Interaction in Hierarchical Regression I need some helps to interpret results of a hierarchical regression that included an interaction in the last stage.


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*Dependent Variable is Well-being.

*Predictors are A-H, as well as the interaction of G and H.


Question


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*Is stage 3 only for the interaction analysis purpose? Which stage should be used to report significant predictor G and H, stage 2 (without interaction) or stage 3 (with interaction)?


2.The variable G changed negative (stage 2) to positive (stage 3), while the interaction effect is negative. Still, relation between G and DV. is positive over all?
Thank you.
 
 A: Welcome to the site, StudentY. The key thing to remember with interactions is that in a model with two interacting variables, the "main effects" coefficients for those variables are their coefficient at the 0 value of the other variable. 
So, in your stage 3 model, the coefficient of G is the change in the outcome for a 1 unit change in G at H==0. Likewise the coefficient of H is the change in the outcome for a 1 unit change in H at G==0. 
The interaction is the degree to which the slope of G is altered for every unit increase in H. Or equivalently, the degree to which the slope of H is altered for every unit increase in G. 
It is easiest to understand these by graphing them. If you are using R, this can be done with the ggeffects package:
library(ggeffects)
ggpredict(stage3, c("G", "H")) %>% plot()

In terms of your questions:

  
*
  
*Is stage 3 only for the interaction analysis purpose? Which stage should be used to report significant predictor G and H, stage 2
  (without interaction) or stage 3 (with interaction)?
  

Yes, stage 3 is the model you want to use to understand your interaction and stage 2 is the model to understand the unique effects of predictors G and H. 


  
*The variable G changed negative (stage 2) to positive (stage 3), while the interaction effect is negative. Still, relation between G
  and DV. is positive over all?
  

The reason that variable G changed is because, as said above, in this model the coefficient on G is telling you about the association between G and the outcome at H==0. At H==0, the association is positive. But when you adjust for all levels of H in stage 2, the overall association between G and the outcome is negative. 
By the way, when you report results from mixed models, you should report the variance estimates in addition to the coefficients. 
