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

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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.