# Interaction wipes out my direct effects in regression (non zero variable)

I have the following regression

$children = \beta_0 + \beta_1 \log(earnings) + \beta_2 grandparents + \epsilon$

and $\beta_1>0$ with $p$=0.01 and $\beta_2>0$ with $p$=0.01, and N is large (N>10.000) and grandparents takes values 0,1,2,3,4.

Then I add the interaction term ($\log(earnings)*grandparents$) to equation 1, such that:

$children = \beta_0 + \beta_1 \log( earnings) + \beta_2 grandparents+ \beta_3 \log( earnings)*grandparents + \epsilon$

and $\beta_1>0$ with $p$=0.01, $\beta_2$ is no longer statistically significant and also $\beta_3$ is not statistically significant.

I do not understand how to interpret the results and if the interaction term wipes out the direct effect of grandparents since $\log(earnings)$ is always different from 0.

There is a way to test the stat. sign. of the effect of Grandparents in the interacted model? (Thanks Maarten for your previous answer)

• Look here, & at Ray's answer in particular. There is no sense at all in worrying about the significance or otherwise of main effects if you have an interaction term in the model. Commented Oct 11, 2013 at 10:23
• The relevant concept here is 'marginal effect'. Ask instead whether (i.e. within what range or setting) that is significant. Commented Oct 11, 2013 at 14:34

$\beta_2$ in equation 2 is the effect of $grandparents$ when $\log(earnings) = 0$, i.e. $earnings = 1$. This is apperently outside the range of your data, so it is an extrapolation. The easiest way around that is to center $earnings$ before taking the logarithm or creating the interaction term at some meaningfull value withing the range of the data, for example, the median. That way the main effect of $grandparents$ will be the effect of grandparents when one has a median income instead of a fictional income of 1.