Questions of value, questions of magnitude: An exploration and application of methods for comparing indirect effects in multiple mediator models

Abstract

Mediation analysis is widely used to test and inform theory and debate about the mechanism(s) by which causal effects operate, quantitatively operationalized as an indirect effect in a mediation model. Most effects operate through multiple mechanisms simultaneously, and a mediation model is likely to be more realistic when it is specified to capture multiple mechanisms at the same time with the inclusion of more than one mediator in the model. This also allows an investigator to compare indirect effects to each other. After an overview of the mechanics of mediation analysis, we advocate formally comparing indirect effects in models that include more than one mediator, focusing on the important distinction between questions and claims about value (i.e., are two indirect effects the same number?) versus magnitude (i.e., are two indirect effects equidistant from zero or the same in strength?). After discussing the shortcomings of the conventional method for comparing two indirect effects in a multiple mediator model—which only answers a question about magnitude in some circumstances—we introduce several methods that, unlike the conventional approach, always answer questions about difference in magnitude. We illustrate the use of these methods and provide code that implements them in popular software. We end by summarizing simulation findings and recommending which method(s) to prefer when comparing like- and opposite-signed indirect effects.