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I am looking for literature dealing broadly with the hunch pretty much everyone has in econ/social sciences: main effects of a treatment are typically larger than interaction effects. Of course, this is not true in general and depends on the research question. But for the social sciences, such observation should hold on average.

Any suggestions/tips?

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  • $\begingroup$ An alternative view: in this post Andrew Gelman thinks that interactions tend to be smaller than main effects. There's some further discussion in the comments there. $\endgroup$
    – fblundun
    Commented Dec 15, 2020 at 15:29
  • $\begingroup$ Some examples: bmcmedresmethodol.biomedcentral.com/articles/10.1186/… ncbi.nlm.nih.gov/pmc/articles/PMC6815379 $\endgroup$
    – kjetil b halvorsen ♦
    Commented Dec 15, 2020 at 15:29
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    $\begingroup$ This is very similar to my old question Relative variances of higher-order vs. lower-order random terms in mixed models. IMO it's close enough that I consider this a duplicate -- for example, I think my answer to that old question also works as an answer to this question -- but I'll let OP be the judge I guess... $\endgroup$
    – Jake Westfall
    Commented Dec 15, 2020 at 15:32
  • $\begingroup$ I'm sorry. I meant main effects are typically larger, of course! This is a typo! Thanks for the suggestions! $\endgroup$
    – persephone
    Commented Dec 15, 2020 at 17:53
  • $\begingroup$ Can you define the interactions effect more precisely? In a model like $E[Y \vert X]=\alpha +\beta \cdot X + \gamma \cdot X \times Z$, is the main effect of $X$ given by $\beta$, and the interaction effect by $\gamma \cdot Z$? Or is the interaction effect just $\gamma$ (which is often quite small relative to $\beta$, before multiplication by $Z$)? $\endgroup$
    – dimitriy
    Commented Dec 15, 2020 at 19:42

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This is sometimes called the hierarchical ordering principle:

“Hierarchical ordering […] is a term denoting the observation that main effects tend to be larger on average than two-factor interactions, two-factor interactions tend to be larger on average than three-factor interactions, and so on” (Li, Sudarsanam, & Frey, 2006, p. 34).

It is discussed most often (as far as I can tell) in the literature on Design of Experiments. In particular, it is one of the main ideas motivating and justifying the use of fractional factorial designs.

My first ever blog post was about exploring some different possible reasons why hierarchical ordering might be true more often than not: Cookie Scientist: The hierarchical ordering principle

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