When I added some control variables at Level 1 in a Multilevel Model, my interaction term changes its sign from positive to negative as well my main effect of one variable. Why is that happening? It would be great also, if you could recommend some resources to understand and handle this.
Thanks
Ibrahim
When adding additional covariates (i.e., predictor variables) the effects estimated are conditional in a statistical sense on the covariates. Therefore, they are not the same effects so often will not be the same sign. It would be good if the software estimating multiple regressions didn't just say the effect for x1, but correctly said it was x1|x2,x3,x4 (assuming 4 predictors).
This will be discussed in all introductory stats books that cover multiple regression. These conditional effects may become less reliable, so be careful. If you have lots of predictors you might consider seeking a more sparse solution (Hastie et al's Elements of Statistical Learning covers many candidate techniques).
One of the assumption of the regression model is all predictors are independent, if this is true , adding or removing one variable, say x2 , following Daniel example, the effect of X1 should be no change at all. However, it might not be true. if x1 and x2 are correlated, adding x2, the effect of x1 could be changed irregularly.
For interaction, adding X1*x2 in the regression, if x2 is numerical, then the main effect of X1 on the regression out put is not overall effect anymore, it is the conditional effect, when x2=0, you can calculate the conditional effect for any given x2 value, which is beta1 (x1)+betata2(x1*x2)*x2, ..., the beta1 of x1, could be very different from the overall x1 effect in the model without interaction.
if x2 is binary, say gender, x2=0, male, x2=1 female. then most procedure using 0-1 coding, with interaction, the x1 effect is for male only.
The interaction is the difference of x1 effects between female and male.. To find the female effect, you need add the male effect (beta of x1) + the interaction beta of x1*x2.
The effect of x1 could be very different between genders, even in different direction .
Without interaction, you assume there is no difference of x1 effect by gender.
Hope it help.
The change in sign from positive to negative when you include the moderator variable simply means the interaction between you IV and your variable just included reduce the effects on DV. Thus, you can say that the interaction brings reduction on DV. Sometimes the interaction also may enhance the effects on DV. In this case you will find positive sign for interaction variable.
yuanzhang Li ·How would you then interpret a sign change on the beta coeff. on x2, if it is a gender dummy after the inclusion of the interaction?
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