The Rasch paradox, conjoint measurement, and psychometrics: Response to Humphry and Sijtsma

Abstract

This response to Humphry (2013) and Sijtsma (2012) is confined to three issues: the nature of the Rasch paradox, the relevance of the theory of conjoint measurement to psychometrics, and the relationship between test items on the one hand and the character of the attributes they assess on the other. First, contrary to Sijtsma’s view, it is argued that the Rasch model does involve a genuine paradox. Second, typical of psychometricians generally, both Humphry and Sijtsma misunderstand the role the theory of conjoint measurement is able to play in psychometrics. It is argued that in conjunction with item response theory models, it has a significant role. Finally, complementary to Humphry’s and Sijtsma’s insistence upon the importance of theories of the attribute, I argue that features of attribute structure can be inferred from the character of test items and briefly sketch an argument that in the first instance at least, the attributes tests assess contain a feature logically incompatible with quantitative structure.