# Why does it not make sense to compute effects for lower-level interactions in the absence of higher-order interactions?

The documentation of effects package says

"If asked, the effect function will compute effects for terms that have higher-order relatives in the model, averaging over those terms (which rarely makes sense)"

My question is why does it rarely make sense? What if we have a mixed model like y ~ f1*f2*f3 + (1|sub) and only the f1:f2 interaction is significant? Isn't it reasonable to ignore the 3-way interaction and look at the simpler (and significant) 2-way interaction(s)?

• what will you do to ignore the 3-way interaction? Nov 4, 2018 at 1:52
• Your current model has f1, f2, f3, f1*f2, f1*f3, f2*f3 and f1**f2,f3. The new model should have f1, f2, f3, f1*f2, f1*f3 and f2*f3. I do not know how to specify the new model in R, but I think there is a way to do it in R. Nov 4, 2018 at 18:11
• What I will do is getting the satisfied model first. Before fitting model, set up the p-value level for excluding item from the model, for example, 0.10. Suppose there are 4 factors, fit a model with all of the interaction, including f1*f2*f3*f4. If f1*f2*f3*f4 can be excluded, fit a new model, check the third order interactions,..., until no more item can be excluded. Next, read the model carefully, and make the decision on what to estimate/test, ==> construct L matrix,==> perform the estimate/test. Nov 6, 2018 at 3:54
• Need to be step by step. Given p> 010 for 4 way-interaction, fit a model just exclude 4 way interaction, then check 3 3-way-interactions, if largest p > 0.10, exclude it, fit another new model. Sometimes, the not-sig-terms will become sig. after you exclude others. Nov 6, 2018 at 21:33
• Yes. After the model is selected, then figure out what special things needing to be tested/estimated. Nov 6, 2018 at 23:52

• Thanks for your answer Isabella. Imagine I'm interested in predicting consumer's satisfaction (y) from the type of product (f1), and quality of service (f2). I expect y to increase the better f1 and f2 are. Let's also assume I registered the type of store (f3). I don't have specific predictions about f3, but would like to include it in the model to see if interacts with the other levels. If I get an f1:f2 interaction but not a f1:f2:f3 interaction, why would it not make sense to look at f1:f2? Nov 4, 2018 at 17:38