A comparison of frameworks for the joint analysis of mediation and moderation effects

Models for the investigation of mediation and moderation effects were reviewed and a general framework that encompasses these models was presented. A point estimator that examines whether a mediated effect is the same across levels of a moderator variable was proposed and compared to other tests of the effect. Tests to examine moderation of the product were examined in a statistical simulation study where the relative bias of point and standard error estimators, power, Type 1 error, and confidence interval coverage for the tests were examined.;Relative bias for the product of coefficients point and standard error estimators was less than .1 across simulation conditions. Simple slope estimators had excessive relative bias in most conditions. Standard error estimators for the simple slope tests were less biased. The multivariate delta test of the mediated effect had at least .8 power for sample sizes greater or equal to 500 when the effect size of both paths was medium. Type 1 error rates for the test were less than .05 across parameter combinations. The distribution of the product test and the test of joint significance had at least .8 power when the effect size of both paths was medium for sample sizes greater or equal to 300. Type 1 error rates for the tests were less than .05 across simulation conditions. Several of the simple slope estimators were underpowered, and others had excessive Type 1 error rates. Tests based on the significance of moderation in individual paths had the most power of any test, but also had excessive Type 1 error rates. Finally, other tests for moderation of the product such as the causal steps test were underpowered in every condition and had elevated Type 1 error rates. In general, results from the study support tests based on the product of coefficients estimator of the mediated effect.