(2014-Sep-18, 15:26:09)Emil Wrote: P1 = predictor 1, P2 = predictor 2, etc.

V1 = outcome var 1, V2 = outcome var 2, etc.

I understand the labels, but I quoted this sentence "An interaction would be that a given predictor P1 is better at predicting variable V1 than P2, but that P2 is better at predicting V2 than P1" for another reason; it's that I don't understand the meaning of it. By saying V1 and then V2, you have in mind two different regression models.

Originally, the question was asked by Dalliard :

Quote:3) "Are some predictors just generally better at predicting than others, or is there an interaction effect between predictor and variables?"

Not sure what you mean by interaction here. The question is whether any of the predictors have unique predictive power.

What you said is whether or not the inclusion of interaction terms will affect the (independent) relative strength of your independent variables, within the same regression. But not two different ones.

Another thing I don't understand, it's because an interaction between predictors is aimed to answer the question about if adding interaction such as P1*P2, with or without squaring them (P1+P2+P2^2+P2^3+P1*P2+P1*P2^2+P1*P2^3), can change your independent coefficients. If the slopes are not linear but curvilinear, the addition of an interaction term will fit the data better. In general, what happens when an interaction is meaningful, is that the main effects (i.e., P1 and P2) will be attenuated. Even if one of the two predictors is more attenuated than the other, I don't think it's relevant here. The interpretation of the main effects becomes totally different when you add interactions. With an interaction, P1 and P2 are the effects net of the interaction, but the interaction itself includes and confounds the effect of both.

I remember several months ago when I attempted to perform regression with wordsum (dep) and race + SES (indep) variables. With the interaction of race*SES, the coefficient of race was near zero. A plot of the predicted values from the model revealed that at the very low SES levels, the BW gap in Wordsum was just meaningless, but that it increases considerably when SES increases. In such a situation, how can we say that race has become less important ?

You cannot say that SES is more important than race just because the interaction term nullifies the main effect of race, because the interaction term confounds the two effects. (when I say "more important", I am of course talking about the direct effects of the independent variables)