there is one exception of omitting the constituent term (main) effects in the multiplicative interaction model as suggested by the influential paper of Brambor (2006). If the model involves a variable with natural zero then in that case omitting the constituent term does not lead to any errors (See Page 68, 2nd paragrah)

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]]>If the coefficient of an interaction effect is substantial, net of the main effects, then there are really only two possible things going on: the main effects have not been scaled properly according to one’s theory and/or there is a meaningful omitted variable that, if it were included in the model, would explain away the interaction effect. Thus, the only good model is a model in which there are no interaction effects of substance.

This subversive line of argument is (if my memory is correct) attributable to Bob Hauser’s 1970s critique of Raymond Boudon’s book that rested on an interaction effect. But, really, it is a point straight out of statistics.

All that being said, heterogeneity of causal effects is of the utmost importance substantively, and regression is a poor framework for revealing all of it. The Angrist and Heckman work in econometrics over the past decade is devastating on this point.

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]]>Gabriel, I wouldn’t worry too much about interpretation and/or collinearity. Friedrich (1982) showed a while ago that both of those concerns tend to be highly overstated in the literature. For those who are interested, Brambor keeps a nice page at NYU with examples (and Stata code) on how to deal with most common issues with interaction models.

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]]>in such a case you’re failing to make conservative assumptions. the best example of this i can think of is a 1982 ASR article by James Davis where he tested the “nouveau riche” hypothesis (which is basically an argument about the interaction effect of origin and destination class on attitudes) and found it to be entirely explicable by the main effects. if you had a theory of the nouveau riche that strongly suggested they would be more conservative than old money, you wouldn’t include the main effects and you would spuriously find your theory confirmed.

(myself, i’m skittish about interaction effects because i worry about the interpretation, especially colinearity)

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