Analytical Investigation of Mediated Effect Size Measures for Single and Two Mediator Models

Introduction: Several effect size measures have been proposed for single and multiple mediator models. Simulations have investigated statistical of mediated effects for the single mediator model and two mediator model. Recent research showed that κ² does not increase monotonically for the single mediator model. The purpose of this project is to compare analytical mediation effect size measures and evaluate the relation of effect sizes to mediated effects for the single and two mediator models.

Method: A SAS computer program was used to compute true values of the proportion, ratio, partially standardized, fully standardized, R², and κ² mediated effects for the single mediator model and corresponding effect sizes for the two mediator model excluding R². The true values of the mediated effect for each model were compared with values of each effect size to determine the monotonicity (or lack of monotonicity) of each effect size, and were plotted to display results.  

Results: For both models, each effect size investigated increased monotonically with the increase of one coefficient holding all others constant (for example, comparing κ² to a while holding values of b constant). For the single mediator model, the proportion and ratio mediated effect sizes also increased monotonically with values of ab. Replicating prior research, the single mediator model κ² increased non-monotonically as ab increased, and the partially and fully standardized mediated effect sizes and R² increased non-monotonically. For the two mediator model, the pattern of results was the same as for the single mediator model.

Discussion: The proportion and ratio mediated effects have performed poorly in prior research and yet these are the effect sizes that increased monotonically for the single and two mediator models. The standardized effect sizes and κ² are more stable and have less bias, but do not have the property of monotonicity. These findings indicate that multiple measures of performance and statistical properties are required to determine appropriate effect size measures for mediation.