Reversing Arrows in Mediation Models Does Not Distinguish Plausible Models

Abstract

Reversing arrows in the classic tri-variate X-M-Y mediation models as a test to check whether one mediation model is superior to another is inadmissible. Presenting evidence that one tri-variate mediation model yields a significant indirect effect, whereas one with some reversed arrows does not, is not proof or even evidence that one model should be preferred. In fact, the significance of the indirect or any other effect can never be used to infer whether one model should be preferred over another, if the models are in the same so-called equivalence class. The practice of running several mediation models with reversed arrows to decide which model to prefer should be abandoned. The only way to choose among equivalent models is through assumptions that are either fulfilled by design features or invoked based on theory. Similar arguments about reversing arrows in mediation models have been made before, but this current work is the first to derive this result analytically for the complete (Markovian) equivalence class of the tri-variate mediation model.

ACKNOWLEDGEMENTS

The author would like to thank Nathan Spreng, Garett Howardson, and Sarah Moore for feedback, and Marina Yamasaki for derivation of some implied effects.

Notes

¹If one allows replacement of directed with bidirected arrows, 27 models can be formed, and again these are statistically indistinguishable from each other, and none can be preferred over the other based on any of the resulting effects.

²The advantage of using standardized variables is that some of the underlying algebra simplifies and that path coefficients are automatically completely standardized.