Our primary aim was to re-parameterize the standard linear regression model to allow clearer distinctions between ordinal and disordinal interactions. Researchers often hypothesize interactive effects of predictors in fairly nonspecific terms. In our opinion, researchers should be challenged to make stronger predictions about the form of an interaction, such as whether the interaction is ordinal or disordinal. If such a prediction were warranted, then a re-parameterized regression model that estimates explicitly the cross-over point of predicted values and its CI would enable stronger tests of the match between theoretical predictions and trends in data.
