Power Analysis for Complex Mediational Designs Using Monte Carlo Methods

Abstract

Applied researchers often include mediation effects in applications of advanced methods such as latent variable models and linear growth curve models. Guidance on how to estimate statistical power to detect mediation for these models has not yet been addressed in the literature. We describe a general framework for power analyses for complex mediational models. The approach is based on the well known technique of generating a large number of samples in a Monte Carlo study, and estimating power as the percentage of cases in which an estimate of interest is significantly different from zero. Examples of power calculation for commonly used mediational models are provided. Power analyses for the single mediator, multiple mediators, three-path mediation, mediation with latent variables, moderated mediation, and mediation in longitudinal designs are described. Annotated sample syntax for Mplus is appended and tabled values of required sample sizes are shown for some models.

A Multiple Mediator Model: Power Analysis Based on Monte Carlo Simulation

“…[4,8,11,16,17]). However, only a handful of published studies focus on statistical power of complex mediation models, such as multiple mediator models [9,18]. Only with adequate power, the sample size in a study will be sufficient to find and confirm a significant mediating effect which is of small effect size [9].…”

“…Moreover, in psychology, a desirable power is at 0.8 [8]. One unique function of statistical power is to calculate required sample size to reach 0.8 power to reject a false null hypothesis [9]. If the power in a study is less than 0.8, a researcher should consider increasing the sample size [22].…”

“…If the power in a study is less than 0.8, a researcher should consider increasing the sample size [22]. Under certain circumstances, higher power is also desired [9,23]. In fact, power analyses are only meaningful when conducted prior to data collection [24].…”

“…That is to say the cause-effect relation between two variables is accounted for by several mediators. In this manner, a single mediator model should be replaced by a multiple mediator model [9]. A multiple mediator model with j mediators is shown in Figure 2 [10].…”

Enhancing flourishing mental health in the general population as a new strategy for the prevention of anxiety and depressive disorders

“…When including all six well-being processes in one model, it turned out that positive relations remained a significant mediator while optimism did not. It might be tempting to conclude that the latter finding is correct, but by including multiple variables in one model the sampling variance increases and might have reduced statistical power Thoemmes, MacKinnon, & Reiser, 2010).…”