Interpreting the coefficient of two continuous interaction terms

[Fimi Karimi]

Hello everyone,

I am confused about interpreting the coefficients of two continuous interaction terms. I would greatly appreciate it if you could help me understand the meaning of these coefficients.

Does it imply that the quota, on its own, has a more influential effect compared to when trust in society increases or trust lose its effect with the presence of formal rules? In column 2, when trust is interacted with the rule of law, trust is no longer significant, and the coefficient of the interaction term is smaller than that of the rule of law. I am uncertain if this suggests that trust works better in conjunction with effective regulatory institutions in society, or if it means that when regulatory institutions are efficient, trust becomes less impactful or even redundant. Could you please clarify this?

[Maxence Morlet]

Let's focus on your first column, and assume the model you used is OLS.

When quota is zero (unless you demeaned quota), when trust rises by 1, the outcome rises by 2.987. When trust is zero, a unit rise in quota increases the outcome by 5.034 (I do not know the unit of the outcome). When quota increases by 1, it significantly increases the marginal effect of trust on the outcome by 0.527.

[Maxence Morlet]

With this being said, I recommend you demean quota and trust and all continuous variables you want to interact.

[Carlo Lazzaro]

Fimi:
see https://cscu.cornell.edu/wp-content/uploads/centering.pdf

[Richard Williams]

Here is my handout on continuous interactions. Centering and/or the use of marginal effects can help.

https://www3.nd.edu/~rwilliam/stats2/l55.pdf

This handout talks about interaction effects when one variable is categorical and the other is continuous

https://www3.nd.edu/~rwilliam/stats2/l53.pdf

Incidentally, centering doesn't have to be about the mean. It could be some other relevant value. For example, if the var is years of education, you might subtract 12 from each case, so that a value of 0 means high school graduate.

[Fimi Karimi]

Thank you so much, Maxence for your help!

[Fimi Karimi]

Thank you, Richard. The documents you sent were super helpful.

[Fimi Karimi]

Thanks for the link you shared with me, Carlo.

[Fimi Karimi]

I came across another question. My Trust variable is a PCA of 5 variables. Do I need to demean (center) Trust as well, or is it enough to center the other variables in the interaction terms? When I center the other variables but not Trust, all other coefficients remain the same. However, the coefficient for Trust changes and becomes strongly significant. When I try to center Trust like other variables, the new variable is the same and It doesn't change.

[Richard Williams]

Isn’t the mean of Trust already 0 when you create it? If in doubt, run descriptive stats on it.

[Fimi Karimi]

Oh, my bad. Yes. It's zero. Thank you so much.