Substantive Theory and Statistical Interaction: Five Models

For a series of theoretical models involving two independent interval-scale variables acting together to produce a joint causal effect, different modes of analysis are described. In each case statistical interaction is involved, but the form of this interation differs with each model. Methods for deriving appropriate interaction terms are given. These models provide a flexibility for statistical analyses appropriate to a broader range of theories than can be treated well by conventional regression procedures. If, as seems likely, theoretical propositions are often stated in empirical research in a form appropriate to additive multiple regression, these methods suggest that such propositions might be reexamined and reformulated. It is possible that the methods have particular relevance for some aspects of functional, equilibrium, balance, and conflict theories.