Folded additive structures: A nonpolynomial model of some factorial interactions

Abstract

A nonpolynomial measurement model for representing nonadditive compositions of stimulus dimensions is presented. This representation, which is referred to as a folded additive structure, permits the decomposition of a behavioral ordering into independent factors in some of the cases where the behavior itself does not directly reflect this independence. Psychologically, this representation corresponds to a model of behavior which assumes that (1) the effect stimulus attributes have on behavior is mediated by a single relevent psychological dimension, (2) the behavioral ordering is single-peaked over this mediating dimension and (3) the mediating dimension has a conjoint additive ordering over a set of relevent stimulus dimensions. Necessary and sufficient tests for folded additive structures are given. In addition, five psychological theories which make these assumptions are discussed.