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Chapter 9 - Extensions and Applications

Published online by Cambridge University Press:  16 September 2025

Wolfgang Wiedermann
Affiliation:
University of Missouri, Columbia
Alexander von Eye
Affiliation:
Michigan State University
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Summary

Chapter 9 introduces extensions and presents applications of Direction Dependence Analysis. Specifically, it focuses on probing the causal direction of effects in moderated regression (i.e., Conditional Direction Dependence Analysis; CDDA), mediation, and nonlinear models. CDDA allows researchers to detect potential reverse causation and confounding biases of conditional variable relations. CDDA components can be used to identify value regions of a continuous moderator or groups of a categorical moderator that differ in the direction of causation of x and y or the magnitude of hidden confounding. Furthermore, DDA is introduced in the context of mediation models, that is, mechanisms in which a causal effect of x on y is transmitted via a third variable (the mediator). Incorporating principles of direction of dependence in statistical mediation analysis leads to a useful tool for empirically testing the causal inference assumptions embedded in statistical mediation analysis. The chapter closes with a discussion of direction dependence principles for nonlinear variable relations, extensions of DDA’s predictor-error independence component to nonlinear additive models, and discusses DDA in the context of linearizable regression scenarios. The latter opens the door to utilize the full DDA framework under nonlinearity of variable relations.

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Chapter
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Direction Dependence Analysis
Foundations and Statistical Methods
, pp. 255 - 302
Publisher: Cambridge University Press
Print publication year: 2025

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