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. Lastly, a marketing application is provided examining consumer preferences for various brands of luxury automobiles.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
BERGER, J. (1985): Statistical Decision Theory and Bayesian Analysis. Springer Verlag, New York, NY.
BERNARDO, J.M. and SMITH, A.F.M. (1994): Bayesian Theory. John Wiley & Sons Ltd., Chichester.
BINDER, D.A. (1978): Bayesian Cluster Analysis. Biometrika, 65, 31–38.
DESARBO, W.S. and JEDIDI, K. (1995): The Spatial Representation of Heterogeneous Consideration Sets. Marketing Science, 14, 326–342.
DESARBO, W.S., FONG, D.K.H, LIECHTY, J., and SAXTON, M.K. (forthcoming): A Hierarchical Bayesian Procedure for Two-Mode Cluster Analysis. Psychometrika.
DIEBOLT, J. and ROBERT, C. (1994): Estimation of Finite Mixture Distributions Through Bayesian Sampling. Journal of the Royal Statistical Society, 56, 163–175.
EVANS, M., GUTTMAN, I., and OLKIN, I. (1992): Numerical Aspects in Estimating the Parameters of a Mixture of Normal Distributions. Journal of Computational and Graphical Statistics, 1, 351–365.
GELMAN, A. and KING, G. (1990): Estimating the Electoral Consequence of Legislative Redirecting. Journal of the American Statistical Association, 85, 274~282.
GILKS, W.R., OLDFIELD, L., and RUTHERFORD, A. (1989): Bayesian Approaches to Mixtures. In: W. Knapp, B. Dorken, W.R. Gilks, and S.F. Schlossman (Eds.): Levcoctye Typing IV. Oxford University Press, London, 6–12.
GILKS, W.R., RICHARDSON, S., and SPIEGELHALTER, D.J. (1996): Markov Chain Monte Carlo in Practice. Chapman & Hall, London.
JEFFREYS, H. (1961): Theory of Probability. 3rd ed., Oxford University Press, London.
KASS, R. and RAFTERY, A.E. (1995): Bayes Factors. Journal of the American Statistical Association, 90, 40–60.
LAVINE, M. and WEST, M. (1992): A Bayesian Method of Classification and Discrimination. Canadian Journal of Statistics, 20, 451–461.
NEWTON, M.A. and RAFTERY, A.E. (1994): Approximate Bayesian Inference by the Weighted Likelihood Bootstrap (with Discussion). Journal of the Royal Statistical Society, Series B, 56, 3–48.
O’HAGAN, A. (1994): Kendall’s Advanced Theory of Statistics: Volume 2b Bayesian Inference. John Wiley and Sons, New York, NY.
VERDINELLI, I. and WASSERMAN, L. (1991): Bayesian Analysis of Outlier Problems Using the Gibbs Sampler. Statistics and Computing, 1, 105–177.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
DeSarbo, W.S., Fong, D.K.H., Liechty, J. (2005). Two-Mode Cluster Analysis via Hierarchical Bayes. In: Baier, D., Wernecke, KD. (eds) Innovations in Classification, Data Science, and Information Systems. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26981-9_3
Download citation
DOI: https://doi.org/10.1007/3-540-26981-9_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23221-6
Online ISBN: 978-3-540-26981-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)