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A Hierarchical Bayesian Procedure for Two-Mode Cluster Analysis

Published online by Cambridge University Press:  01 January 2025

Wayne S. DeSarbo ,
Duncan K. H. Fong ,
John Liechty  and
M. Kim Saxton
Wayne S. DeSarbo*
Affiliation:
Pennsylvania State University
Duncan K. H. Fong
Affiliation:
Pennsylvania State University
John Liechty
Affiliation:
Pennsylvania State University
M. Kim Saxton
Affiliation:
Eli Lilly and Co.
*
Requests for reprints or further information may be directed to Wayne S. DeSarbo, 701 Business Administration Building, University Park, PA, 16802, Email: WSD6@psu.edu.
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Abstract

This manuscript introduces a new Bayesian finite mixture methodology for the joint clustering of row and column stimuli/objects associated with two-mode asymmetric proximity, dominance, or profile data. That is, common clusters are derived which partition both the row and column stimuli/objects simultaneously into the same derived set of clusters. In this manner, interrelationships between both sets of entities (rows and columns) are easily ascertained. We describe the technical details of the proposed two-mode clustering methodology including its Bayesian mixture formulation and a Bayes factor heuristic for model selection. We present a modest Monte Carlo analysis to investigate the performance of the proposed Bayesian two-mode clustering procedure with respect to synthetically created data whose structure and parameters are known. Next, a consumer psychology application is provided examining physician pharmaceutical prescription behavior for various brands of prescription drugs in the neuroscience health market. We conclude by discussing several fertile areas for future research.

Keywords

Cluster analysishierarchical Bayesian analysisfinite mixture modelsconsumer psychology
Type
Theory And Methods
Information
Psychometrika , Volume 69 , Issue 4 , December 2004 , pp. 547 - 572
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

Wayne S. DeSarbo is the Smeal Distinguished Professor of Marketing at the Smeal School of Business at Pennsylvania State University in University Park, PA. Duncan K.H. Fong is Professor of Marketing and Professor of Statistics at the Smeal School of Business at Pennsylvania State University in University Park, PA. John Liechty is an Assistant Professor of Marketing and Assistant Professor of Statistics at the Smeal School of Business at Pennsylvania State University in University Park, PA. M. Kim Saxton is Consultant of Marketing Research at the Eli Lilly and Co. in Indianapolis, IN.

The authors wish to recognize and thank several anonymous referees, the Associate Editor, and the Editor for their insightful and constructive comments.

References

Arabie, P., Schleutermann, S., Daws, J., Hubert, L.J. (1988). Marketing applications of sequencing and portioning of nonsymmetric and/or two-mode matrices. In Gaul, W., Schader, M. Berlin (Eds.), Data, Expert Knowledge and Decisions, New York: Springer-VerlagGoogle Scholar
Berger, J. (1985). Statistical Decision Theory and Bayesian analysis, New York: Springer-VerlagCrossRefGoogle Scholar
Bernardo, J.M., Smith, A.F.M. (1998). Bayesian Theory, Chichester, UK: WileyGoogle Scholar
Both, M., Gaul, W. (1986). Ein vergleich zweimodaler Clusteranalysevertahren. Methods of Operations Research, 57, 593–605Google Scholar
Bryant, P.G. (2001). Large sample results for optimization based clustering methods. Journal of Classification, 8, 1–44Google Scholar
Bryant, P., Williamson, J.A. (1978). Asymptotic behaviour of classification maximum likelihood estimates. Biometrika, 65, 273–281CrossRefGoogle Scholar
Celeux, G., Govaert, G. (2002). A classification EM algorithm for clustering and two stochastic versions. Computational Statistics and Data Analysis, 14, 315–332CrossRefGoogle Scholar
DeSarbo, W.S. (1982). GENNCLUS: New models for general nonhierarchical clustering analysis. Psychometrika, 47, 446–459CrossRefGoogle Scholar
DeSarbo, W.S., DeSoete, G. (1984). On the use of hierarchical clustering for analysis of nonsymmetric proximities. Journal of Consumer Research, 11, 601–610CrossRefGoogle Scholar
DeSarbo, W.S., Mahajan, V. (1984). Constrained classification: The use of a priori information in cluster analysis. Psychometrika, 49, 187–216CrossRefGoogle Scholar
DeSoete, G., DeSarbo, W.S., Furnas, G.W., Carroll, J.D. (1984). Tree representations of rectangular proximity matrices. In Degreef, E., Van Buggenhaut, J. (Eds.), Trends in Mathematical Psychology, Amsterdam: North-HollandGoogle Scholar
Diebolt, J., Robert, C. (1998). Estimation of finite mixture distributions through Bayesian sampling. Journal of the Royal Statistical Society, 56, 163–175Google Scholar
Eckes, T., Orlik, P. (2001). An agglomerative method for two-mode hierarchical clustering. In Bock, H.H., Ihm, P.P. (Eds.), Classification, Data Analysis, and Knowledge Organization, New York: Springer-VerlagGoogle Scholar
Eckes, T., Orlik, P. (2003). An error variance approach to two-mode hierarchical clustering. Journal of Classification, 10, 51–74CrossRefGoogle Scholar
Espejo, E., Gaul, W. (1986). Two-mode hierarchical clustering as an instrument for marketing research. In Gaul, W., Schader, M. (Eds.), Classification as a Tool of Research, Amsterdam: North-HollandGoogle Scholar
Fraley, C., Raftery, A.E. (2002). Model based-clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association, 97, 611–631CrossRefGoogle Scholar
Furnas, G.W. (1980). Objects and their features: The metric representation of two class data, Stanford, CA: Stanford UniversityGoogle Scholar
Gelman, A., King, G. (1990). Estimating the electoral consequence of legislative redirecting. Journal of the American Statistical Association, 85, 274–282CrossRefGoogle Scholar
Gilks, W.R., Richardson, S., Spiegelhalter, D.J. (2004). Markov Chain Monte Carlo in Practice, London: Chapman & HallGoogle Scholar
Jeffreys, H. (1961). Theory of Probability 3rd ed,, London: Oxford University PressGoogle Scholar
Kass, R., Raftery, A.E. (1995). Bayes factors. Journal of the American Statistical Association, 90, 40–60CrossRefGoogle Scholar
Lavine, M., West, M. (2002). A Bayesian method of classification and discrimination. Canadian Journal of Statistics, 20, 451–461CrossRefGoogle Scholar
McCormick, W.T., Schweitzer, P.J., White, T.W. (1972). Problem decomposition and data reorganization by a clustering technique. Operations Research, 20, 993–1009CrossRefGoogle Scholar
McLachlan, G.J., Krishnan, T. (1997). The EM Algorithm and Extensions, New York: WileyGoogle Scholar
McLachlan, G.J., Peel, D. (2000). Finite Mixture Models, New York: WileyCrossRefGoogle Scholar
Mirkin, B., Arabie, P., Hubert, L.J. (1995). Additive two-mode clustering: the error-variance approach revisited. Journal of Classification, 12, 243–264CrossRefGoogle Scholar
Newton, M.A., Raftery, A.E. (1998). Approximate Bayesian inference by the weighted likelihood bootstrap (with discussion). Journal of the Royal Statistical Society, 56, 3–48CrossRefGoogle Scholar
O'Hagan, A. (1998). Kendall's Advanced Theory of Statistics: Volume 2b Bayesian Inference, New York: WileyGoogle Scholar
Shepard, R.N., Arabie, P. (1979). Additive clustering: Representation of similarities as combinations of discrete overlapping properties. Psychological Review, 86, 87–123CrossRefGoogle Scholar
Steckel, J., DeSarbo, W.S., Mahajan, V. (2001). On the creation of feasible conjoint analysis experimental designs. Decision Sciences, 22, 435–442CrossRefGoogle Scholar
Tanner, M.A. (2001). Tools for statistical inference: Observed data and data augmentation methods. Lecture Notes in Statistics: Vol. 67, New York: Springer-VerlagGoogle Scholar