How to interpret regression negative interaction coefficient

Question

1. How do I interpret a negative interaction coefficient in multiple regression, with negative coefficients for main effects? 2) When I run the model without the interaction, the relationship is positive. Does anyone have any ideas why this is happening?

The variables in my model are all continuous. I'm testing the interaction between school climate (x) and activism predicting school belonging (y). I added grade level to the first block with my deviation scores for school climate and activism. Variables were centered before creating interaction term.

Answer 1

If the coefficients of your main effects are flipping directions after you've added an interaction term, and variables were mean-centered prior to constructing the interaction term (and you're using the mean-centered variables in the regression), then probably what's happening is that your variables are skewed. Interaction terms are uncorrelated with the constituent variables only when variables are normally distributed. So, you should interpret the interaction coefficient relative to the main effect coefficients from the model without the interaction term. It can also help to plot the interaction.

Answer 2

Don't waste much time thinking about the "main effect" coefficients when there's an interaction involved. The "main effect" coefficients only hold when the interacting continuous predictor has a value of 0. Furthermore, recall that the product of a negative "main" effect and a negative "interaction" coefficient is positive.

This page discusses a similar situation, with a positive interaction instead.

Focus instead on model predictions (with associated error estimates) for specific scenarios of interest. Whether or not you first center the predictors, you will get the correct results for such predictions from the model.