Quantifying Inconsistent Mediation: The Mediated Magnitude Share and the Degree of Suppression
Abstract
The proportion mediated (PM), defined as the indirect effect divided by the total effect, is intuitive when direct and indirect effects operate in the same direction. Under inconsistent mediation, however, opposing pathways partially cancel each other, causing PM to fall outside the unit interval or become unstable as the total effect approaches zero. We introduce two complementary effect-scale measures: the Mediated Magnitude Share (MMS), which quantifies the absolute magnitude of an indirect pathway relative to the combined absolute magnitudes of the direct and indirect pathways, and the degree of suppression, which quantifies the fraction of this combined magnitude that is cancelled by opposing pathways. We establish the bounds and limiting behavior of both measures in the two-pathway case, show that MMS reduces to PM under consistent mediation, and extend both measures to settings with multiple indirect pathways. For binary outcomes, we extend the framework to odds-ratio and risk-ratio scales by using logarithms to convert multiplicative effects into additive ones, enabling direct application of MMS and the degree of suppression. Together, these measures provide bounded and interpretable characterizations of mediation systems in which pathway directions are not uniform.
Related
- Graph splitting algorithms for inconsistent feasibility problems
- Local W2,1p convergence of penalization for time-inconsistent stopping problems
- Quantitative Convergence of Markov Equilibria for Time-Inconsistent Controlled Diffusions
- Equilibria for Time-inconsistent Regular-singular Control Problems
- Computing Approximate Solutions of Inconsistent Max-Min Fuzzy Relational Equations by Mixed-Integer Programming
BibTeX
@misc{sium2026quantifying,
title = {{Quantifying Inconsistent Mediation: The Mediated Magnitude Share and the Degree of Suppression}},
author = {Md. Niamul Islam Sium and Shafayet Khan Shafee and Mohammad Hridoy Patwary and Bishal Sarker},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33846},
eprint = {2609.33846},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33846},
}
RIS
TY - UNPB
TI - Quantifying Inconsistent Mediation: The Mediated Magnitude Share and the Degree of Suppression
AU - Md. Niamul Islam Sium
AU - Shafayet Khan Shafee
AU - Mohammad Hridoy Patwary
AU - Bishal Sarker
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33846
UR - https://arxiv.org/abs/2609.33846
AB - The proportion mediated (PM), defined as the indirect effect divided by the total effect, is intuitive when direct and indirect effects operate in the same direction. Under inconsistent mediation, however, opposing pathways partially cancel each other, causing PM to fall outside the unit interval or become unstable as the total effect approaches zero. We introduce two complementary effect-scale measures: the Mediated Magnitude Share (MMS), which quantifies the absolute magnitude of an indirect pathway relative to the combined absolute magnitudes of the direct and indirect pathways, and the degree of suppression, which quantifies the fraction of this combined magnitude that is cancelled by opposing pathways. We establish the bounds and limiting behavior of both measures in the two-pathway case, show that MMS reduces to PM under consistent mediation, and extend both measures to settings with multiple indirect pathways. For binary outcomes, we extend the framework to odds-ratio and risk-ratio scales by using logarithms to convert multiplicative effects into additive ones, enabling direct application of MMS and the degree of suppression. Together, these measures provide bounded and interpretable characterizations of mediation systems in which pathway directions are not uniform.
ER -