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

Andrew Kyngdon

METAMETRICS, INC., akyngdon{at}lexile.com

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.

Key Words: axiomatic conjoint measurement • homomorphism • Rasch model • real numbers • representation theorem

Theory & Psychology, Vol. 18, No. 1, 89-109 (2008)
DOI: 10.1177/0959354307086924
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This article has been cited by other articles:


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 Theory PsychologyHome page
D. Borsboom and A. Z. Scholten
The Rasch Model and Conjoint Measurement Theory from the Perspective of Psychometrics
Theory Psychology, February 1, 2008; 18(1): 111 - 117.
[Abstract] [PDF]

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 Theory PsychologyHome page
J. Michell
Conjoint Measurement and the Rasch Paradox: A Response to Kyngdon
Theory Psychology, February 1, 2008; 18(1): 119 - 124.
[Abstract] [PDF]

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 Theory PsychologyHome page
A. Kyngdon
Conjoint Measurement, Error and the Rasch Model: A Reply to Michell, and Borsboom and Zand Scholten
Theory Psychology, February 1, 2008; 18(1): 125 - 131.
[Abstract] [PDF]