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Graded Responses and Joining Categories: A Rejoinder to Andrich' “Models For Measurement, Precision, and Nondichotomization of Graded Responses”

Published online by Cambridge University Press:  01 January 2025

Edw E. Roskam
Edw E. Roskam*
Affiliation:
Nijmegen Institute of Cognition and Information, University of Nijmegen
*
Requests for reprints should be sent to E. E. Ch. I. Roskam, University of Nijmegen/NICI, Department of Mathematical Psychology, PO Box 9104, 6500 HE Nijmegen, THE NETHERLANDS.
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Extract

Andrich (1995) claims that the “probability distribution [of graded responses] reflects the precision with which the data are collected” (p. 7), and that an “increase in precision of responses [ . . . ] destroys the joining assumption” (p. 22). He stressed “that Jansen and Roskam simply asserted this equivalence [of the joining assumption and ξ-invariance], and did not derive it.” However, Jansen and Roskam (1986) and Roskam and Jansen (1989)—in the sequel referred to as JR—have neither asserted an equivalence between ξ-invariance and the joining assumption, nor defined ξ-invariance such that it could be considered in terms of estimation.

Type
Original Paper
Information
Psychometrika , Volume 60 , Issue 1 , March 1995 , pp. 27 - 35
Copyright
Copyright © 1995 The Psychometric Society

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