Abstract
Direction dependence analysis is attracting growing attention in the social sciences for its potential to help decide concerning the direction of effects of linear regression models. Direction dependence analysis assumes that observed data deviate from normality. Various tests have been proposed that can be applied when observed variables are skewed. However, these tests cannot be used when data are nonnormal and symmetric. The present chapter discusses direction dependence approaches for symmetric nonnormal data based on the fourth central moment. A new direction dependence approach based on regression residuals obtained from competing linear regression models is proposed. Three significance tests are described which can be used to test hypotheses compatible with direction dependence when data are nonnormal and symmetric. Results of a Monte Carlo simulation are reported which suggest that the significance tests perform well under various data scenarios. An empirical example from research on intimate partner violence is given to illustrate the application of the direction dependence tests.
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