Field (2013) stated that “It’s also worth bearing in mind that if you have interaction terms in your model then for that interaction term to be valid you must retain the main effects involved in the interaction term as well (even if they don’t appear to contribute much)” (p. 768). Does anyone know why ? If main effects do not increase significantly the fit of the model (tested with likelihood ratio test for example), then according to the parsimony principle, shouldn’t we pull them off? Further, what about the reverse pattern in reasoning: shouldn’t we also remove the interactions terms that are not of interest and that do not increase the fit of the model (or even lessen the fit of the model!)? Last question: Is the Field’s statement also valid when applying mixed-effects models (Judd, Westfall, & Kenny, 2012)?
In general, I agree with you. Maximum impact for minimum predictors (note that these are predictors or correlations not ‘effects’). Field is, I think, wrong about this, just as he was wrong about significance tests, confidence intervals, power etc. when he started writing.