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Detecting heterogeneity in the causal direction of dependence: A model-based recursive partitioning approach


Methods of causal discovery and direction of dependence to evaluate causal properties of variable relations have experienced rapid development. The majority of causal discovery methods, however, relies on the assumption of causal effect homogeneity, that is, the identified causal structure is expected to hold for the entire population. Because causal mechanisms can vary across subpopulations, we propose combining methods of model-based recursive partitioning and non-Gaussian causal discovery to identify such subpopulations. The resulting algorithm can discover subpopulations with potentially varying magnitude and causal direction of effects under mild parameter inequality assumptions. Feasibility conditions are described and results from synthetic data experiments are presented suggesting that large effects and large sample sizes are beneficial for detecting causally competing subgroups with acceptable statistical performance. In a real-world data example, the extraction of meaningful subgroups that differ in the causal mechanism underlying the development of numerical cognition is illustrated. Potential extensions and recommendations for best practice applications are discussed.

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The authors are indebted to Dr. Ingrid Koller and Dr. Michaela Pötscher-Gareiß for providing the data used for illustrative purposes, and to Dr. Ed Merkle for valuable comments on an earlier version of the article. DS was partially supported by an ASPIRE grant from the Office of the Vice President for Research at the University of South Carolina.

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Correspondence to Wolfgang Wiedermann.

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DDA source code is available at A synthetic data example is given in the online supplement of the article.

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Wiedermann, W., Zhang, B. & Shi, D. Detecting heterogeneity in the causal direction of dependence: A model-based recursive partitioning approach. Behav Res (2023).

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