The Logic of State-Trace Analysis

Abstract

State-trace analysis (STA) was introduced by Bamber (J Math Psychol 19(2):137–181, 1979) as a general method to determine properties of the latent structure that mediates the effects of one or more independent variables on two or more dependent variables. STA offers a principled way of adjudicating between theories proposing different numbers of latent variables under very general conditions and with minimal assumptions we introduce the concept of the general structure which provides a framework for representing the functional relationships between sets of independent, latent, and dependent variables. Within this framework, we distinguish between the observational structure that consists of the physical components that can be observed and the theoretical structure that consists of the theoretical components that must be inferred. We discuss the dimensionality of the state-trace and show how it can be used to infer properties of the theoretical structure. We derive the central idea of STA that the dimensionality of the theoretical structure—the number of latent variables—cannot be less than the dimensionality of the state-trace.