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

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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.

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