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Joint-Space Analysis of “pick-any” Data: Analysis of Choices from an Unconstrained Set of Alternatives

Published online by Cambridge University Press:  01 January 2025

Joel H. Levine
Joel H. Levine*
Affiliation:
Dartmouth College
*
Requests for reprints should be sent to Joel H. Levine, Math/Social Science Program, Dartmouth College, Hanover, N.H. 03755.
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Abstract

Social and naturally occurring choice phenomena are often of the “pick-any” type in which the number of choices made by a subject as well as the set of alternatives from which they are chosen is unconstrained. These data present a special analytical problem because the meaning of non-choice among pick-any choice data is always ambiguous: A non-chosen alternative may be either unacceptable, or acceptable but not considered, or acceptable and considered but not chosen. A model and scaling method for these data are introduced, allowing for this ambiguity of non-choice. Subjects are represented as points whose coordinates are proportional to the centroids of the points representing their choices. Alternatives are represented at points whose coordinates are proportional to the centroids of the points representing subjects who have chosen them. This centroid scaling technique estimates multidimensional joint spaces from the pick-any data.

Keywords

multidimensional scalingnon-metric scalingchoice
Type
Original Paper
Information
Psychometrika , Volume 44 , Issue 1 , March 1979 , pp. 85 - 92
Copyright
Copyright © 1979 The Psychometric Society

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Footnotes

I am indebted to John Baird, Clyde Coombs, David Eames, John Hunter, Michael J. Levine, Elliot Noma, Robert Z. Norman, William S. Roy, Joseph Schwartz, Daniel Velleman, the editor, and anonymous reviewers for ideas and suggestions that have been incorporated into this work. Conferences organized by Hans J. Hummel for the Deutsche Forschungsgemeinschaft (1977) and by Samuel Leinhardt for the National Science Foundation (1975) were instrumental in the development of this work.

References

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