I was asked to review a report and in the regression analysis several independent variables were shown to not have a significant relationship with the dependent variable. While I have no access to the raw data, to me it was obvious that there must be at least one significant interaction effect among the independent variables and hence I decided to start off 2014 by writing about interactive effects in regression!
This can be a very long discussion but to be in-line with my approach here at IntroSpective Mode, is we keep things brief and concise, and leave it up to the reader to go elsewhere for the details if you really need to.
Often, in fact almost always, the effect of individual independent variables is lesser than the effect of interacting independent variables on the dependent. Think about it: We live in an interactive world where everything is intertwined with each other! So why would we expect no, or little interaction among our independent variables. I know why: Researchers don’t think about it. Likely they have never been trained to look at interaction effects!
Lets briefly define it:
Main effect: the impact of any single independent variable on a dependent variable.
Interaction effect: The combined effect of two (or more) independent variables on a dependent variable(s) in addition to the main effects of the single independent variables. Here we rightly assume that the effect of one independent variable depends on the level of the other independent variable(s). In other words, the difference between groups on one treatment variable depends on the level of a second treatment variable.
Don’t forget the Blocking Variable (grouping variable) which we don’t control or manipulate at all. Its often used as a “control variable” which reduces error variance
Enough said for now. Read more about it elsewhere and next time don’t conclude that there are no significant effects by individual independent variable without having a look at possible significant interaction effects.