moderator enigma

[ajay pasi]

I need some help here_ statalist community

In a multiple regression analysis using large scale data.


I think B should theoretically be a moderator of A


So, after taking interaction of A and B, is significant. Moreover, A is significant. But B turns insignificant. Can B be termed as a moderator of A.

[Clyde Schechter]

Using the framework of statistical significance, which I wouldn't myself, but will work with here, the presence a moderating effect depends only on the significance of the coefficient of the interaction term itself. It is not necessary that either the A or B coefficient be statistically significant. Remember, also, that in an interaction model, the coefficient of B is no longer the marginal effect of B. In fact, in an interaction model, there is no such thing as the marginal effect of either A or B. Rather, A and B each have several, possibly infinitely many, different marginal effects, as many as there are value of the other variable. The coefficient of A in the interaction model is the marginal effect of A when B = 0, and the coefficient of B is the marginal effect of B when A = 0.

The marginal effects of B at other values of A can be calculated from the coefficient of B, the interaction coefficient, and the designated value of A using either the -lincom- command or -margins-. Note that the statistical significance of the marginal effect of B at a value of A is a problematic concept because mathematically there will always be some values of A for which the corresponding marginal effect of B is statistically significant and other values of A for which it is not. (Some of those values of A, though they exist mathematically, may not be possible values of A in the real world.)

For an exceptionally lucid explanation of interaction models, I recommend the excellent Richard Williams' https://www3.nd.edu/~rwilliam/stats2/l53.pdf.

[ajay pasi]

Thanks Clyde. It really helps. Appreciate that.