IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00458377.html
   My bibliography  Save this paper

A three-way clusterwise multidimensional unfolding procedure for the spatial representation of context dependent preferences

Author

Listed:
  • Selin Atalay

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Wayne Desarbo
  • Simon Blanchard

Abstract

Various deterministic and latent structure approaches for combining forms of multidimensional scaling and cluster analysis have been previously discussed. A new clusterwise three-way unfolding methodology for the analysis of two-way or three-way metric dominance/preference data is proposed. The purpose of this proposed methodology is to simultaneously estimate a joint space of stimuli and cluster ideal point representations, as well as the clusters themselves, such that the geometry underlying the clusterwise model renders some indication of the underlying structure in the data. In the three-way case, it is shown how multiple ideal points can represent preference change over contexts or situations. Partitions, overlapping clusters, stationary and context dependent preference representations are allowed. After a literature review of related methodological research, the technical details of the proposed three-way clusterwise spatial unfolding model are presented in terms of modeling context/situational dependent preferences (i.e., preferences for various stimuli collected over the same set of subjects over time, situation, etc.). The psychological basis for the models is provided in terms of the extensive behavioral decision theory and consumer psychology literature on contextual preferences and situational effects. An application to a data set exploring preferences for breakfast/snack food data over a number of different usage situations is then presented, followed by a discussion on future potential research directions.

Suggested Citation

  • Selin Atalay & Wayne Desarbo & Simon Blanchard, 2009. "A three-way clusterwise multidimensional unfolding procedure for the spatial representation of context dependent preferences," Post-Print hal-00458377, HAL.
  • Handle: RePEc:hal:journl:hal-00458377
    DOI: 10.1016/j.csda.2008.04.011
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00458377
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jacqueline Meulman & Peter Verboon, 1993. "Points of view analysis revisited: Fitting multidimensional structures to optimal distance components with cluster restrictions on the variables," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 7-35, March.
    2. Vichi, Maurizio & Kiers, Henk A. L., 2001. "Factorial k-means analysis for two-way data," Computational Statistics & Data Analysis, Elsevier, vol. 37(1), pages 49-64, July.
    3. Ulf Böckenholt & Ingo Böckenholt, 1991. "Constrained latent class analysis: Simultaneous classification and scaling of discrete choice data," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 699-716, December.
    4. Geert Soete & Suzanne Winsberg, 1993. "A latent class vector model for preference ratings," Journal of Classification, Springer;The Classification Society, vol. 10(2), pages 195-218, December.
    5. Wayne DeSarbo & Duncan Fong & John Liechty & Jennifer Coupland, 2005. "Evolutionary preference/utility functions: A dynamic perspective," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 179-202, March.
    6. Belk, Russell W, 1975. "Situational Variables and Consumer Behavior," Journal of Consumer Research, Oxford University Press, vol. 2(3), pages 157-164, December.
    7. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    8. Wayne DeSarbo & Vithala Rao, 1984. "GENFOLD2: A set of models and algorithms for the general UnFOLDing analysis of preference/dominance data," Journal of Classification, Springer;The Classification Society, vol. 1(1), pages 147-186, December.
    9. Joseph Bennett & William Hays, 1960. "Multidimensional unfolding: Determining the dimensionality of ranked preference data," Psychometrika, Springer;The Psychometric Society, vol. 25(1), pages 27-43, March.
    10. J. Douglas Carroll & Sandra Pruzansky & Joseph Kruskal, 1980. "Candelinc: A general approach to multidimensional analysis of many-way arrays with linear constraints on parameters," Psychometrika, Springer;The Psychometric Society, vol. 45(1), pages 3-24, March.
    11. K. Deun & P. Groenen & W. Heiser & F. Busing & L. Delbeke, 2005. "Interpreting degenerate solutions in unfolding by use of the vector model and the compensatory distance model," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 45-69, March.
    12. Puto, Christopher P, 1987. "The Framing of Buying Decisions," Journal of Consumer Research, Oxford University Press, vol. 14(3), pages 301-315, December.
    13. Frank Busing & Patrick Groenen & Willem Heiser, 2005. "Avoiding degeneracy in multidimensional unfolding by penalizing on the coefficient of variation," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 71-98, March.
    14. Ben-Akiva, Moshe & Morikawa, Takayuki & Shiroishi, Fumiaki, 1992. "Analysis of the reliability of preference ranking data," Journal of Business Research, Elsevier, vol. 24(2), pages 149-164, March.
    15. Henk Kiers & Donatella Vicari & Maurizio Vichi, 2005. "Simultaneous classification and multidimensional scaling with external information," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 433-460, September.
    16. Stef Buuren & Willem Heiser, 1989. "Clusteringn objects intok groups under optimal scaling of variables," Psychometrika, Springer;The Psychometric Society, vol. 54(4), pages 699-706, September.
    17. Amos Tversky & Itamar Simonson, 1993. "Context-Dependent Preferences," Management Science, INFORMS, vol. 39(10), pages 1179-1189, October.
    18. Geert Soete & Willem Heiser, 1993. "A latent class unfolding model for analyzing single stimulus preference ratings," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 545-565, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Blasius, J. & Greenacre, M. & Groenen, P.J.F. & van de Velden, M., 2009. "Special issue on correspondence analysis and related methods," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3103-3106, June.
    2. Tomoya Okubo & Shin-ichi Mayekawa, 2015. "Modeling Viewpoint Shifts in Probabilistic Choice," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 412-427, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. J. Vera & Rodrigo Macías & Willem Heiser, 2013. "Cluster Differences Unfolding for Two-Way Two-Mode Preference Rating Data," Journal of Classification, Springer;The Classification Society, vol. 30(3), pages 370-396, October.
    2. Geert Soete & Willem Heiser, 1993. "A latent class unfolding model for analyzing single stimulus preference ratings," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 545-565, December.
    3. Vera, J. Fernando & Macas, Rodrigo & Heiser, Willem J., 2009. "A dual latent class unfolding model for two-way two-mode preference rating data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3231-3244, June.
    4. Monia Ranalli & Roberto Rocci, 2017. "A Model-Based Approach to Simultaneous Clustering and Dimensional Reduction of Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1007-1034, December.
    5. Masaki Mitsuhiro & Hiroshi Yadohisa, 2015. "Reduced $$k$$ k -means clustering with MCA in a low-dimensional space," Computational Statistics, Springer, vol. 30(2), pages 463-475, June.
    6. Willem Heiser, 2004. "Geometric representation of association between categories," Psychometrika, Springer;The Psychometric Society, vol. 69(4), pages 513-545, December.
    7. José Fernando Romero Cañizares & Purificación Vicente Galindo & Yannis Phillis & Evangelos Grigoroudis, 0. "Graphical sustainability analysis using disjoint biplots," Operational Research, Springer, vol. 0, pages 1-22.
    8. Kamel Jedidi & Wayne DeSarbo, 1991. "A stochastic multidimensional scaling procedure for the spatial representation of three-mode, three-way pick any/J data," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 471-494, September.
    9. Frank Busing & Mark Rooij, 2009. "Unfolding Incomplete Data: Guidelines for Unfolding Row-Conditional Rank Order Data with Random Missings," Journal of Classification, Springer;The Classification Society, vol. 26(3), pages 329-360, December.
    10. Wayne DeSarbo & Michael Johnson & Ajay Manrai & Lalita Manrai & Elizabeth Edwards, 1992. "Tscale: A new multidimensional scaling procedure based on tversky's contrast model," Psychometrika, Springer;The Psychometric Society, vol. 57(1), pages 43-69, March.
    11. Tomoya Okubo & Shin-ichi Mayekawa, 2015. "Modeling Viewpoint Shifts in Probabilistic Choice," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 412-427, June.
    12. Naoto Yamashita & Shin-ichi Mayekawa, 2015. "A new biplot procedure with joint classification of objects and variables by fuzzy c-means clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(3), pages 243-266, September.
    13. Wayne DeSarbo & Kamel Jedidi & Joel Steckel, 1991. "A stochastic multidimensional scaling procedure for the empirical determination of convex indifference curves for preference/choice analysis," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 279-307, June.
    14. Woodside, Arch G. & Ozcan, Timucin, 2009. "Customer choices of manufacturer versus retailer brands in alternative price and usage contexts," Journal of Retailing and Consumer Services, Elsevier, vol. 16(2), pages 100-108.
    15. van de Velden, M. & Iodice D' Enza, A. & Palumbo, F., 2014. "Cluster Correspondence Analysis," Econometric Institute Research Papers EI 2014-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    16. Michio Yamamoto, 2012. "Clustering of functional data in a low-dimensional subspace," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(3), pages 219-247, October.
    17. Tatiana Dyachenko & Rebecca Walker Reczek & Greg M. Allenby, 2014. "Models of Sequential Evaluation in Best-Worst Choice Tasks," Marketing Science, INFORMS, vol. 33(6), pages 828-848, November.
    18. J. Vera & Rodrigo Macías & Willem Heiser, 2009. "A Latent Class Multidimensional Scaling Model for Two-Way One-Mode Continuous Rating Dissimilarity Data," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 297-315, June.
    19. Wayne DeSarbo & Vithala Rao, 1984. "GENFOLD2: A set of models and algorithms for the general UnFOLDing analysis of preference/dominance data," Journal of Classification, Springer;The Classification Society, vol. 1(1), pages 147-186, December.
    20. Yoshio Takane & Tadashi Shibayama, 1991. "Principal component analysis with external information on both subjects and variables," Psychometrika, Springer;The Psychometric Society, vol. 56(1), pages 97-120, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00458377. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://hal.archives-ouvertes.fr/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.