# Interaction in Hierarchical Regression

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

• Dependent Variable is Well-being.
• Predictors are A-H, as well as the interaction of G and H.

Question

1. 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.

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()


1. 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.

1. 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.

• Thank you so much for your detailed explanation. It is really helpful.After a slope test, only high in H can predict DV(well-being) while low and average H were not significant. Feb 17, 2020 at 4:41
• Thank you so much for your detailed explanation. It is really helpful. After a slope test, only "high in H" can predict DV(well-being) while low and average H were not significant. I can make an explicit statement only from one direction? Feb 17, 2020 at 4:51
• I am not familiar with the slope test you mention, @StudentY, and cannot speak to that. From the stage 2 model, H has a significant association with the outcome, adjusting for all the other covariates. That's what I would feel comfortable reporting. Feb 17, 2020 at 15:06
• Thank you again, Erik Ruzek!I appreciate it so much!! Feb 17, 2020 at 15:21
• Yes, I'll do it definitely when I become eligible to vote after earning 15 reputation points! Feb 18, 2020 at 1:33