The Monotonic Linear Model: Testing for Removable Interactions

Abstract

Loftus (1978) highlighted the distinction between a theoretical concept such as memory or attention, and its observed measure such as hit rate or percent correct. If the functional relationship between the concept and its measure is nonlinear then only some interaction effects are interpretable. This is an example of the wider “problem of coordination” which pervades scientific measurement. Loftus drew on the principles of additive conjoint measurement (ACM) to discuss the consequences when the coordination function is assumed to be monotonic. This led to the distinction between removable interactions that are consistent with an additive effect on the underlying theoretical concept and nonremovable interactions that are not. However, the adoption of these ideas by researchers has been greatly limited by the fact that no statistical procedure exists to determine if and to what extent an interaction is removable or otherwise. The lack of such a procedure has similarly limited the impact of ACM on research practice. The aim of this article is to present such a procedure.