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Probabilistic Subset Conjunction

Published online by Cambridge University Press:  01 January 2025

Rajeev Kohli  and
Kamel Jedidi
Rajeev Kohli
Affiliation:
Graduate School of Business, Columbia University
Kamel Jedidi*
Affiliation:
Graduate School of Business, Columbia University
*
Request for reprints should be sent to Kamel Jedidi, Columbia University, Graduate School of Business, 518 Uris Hall, 3022 Broadway, New York, NY 10027, USA. E-mail: kj7@columbia.edu
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Abstract

The authors introduce subset conjunction as a classification rule by which an acceptable alternative must satisfy some minimum number of criteria. The rule subsumes conjunctive and disjunctive decision strategies as special cases.

Subset conjunction can be represented in a binary-response model, for example, in a logistic regression, using only main effects or only interaction effects. This results in a confounding of the main and interaction effects when there is little or no response error. With greater response error, a logistic regression, even if it gives a good fit to data, can produce parameter estimates that do not reflect the underlying decision process. The authors propose a model in which the binary classification of alternatives into acceptable/unacceptable categories is based on a probabilistic implementation of a subset-conjunctive process. The satisfaction of decision criteria biases the odds toward one outcome or the other. The authors then describe a two-stage choice model in which a (possibly large) set of alternatives is first reduced using a subset-conjunctive rule, after which an alternative is selected from this reduced set of items. They describe methods for estimating the unobserved consideration probabilities from classification and choice data, and illustrate the use of the models for cancer diagnosis and consumer choice. They report the results of simulations investigating estimation accuracy, incidence of local optima, and model fit.

Keywords

noncompensatory decision strategiesconjunctive/disjunctive strategiessubset-conjunctive strategiesconsideration setsbinary datachoice modelsmaximum likelihood estimation
Type
Theory and Methods
Information
Psychometrika , Volume 70 , Issue 4 , December 2005 , pp. 737 - 757
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

The authors thank the Editor, the Associate Editor, and three anonymous reviewers for their constructive suggestions, and also thank Asim Ansari and Raghuram Iyengar for their helpful comments. They also thank Sawtooth Software, McKinsey and Company, and Intelliquest for providing the PC choice data, and the University of Wisconsin for making the breast-cancer data available at the machine learning archives.

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