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Log-linear models to evaluate direction of effect in binary variables

Author

Listed:
  • Wolfgang Wiedermann

    (University of Missouri)

  • Alexander Eye

    (Michigan State University)

Abstract

In this article, we present a new approach to determining direction of effects in binary variables. A variable is considered explanatory if it explains the probability distribution of another variable. In cross-classifications of binary variables, the univariate probability distribution of variables can be considered explained if omitting the univariate effects of this variable does not lead to an ill-fitting model. Directional (non-hierarchical) log-linear models are introduced that allow statements concerning the direction of association in binary data. Cases in which variables of latent linear regression processes are partially observed as binary variables reveal a close conceptual link between the proposed log-linear approach and existing direction of effect methodology for metric variables. A Monte Carlo study is presented that shows that the proposed approach has good power and enables researchers to distinguish the correct model from the incorrect, reverse model. The approach can be extended to multiple explanatory and multiple outcome variables. Empirical data examples from research on aggression development in adolescence illustrate the proposed direction dependence approach.

Suggested Citation

  • Wolfgang Wiedermann & Alexander Eye, 2020. "Log-linear models to evaluate direction of effect in binary variables," Statistical Papers, Springer, vol. 61(1), pages 317-346, February.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0936-2
    DOI: 10.1007/s00362-017-0936-2
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    References listed on IDEAS

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    1. A. Gupta & T. Nguyen & L. Pardo, 2007. "On Christensen's conjecture," Statistical Papers, Springer, vol. 48(3), pages 523-523, September.
    2. K. Gupta & T. Nguyen & L. Pardo, 2007. "On Christensen's conjecture," Statistical Papers, Springer, vol. 48(2), pages 313-319, April.
    3. J. A. Nelder, 1974. "Log Linear Models for Contingency Tables: A Generalization of Classical Least Squares," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 23(3), pages 323-329, November.
    4. Yadolah Dodge & Iraj Yadegari, 2010. "On direction of dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 139-150, July.
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