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A Conjunctive Parallelogram Model for Pick any/n Data

Published online by Cambridge University Press:  01 January 2025

Iwin Leenen  and
Iven Van Mechelen
Iwin Leenen
Affiliation:
Katholieke Universiteit Leuven
Iven Van Mechelen*
Affiliation:
Katholieke Universiteit Leuven
*
All correspondence concerning this paper is to be addressed to Iven Van Mechelen, Department of Psychology, K.U.Leuven, Tiensestraat 102, B-3000 Leuven, Belgium; email: [email protected]
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Abstract

This paper proposes a multidimensional generalization of Coombs' (1964) parallelogram model for “pick any/n” data, which result from each of a number of subjects having selected a number of objects (s)he likes most from a prespecified set of n objects. In the model, persons and objects are represented in a low dimensional space defined by a set of ordinal variables with a prespecified number of categories; objects are represented as points and persons as intervals on each dimension. A conjunctive combination rule is assumed implying that a person selects an object if and only if the object is within the subject's interval on each dimension. An algorithm for fitting the model to a data set is presented and evaluated in a simulation study. The model is illustrated with data on preferences regarding holiday trips.

Keywords

Choice data analysisbinary dataparallelogram analysisnoncompensatory combination rule
Type
Theory and Methods
Information
Psychometrika , Volume 69 , Issue 3 , September 2004 , pp. 401 - 420
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

The research reported in this paper was partially supported by the Research Council of K.U.Leuven (PDM/99/037).

The authors gratefully acknowledge the contribution of Veerle De Wael in running the study used in the application section and of Paul De Boeck, Luc Delbeke, and an anonymous referee for their helpful comments on a previous draft of the manuscript.

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