Abstract
A new model for analyzing two-way, two-mode preference data is proposed. MultiDimensional Unfolding models (MDU) have been used widely. In these model, the observed preference value is related to the distance between the ideal point and object point only. The market share of each brand is ignored or assumed to be be the same for all objects. The attraction of each object, such as the market share of that object, must be incorporated in the analysis of marketing data. A gravity-based multidimensional unfolding model will be proposed. One specific characteristic of preference data of N subjects is that observed preference values of individuals are often not compatible between individuals. The de-generated configuration problem on applying the non-metric MDU method to a real data set will be caused by the week condition on the data matrix. A linearly constrained non-metric approach is also proposed to try to rescue from obtaining the de-generated configuration.
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References
BOTTUM, M.S. (1989): Retail Gravity Model. The Appraisal Journal, 557, 166–172.
BORG, I, and GROENEN, P. (1997): Modern Multidimensional Scaling. Springer, New York.
DESARBO, W.S., KIM, J., CHOI, S.C., and SPAULDINGS, M. (2002): A Gravity-Based Multidimensional Scaling Model for Deriving Spatial Structures Underlying Consumer Preference Judgements. Journal of Consumer Research, 29, 91–100.
GREEN, P.E. and RAO, V.R. (1972): Applied Multidimensional Scaling. Dryden Press, Hinsdale, IL.
KRUSKAL, J.B. (1964): Nonmetric Multidimensional Scaling: A Numerical Method. Psychometrika, 29, 115–129.
RUSHTON, G. (1969): The Scaling of Locational Preferences. In: K.R. Cox and R.G. Gooedge (Eds): Behavioral Problems in Geography: A Symposium. Studies in Geography, 17, 192–227, Department of Geography, Northwestern University.
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Imaizumi, T. (2005). A Gravity-Based Multidimensional Unfolding Model for Preference Data. 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_39
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DOI: https://doi.org/10.1007/3-540-26981-9_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23221-6
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