Exploring Statistical Power and Mediation Analysis: Understanding the Impact of Antecedent-Mediator-Outcome Relationships

Szilárd Nemes

Abstract

This paper explores the phenomenon of statistical power stagnation and decline in mediation analysis, specifically focusing on the interplay between the antecedent variable, mediator, and outcome. Mediation analysis is a critical statistical tool used to understand the causal pathways between variables. However, statistical power may not always increase with stronger relationships between the antecedent and mediator, often stagnating or even declining due to variance inflation caused by multicollinearity. We provide a in detail examination of this issue, including key theoretical concepts, the mathematical foundations of variance inflation, and the impact of mediator-antecedent correlations on power. A simulation study further illustrates how varying these correlations affects statistical power, variance estimates, and possible bias in mediation effects. Our findings indicate that while increasing the strength of the relationship between the antecedent and mediator improves mediation detection initially, beyond a certain threshold, it results in inflated variance estimates, leading to decreased precision and power. Variance inflation of the mediated effect is more accentuated than variance inflation of regression coefficients.

Keywords: mediation; variance inflation; Sobel test

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DOI: https://doi.org/10.13057/ijas.v8i2.93376

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