The Legacies of R. A. Fisher and K. Pearson in the Application of the Polytomous Rasch Model for Assessing the Empirical Ordering of Categories

Abstract

Assessments in response formats with ordered categories are ubiquitous in the social and health sciences. Although the assumption that the ordering of the categories is working as intended is central to any interpretation that arises from such assessments, testing that this assumption is valid is not standard in psychometrics. This is surprising given that it has been known for some 35 years that this assumption can be checked routinely using the psychometric Rasch model for more than two ordered categories. The purpose of this article is twofold. First, to demonstrate three distinct but related legacies of R. A. Fisher that have contributed to the use of the Rasch model to assess the empirical ordering of categories: (a) his construction of sufficient statistics, (b) his recognition that the ordering of categories should be an empirical property of the data, and (c) his integration of the design of empirical studies with statistical analyses of data. Second, to suggest two reasons behind both the indifference, and even the rejection, of both the need and possibility of testing the assumption of the empirical ordering of categories: (a) the lack of recognition of the problem before it was understood that it could be solved using the Rasch model and (b) the legacy of K. Pearson that legitimized the atheoretical modeling of data with parameters that have no substantive meaning.