Locating Event-Based Causal Effects: A Configural Perspective

Statistical models for the analysis of hypotheses that are compatible with direction dependence were originally specified based on the linear model. In these models, relations among variables reflected directional or causal hypotheses. In a number of causal theories, however, effects are defined as resulting from causes that did versus did not occur. To accommodate this type of theory, the present article proposes analyzing directional or causal hypotheses at the level of configurations. Causes thus have the effect that, in a particular sector of the data space, the density of cases increases or decreases. With reference to log-linear models of direction dependence, this article specifies base models for the configural analysis of directional or causal hypotheses. In contrast to standard configural analysis, the models are applied in a confirmatory context. Specific direction dependence hypotheses are analyzed. In a simulation study, it is shown that the proposed methods have good power to identify the sectors in the data space in which density exceeds or falls below expectation. In a data example, it is shown that the evolutionary hypothesis that body size determines brain size is confirmed in particular for higher vertebrates.