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Including the interaction but not the main effects in a model

I have an experimental design with pretest and posttest. Two groups, experimental and control group. I am interested in finding whether there will be a difference between experimental and control group at the posttest, controlling for pretest. Therefore, I run ANCOVA with pretest as covariate, posttest as DV, and group as IV.

I am also interested to see if there will be a gender differences for the experimental effect. Thus, I am interested in looking at the interaction term group*gender. I am not interested in looking at gender main effect alone, as it doesn't mean much to this experimental design.

I customized the model and excluded the main effect of gender, and the results showed only the main effect of group and the interaction effect of group*gender.

Is this okay, or do I need to run a full model including gender main effect? Thank you.


marked as duplicate by whuber Sep 6 '12 at 15:04

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  • $\begingroup$ I realized that excluding the gender main effect would affect the p value of both the group main effect and the interaction effect. Which is why I am unsure of whether to exclude it or not. $\endgroup$ – Wei Sep 6 '12 at 3:57
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    $\begingroup$ This question should also be of interest: do-all-interactions-terms-need-their-individual-terms.... $\endgroup$ – gung Sep 6 '12 at 12:20

There's a rather extensive and interesting discussion of this issue in this thread. To summarize, excluding a main effect makes the interpretation of your parameters tricky. However, there are a few situations (discussed in the thread) where this makes sense, such as a pure prediction model.


I see nothing wrong with it. Another approach (but not preferable) is to see if there is a significant change from baseline due to the intervention.

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    $\begingroup$ I don't think this is wrong, but I do think it's dangerous advice to tell someone it's OK to exclude the main effects terms but include the interaction. You may want to read through the questions @user1188407 & I have linked. $\endgroup$ – gung Sep 6 '12 at 12:23
  • $\begingroup$ @gung I have been involved in some of the posts discussing including interactions without main effect terms. Aside from the statistical dogma of it, their is no logical reasonwhy both main effects need to be included. It could make sense to exclude them based on knowledge of the datqa. $\endgroup$ – Michael Chernick Sep 6 '12 at 12:51

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