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A Simulated Annealing Methodology for Clusterwise Linear Regression

Published online by Cambridge University Press:  01 January 2025

Wayne S. DeSarbo ,
Richard L. Oliver  and
Arvind Rangaswamy
Wayne S. DeSarbo*
Affiliation:
Marketing and Statistics Departments, Graduate School of Business, University of Michigan
Richard L. Oliver
Affiliation:
Marketing Department, The Wharton School, University of Pennsylvania
Arvind Rangaswamy
Affiliation:
Marketing Department, The Wharton School, University of Pennsylvania
*
Requests for reprints should be sent to Wayne S. DeSarbo, S. S. Kresge Professor of Marketing and Statistics, Marketing and Statistics Departments, Graduate School of Business, University of Michigan, Ann Arbor, MI 48109-1234.
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Abstract

In many regression applications, users are often faced with difficulties due to nonlinear relationships, heterogeneous subjects, or time series which are best represented by splines. In such applications, two or more regression functions are often necessary to best summarize the underlying structure of the data. Unfortunately, in most cases, it is not known a priori which subset of observations should be approximated with which specific regression function. This paper presents a methodology which simultaneously clusters observations into a preset number of groups and estimates the corresponding regression functions' coefficients, all to optimize a common objective function. We describe the problem and discuss related procedures. A new simulated annealing-based methodology is described as well as program options to accommodate overlapping or nonoverlapping clustering, replications per subject, univariate or multivariate dependent variables, and constraints imposed on cluster membership. Extensive Monte Carlo analyses are reported which investigate the overall performance of the methodology. A consumer psychology application is provided concerning a conjoint analysis investigation of consumer satisfaction determinants. Finally, other applications and extensions of the methodology are discussed.

Keywords

cluster analysiscombinatorial optimizationregression analysissimulated annealingconsumer psychology
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 4 , December 1989 , pp. 707 - 736
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

The authors wish to thank the editor, associate editor, and three anonymous reviewers for their insightful comments and thorough review of this manuscript.

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