Marginality of Main Effects and Interactions

Main effects and interactions

The two linear model analyses with interactions explored above have different outcomes. In one case, the analysis supported the interaction, and in the other example, it didn’t. This presents the issue of if it’s better to retain all terms in a statistical analysis or if we should try to simplify models by removing the terms that appear to be unimportant. This issue also applies to unsupported interactions. However, more recent sources suggest that we should keep unimportant interactions in the model as they don’t behave unexpectedly, such as have an unexpected sign. We’ve extended the typical ANCOVA model with one continuous variable and one factor into a general linear model that adds a third variable, in this case, a factor. One complexity that we previously skipped over was exactly the issue raised here—that the importance of the main effects varied depending on whether or not interactions were present in the model.