Simulation-based path analysis for qualitative mediators‎: ‎A continuous proxy approach

Document Type : Original Scientific Paper

Authors

1 Departent of Statistics‎, ‎Payame Noor University‎, ‎Tehran‎, ‎Iran

2 Department of Engineering, University of Ardakan, Ardakan, Iran

10.22034/jsmta.2026.24305.1211

Abstract

Conventional path analysis relies on ordinary least squares assumptions, requiring continuous variables. When mediators are qualitative, researchers typically resort to logistic regression, creating a scale incompatibility problem in which coefficients cannot be directly multiplied to estimate indirect effects. This study proposes a Categorical-to-Continuous Signal Transformation technique to address this limitation. Unlike standard dummy coding, we introduce a simulation-based algorithm that generates a continuous proxy variable for the qualitative mediator. By extracting the probabilistic centroid of each category using the group mean and standard error of the dependent variable, we simulate a distribution that retains the structural signal while satisfying ordinary least squares normality assumptions. The method was validated using both primary and synthetic datasets. Results demonstrate that the simulated proxy variables successfully recover the directional pathways and maintain statistical significance consistent with classical analysis of variance. The approach effectively captures the latent influence of categories without the bias of individual-level noise. The proposed simulation method offers a robust alternative for mediation analysis involving qualitative variables. By bridging the gap between categorical data and linear modeling, it enables the direct calculation of indirect effects within a unified ordinary least squares framework, eliminating the need for complex non-linear approximations.

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Journal of Statistical Modelling: Theory and Applications
Volume 7, Issue 1
January 2026
Pages 37-53

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History

  • Receive Date: 08 February 2026
  • Revise Date: 29 August 2026
  • Accept Date: 13 September 2026

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