# Why does sign of a main effect change in logistic regression when adding an interaction?

I am having problems to understand, and therefore to interpret, why the coefficient of one of my independent variables sign change when I add an interaction. My dependent variable is presence/absence of a bird species and my independent variables are the proportion coverage of an specific plant species ("plant", continuous) and observed species richness ("Sobs", discrete).

This is my logistic model without interactions: $$\newcommand{\logit}{{\rm logit}}\newcommand{\presence}{{\rm presence}} \newcommand{\plant}{{\rm plant}}\newcommand{\Sobs}{{\rm Sobs}} \logit(\presence) = -3.93 + 46.81*\plant + 0.36*\Sobs$$ This is easy to interpret, but when adding interaction (my most plausible model), the sign for the effect of plant coverage changes to negative. $$\logit(\presence) = -2.47 - 32.44*\plant + 0.07*\Sobs + 15.63*\plant*\Sobs$$ Why this is happening and how can I interpret this best model?

• Just to add to previous answers, when there is a real interaction, the main effects have no meaning on their own. Oct 4, 2016 at 19:19

If you take the partial derivative of $logit(presence)$ wrt $plant$ you get $$\frac{\partial logit(presence)}{\partial plant} = -32.44 + 15.63*Sobs$$
Which means the effect of $plant$ on $logit(presence)$ is an increasing function of $Sobs$. When $Sobs= 0$, the effect is going to be $-32.44$. When $Sobs = 10$, the effect is going to be $-32.44 + 156.3 = 123.86$
Only for high values of sobs you plant has a positive effect on presence. For low value of sobs plant has a negative value on presence.