X on Y, when Z=0 and W=0. But I am not sure how to interpret the coefficient of the interaction terms. Should the coefficient of X#Z be interpreted as the interaction effect when W=0 or does the inclusion of X#W not change how to interpret X#Z? And what does it mean if the coefficient of X#Z is significant or not?

Best regards,
Magnus Jensen

[Franz Hopp]

What helps me the most personally with tricky interactions terms is to plot them (e.g. assuming +1SD above the mean of the moderating variable as "high", and -1SD a "low)

[Magnus Jensen]

Hi Franz. Thanks for your advise but actually my question is specifically about the interpretation of the coefficients in the regression output when there are two interaction terms. Plotting the interactions is not my concern.

[Phil Bromiley]

As Franz said, plotting predicted values is an immense help in interpreting interactions. the margins and marginsplot command makes this easy.

Suppose you have a main variable x interacting with z1 and z2. With more than one interaction, the influence of x depends on both z1 and z2 although if you assume the interacting variables are not correlated, you can look at the derivatives independently. A significant parameter on the interaction means the influence of x varies with the level of the interacting variable.

While the if W=0 interpretation is technically correct, in many cases the interacting variable never or seldom equals zero so it is not necessarily informative. You might find Friedrich, Am J of Political Science, 1982 "In defense of multiplicative terms in multiple regression equations" helpful.