The Rasch model and conjoint measurement theory from the perspective of psychometrics

Kyngdon argues that psychometricians have erroneously claimed the Rasch model to be an instance of representational measurement, because the Rasch model does not map a bona fide empirical relational system (ERS) into a numerical relational system (NRS). While we agree that one does not automatically achieve a conjoint measurement representation upon fitting a Rasch model, we do not agree that the Rasch model could not in principle yield such a representation. In our view, whether this is possible depends on what one is prepared to accept as an empirical relational system. This is a philosophical question that extends beyond the scope of the formal structures advanced in representationalism and psychometrics; a question, moreover, that is not currently settled. We examine some of the ways in which one may react to this question, and conclude that Kyngdon’s argument depends on a specific, and perhaps too strong, interpretation of representationalism and psychometric models.