Interaction term negative while main effects are both positive

Question

I'm writing a thesis and encountered a problem. My dependent variable is GINI and my independent variables are logGDPPerCapita and Individualism. I write a paper about the interaction between GDP per capita and Individualism (GDP*individualism). My OLS Model is:Yi = β0 + β1X1i + β2X2i + β3X1iX2i + αXc + εi

Where: Yi = GINI coefficient X1i = GDP per capita X2i = individualism Xc = controls1 εi = error term How can my interaction term (GDP*individualism) be negative if my main effects (GDP&individualism) are both positive? If I correlate GINI versus individualism and GINI versus GDP, I both get a negative correlation while the regression gives a positive coefficient. What do I do wrong or how do I have to interpret this?

Any help would be appreciated.

Answer 1

It seems like you might be misunderstanding what the interaction term is telling you. The sign of the interaction term does not depend on the main effects. It's generally easier to understand in the case where one of your main effects is a grouping variable rather than continuous.

If for example Individualism in your model is just a grouping variable with low and high levels coded as 0 and 1 respectively. Your results would be suggesting that observations with a high individualism show a shallower slope between GINI and GDP.

As to why your correlations are telling you something different than the regression, unless you are controlling for the other variables in your correlations (i.e. partial correlation) then it isn't answering the same question. Your regression is telling you that based on the values of all of these other variables, there is a positive relationship between GINI and GDP (where in this case, one of those other variables is the interaction between GINI and Individualism as well).