The Rasch Model from the Perspective of the Representational Theory of Measurement

2008/02/01 by Andrew Kyngdon · 2 citations
Mathematics · Psychology · Social Sciences · #Academic and Historical Perspectives in Psychology #Argument (complex analysis) #Artificial intelligence #Computer science #Conjoint analysis #Epistemology #Item response theory #Level of measurement #Mathematics #Perspective (graphical) #Philosophy #Polytomous Rasch model #Preference #Psychology #Psychometrics #Qualitative Comparative Analysis Research #Rasch model #Representation (politics) #Social and Intergroup Psychology #Statistics

paper · doi:10.1177/0959354307086924

openalex publication_date 2008/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Representational measurement theory is the dominant theory of measurement within the philosophy of science; and the area in which the theory of conjoint measurement was developed. For many years it has been argued the Rasch model is conjoint measurement by several psychometricians. This paper critiques this argument from the perspective of representational measurement theory. It concludes that the Rasch model is not conjoint measurement as the model does not demonstrate the existence of a representation theorem between an empirical relational structure and a numerical relational structure. Psychologists seriously interested in investigating traits for quantitative structure should use the theory of conjoint measurement itself rather than the Rasch model. This is not to say, however, that empirical relationships between conjoint measurement and the Rasch model are precluded. The paper concludes by suggesting some relevant research avenues.

Citations

• The Axioms of Quantity and the Theory of Measurement
• Additive Conjoint Isotonic Probabilistic Models (ADISOP)
• Order-Constrained Bayes Inference for Dichotomous Models of Unidimensional Nonparametric IRT
• The exchangeable multinomial model as an approach to testing deterministic axioms of choice and measurement
• The Rasch Model as Additive Conjoint Measurement
• Measurement structures and linear inequalities
• Introduction to Axiomatic Set Theory
• Enumerating and testing conjoint measurement models
• Statistical issues in measurement
• The Rasch Model, the Law of Comparative Judgment and Additive Conjoint Measurement
• Simultaneous conjoint measurement: A new type of fundamental measurement
• THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS
• Test Theory

Cited by

• Plausible measurement analogies to some psychometric models of test performance
• Theory of conjoint measurement [wikipedia]