Justification of functional form assumptions in structural models: applications and testing of qualitative measurement axioms

In both theoretical and applied modeling in behavioral sciences, it is common to choose a mathematical specification of functional form and distribution of unobservables on grounds of analytic convenience without support from explicit theoretical postulates. This article discusses the issue of deriving particular qualitative hypotheses about functional form restrictions in structural models from intuitive theoretical axioms. In particular, we focus on a family of postulates known as dimensional invariance. Subsequently, we discuss how specific qualitative postulates can be reformulated so as to allow for conventional statistical hypothesis testing, and we also derive details of a particular likelihood ratio test procedure. An empirical application of the testing procedure is carried out, based on data from a Stated Preference survey.