Interactions in ANCOVA and General Linear Models

Interactions in ANCOVA

We’re now faced with a choice. Do we keep the model as it is and move on to interpret the main effects, after it’s shown that there’s no sign of an interaction. Or do we follow the approach of model simplification and remove unimportant variables until we end up with a minimally adequate model that only includes terms that are supported? Well, unfortunately, there isn’t a definitive answer, but you can read different advice in different places.

Trends have also changed over time, and while model simplification used to be generally recommended, some stasticians now reccomend that we retain all terms. However, this can lead to ambiguity. It’s always safest to check if retaining or dropping the interaction changes the result and the interpretation of the analysis. Model simplification does have the virtue of simplicity. Dropping the interaction here produces a model with the main effects of water stress and ozone. We still have two regressions, but removing the interaction constrains them to share the same slope.