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Is it acceptable to not include high-order interactions (3-way and above) in the model when they are not of interest and not part of the hypothesis that is being tested?

NB. I am not talking about model reduction when a full model was fitted and higher interactions later excluded. I am asking about not including them at the outset, because their effects are not of interest and often uninterpretable.

For example, in a situation where the response is modelled as a function of one experimental factor and several covariables and the data is balanced only with respect to the experimental factor.

I heard somebody argue that it is acceptable, and if so, is there a reference to a credible source? As far as I understand, this is somewhat similar to ANCOVA, where the covariate is included as a main effect term, but not part of an interation.

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  • $\begingroup$ Of course it is acceptable, it's whether or not the rationale for including them is justifiable. $\endgroup$
    – Dan
    Commented Aug 27, 2014 at 16:36
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    $\begingroup$ The risk you take is that if one or more of those interactions actually exist, then the estimates you obtain when leaving them out are biased. Residual plots are always a good idea to make sure the model fits the data. $\endgroup$
    – Russ Lenth
    Commented Aug 27, 2014 at 16:51

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No, it's not acceptable. You are asking whether you can perform model selection in your head based on your "interest", as opposed to based on what data tells you about the nature of relationship between predictors and response. If you were to say that you ASSUME that the 3rd order terms won't be significant, or you simply don't have enough data to fit them, then I would say it's ok.

Note also that ANCOVA may include interactions between a covariate and a categorical term, between two or more covariates, etc. Strictly speaking, one is suppose to do some tests as to whether those "uninteresting" terms should (not) be included.

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