, Volume 61, Issue 3, pp 485–508 | Cite as

A stochastic multidimensional unfolding approach for representing phased decision outcomes

  • Wayne S. DeSarbo
  • Donald R. Lehmann
  • Gregory Carpenter
  • Indrajit Sinha


This paper presents a stochastic multidimensional unfolding (MDU) procedure to spatially represent individual differences in phased or sequential decision processes. The specific application or scenario to be discussed involves the area of consumer psychology where consumers form judgments sequentially in their awareness, consideration, and choice set compositions in a phased or sequential manner as more information about the alternative brands in a designated product/service class are collected. A brief review of the consumer psychology literature on these nested congnitive sets as stages in phased decision making is provided. The technical details of the proposed model, maximum likelihood estimation framework, and algorithm are then discussed. A small scale Monte Carlo analysis is presented to demonstrate estimation proficiency and the appropriateness of the proposed model selection heuristic. An application of the methodology to capture awareness, consideration, and choice sets in graduate school applicants is presented. Finally, directions for future research and other potential applications are given.

Key words

consumer psychology multidimensional scaling maximum likelihood consideration sets multidimensional unfolding successive categories analysis 


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  1. Abelson, R. P., & Levi A. (1985). Decision making and decision theory. In G. Lindzey & E. Aronson (Eds.),The handbook of social psychology (Vol. 1, 213–251). New York: Random House.Google Scholar
  2. Akaike, H. (1974). A new look at statistical model identification.IEEE transactions on automatic control (Vol. 6), 716–723.Google Scholar
  3. Alba, J. W., & Hutchinson, J. W. (1987). Dimensions of consumer expertise.Journal of Consumer Research, 13, 411–454.Google Scholar
  4. Belonax, J. A., Jr. (1979). Decision rule uncertainty, evoked set size, and task difficulty as a function of number of choice criteria and information variability. In William L. Wilkie (Ed.),Advances in consumer research (pp. 232–235). Provo, UT: Association for Consumer Research.Google Scholar
  5. Belonax, J. A., Jr., & Mittelstaedt, R. A. (1978). Evoked set size as a function of choice criteria and information variability. In H. Keith Hunt (Ed.),Advances in consumer research (pp. 48–51). Provo, UT: Association for Consumer Research.Google Scholar
  6. Bettman, J. (1979).An information processing theory of consumer choice. Reading, MA: Addison-Wesley.Google Scholar
  7. Bettman, J. R., & Whan Park, C. (1980). Effects of prior knowledge and experience, and phase of the choice process on consumer decision processes: A protocols analysis.Journal of Consumer Research, 12, 234–248.Google Scholar
  8. Bettman, J. R., Johnson, E. J., & Payne, J. W. (1993). Consumer decision making. In T. S. Robertson & H. H. Kassayain (Eds.),Handbook of consumer behavior (pp. 50–84). Englewood Cliffs, NJ: Prentice Hall.Google Scholar
  9. Biehal, G., & Chakravarti, D. (1986). Consumers' use of memory and external information in choice: Macro and micro perspectives.Journal of Consumer Research, 12, 382–405.Google Scholar
  10. Boccara, B. (1989).Modeling choice set formation in discrete choice models. Unpublished doctoral dissertation, Massachusetts Institute of Technology, Department of Civil Engineering.Google Scholar
  11. Böckenholt, U., & Böckenholt, I. (1991). Constrained latent class analysis: Simultaneous classification and scaling of discrete choice data.Psychometrika, 56, 699–717.Google Scholar
  12. Böckenholt, I., & Gaul, W. (1991). Generalized latent class analysis: A new methodology for market structure analysis. In O. Opitz (Ed.),Conceptual and numerical analysis of data (pp. 367–376). New York: Springer-Verlag.Google Scholar
  13. Bozdogan, H. (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions.Psychometrika, 52, 345–370.Google Scholar
  14. Brisoux, J. E., & Cheron, E. (1990). Brand categorization and product involvement. In Marvin E. Goldberg & Gerald Gorn (Eds.),Advances in consumer research (pp. 101–109). Provo, UT: Association for Consumer Research.Google Scholar
  15. Brisoux, J. E., & Laroche, M. (1980). A proposed consumer strategy of simplification for categorizing brands. In John H. Summey & Ronald D. Taylor (Eds.),Evolving marketing thought for 1980 (pp. 112–114). Carbondale, IL: Southern Marketing Association.Google Scholar
  16. Brisoux, J. E., & Laroche, M. (1981). Evoked set formation and composition: An empirical investigation under a routinized response behavior situation. In Kent B. Monroe (Ed.),Advances in consumer research (pp. 357–361). Provo, UT: Association for Consumer Research.Google Scholar
  17. Brown, J. J., & Wildt, A. R. (1992). Consideration set measurement.Journal of the Academy of Marketing Science, 3, 235–243.Google Scholar
  18. Campbell, B. M. (1969). The existence and determinants of evoked set in brand choice behavior. Unpublished doctoral disseration, Columbia University.Google Scholar
  19. Carroll, J. D. (1980). Models and methods for multidimensional analysis of preferential choice data. In E. D. Lantermann & H. Feger (Eds.),Similarity and choice (pp. 234–289). Bern: Hans Huber.Google Scholar
  20. Crowley, A. E., & Williams, J. H. (1991). An information theoretic approach to understanding the consideration set/awareness set proportion. In Rebecca H. Holman & Michael R. Solomon (Eds.),Advances in consumer research (pp. 780–787). Provo, UT: Association for Consumer Research.Google Scholar
  21. Currim, I. S., Meyer, R. J., & Lee, N. (1988). Disaggregate tree-structured modeling of consumer choice.Journal of Marketing Research, 25, 253–265.Google Scholar
  22. Dawes, R. M., & Corrigan, B. (1974). Linear models in decision making.Psychological Bulletin, 81, 95–106.Google Scholar
  23. DeSarbo, W. S., & Carroll, J. D. (1985). Three-way metric unfolding via weighted alternating least-squares.Psychometrika, 50, 275–300.Google Scholar
  24. DeSarbo, W. S., & Hoffman, D. L. (1986). Simple and weighted unfolding MDS threshold models for the spatial analysis of binary data.Applied Psychological Measurement, 10, 247–264.Google Scholar
  25. DeSarbo, W. S., & Hoffman, D. L. (1987). Constructing MDS joint spaces from binary choice data: A new multidimensional unfolding threshold model for marketing research.Journal of Marketing Research, 24, 40–54.Google Scholar
  26. DeSarbo, W. S., Manrai, A. K., & Manrai, L. A. (1994). Latent class multidimensional scaling: A review of recent development in the marketing and psychometric literature. In R. Bagozzi (Ed.),Handbook of marketing research (pp. 190–222). London, UK: Blackwell Publishing.Google Scholar
  27. DeSarbo, W. S., & Rao, V. R. (1984). GENFOLD2: A set of models and algorithms for the general unfolding analysis of preference/dominance data.Journal of Classification, 1, 146–185.Google Scholar
  28. DeSarbo, W. S., & Rao, V. R. (1986). A new constrained unfolding model for product positioning.Marketing Science, 5, 1–19.Google Scholar
  29. DeSoete, G., Carroll, J. D., & DeSarbo, W. S. (1986). The waundering ideal point model: A probabilistic multidimensional unfolding model for paired comparison data.Journal of Mathematical Psychology, 30, 28–41.Google Scholar
  30. Einhorn, H. J. (1970a). The use of nonlinear, noncompensatory models in decision making.Psychological Bulletin, 73, 221–230.Google Scholar
  31. Einhorn, H. J. (1970b). Use of nonlinear, noncompensatory models as a function of task and amount of information.Organizational Behavior and Human Performance, 6, 1–27.Google Scholar
  32. Einhorn, H. J. (1970c). Use of Nonlinear, noncompensatory models in decision making.Psychological Bulletin, 73, 221–230.Google Scholar
  33. Fishbein, M. (1967). Attitude and prediction of behavior. In M. Fishbein (Ed.),Readings in attitude theory and measurement (pp. 477–492). New York: Wiley and Sons.Google Scholar
  34. Gensch, D. (1987). A two-stage disaggregate attribute choice model.Marketing Science, 6, 223–231.Google Scholar
  35. Hauser, J. R. (1978). Testing the accuracy, usefulness, and significance of probabilistic choice models: An information theoretic approach.Operations Research, 26, 406–421.Google Scholar
  36. Hauser, J. R., & Shugan, S. M. (1983). Defensive marketing strategies.Marketing Science, 3, 327–351.Google Scholar
  37. Hauser, J. R., & Gaskin, S. (1984). Application of the defender consumer model.Marketing Science, 3, 327–351.Google Scholar
  38. Hauser, J. R., & Wernerfelt, B. (1990). An evaluation cost model of evoked sets.Journal of Consumer Research, 16, 393–408.Google Scholar
  39. Himmelblau, D. M. (1972).Applied non-linear programming. New York: Harper & Row.Google Scholar
  40. Howard, J. A., & Sheth, J. N. (1969).The theory of buyer behavior, New York: John Wiley and Sons.Google Scholar
  41. Janis, I. L. (1968). Stages in the decision making process. In R. P. Abelson (Ed.),Theories of cognitive consistency (pp. 577–588). Chicago: Rand McNally.Google Scholar
  42. Janis, I. L., & Mann, L. (1977).Decision making, New York: Free Press.Google Scholar
  43. Jedidi, K., & DeSarbo, W. S. (1991). A stochastic multidimensional scaling methodology for the spatial representation of three-mode, three-way binary data.Psychometrika, 56, 471–494.Google Scholar
  44. Johnson, E. J., & Meyer, R. J. (1984). Compensatory choice models of noncompensatory processes: The effect of varying context.Journal of Consumer Research, 11, 528–541.Google Scholar
  45. Johnson, E. J., Meyer, R. J., & Ghosh, S. (1989). When choice models fail: Compensatory models in negatively correlated environments.Journal of Marketing Research, 26, 255–270.Google Scholar
  46. Kardes, F. R., Kalyanaram, G., Chandrashekaran, M., & Dornoff, R. J. (1993). Brand retrieval, consideration set composition, consumer choice, and the pioneering advantage.Journal of Consumer Research, 20, 62–75.Google Scholar
  47. Klenosky, D. B., & Rethans, A. J. (1989). The formation of consumer choice sets. In M. Houston (Ed.),Advances in consumer research (pp. 13–17). Provo, UT: ACR.Google Scholar
  48. Laurent, G., & Lapersonne, E. (1990).Consideration sets of size one (Working paper). Jouy-en-Josas, France: Ecole Des Hautes Etudes Commerciales, Centre HEC-ISA.Google Scholar
  49. Lehmann, D. R., & Pan, Y. (in press). Context effects, new brand entry, and consideration sets.Journal of Marketing Research.Google Scholar
  50. Lussier, D. A., & Olshavsky, R. W. (1979). Task complexity and contingent processing in brand choice.Journal of Consumer Research, 6, 154–165.Google Scholar
  51. McFadden, D. (1978). Modeling the choice of residential locations. In Anders Karlquist, Lars Lundquist, Folke Snickars, & Jorgen W. Weibull (Eds.),Spatial interaction theory and planning models (pp. 75–96). Amsterdam: North-Holland.Google Scholar
  52. Narayana, C. L., & Markin, R. J. (1975). Consumer behavior and product performance: An alternative conceptualization.Journal of Marketing, 39, 1–6.Google Scholar
  53. Nedungadi, P. (1987).Formation and use of a consideration set: Implications for marketing and research on consumer choice. Unpublished doctoral dissertation, University of Florida, Gainesville.Google Scholar
  54. Nedungadi, P. (1990a). Recall and consumer consideration sets: Influencing choice without altering brand evaluations.Journal of Consumer Research, 17, 245–253.Google Scholar
  55. Nedungadi, P. (1990b). Consideration sets: A brief review of issues (Working paper). Toronto, ON: University of Toronto, Faculty of Management.Google Scholar
  56. Payne, J. W., (1976). Task complexity and cintingent processing in decision making: An information search and protocol analysis.Organizational Behavior and Human Performance, 16, 366–387.Google Scholar
  57. Payne, J. W. (1982). Contingent decision behavior.Psychological Bulletin, 92, 382–402.Google Scholar
  58. Payne, J. W., Bettman, J. R., & Johnson, E. J. (1990). The adaptive decision maker. In R. M. Hogarth (Ed.),Insights in decision making (pp. 129–153). Chicago: University of Chicago Press.Google Scholar
  59. Powell, M. J. D. (1977). Restart procedures for the conjugate gradient method.Mathematical Programming, 12, 241–254.Google Scholar
  60. Punj, G. N., & Staelin, R. (1978). The choice process for graduate business schools.Journal of Marketing Research, 15, 588–598.Google Scholar
  61. Ratneshwar, S., & Shocker, A. D. (1991). Substitution in use and the role of usage context in product category structures.Journal of Marketing Research, 28, 281–295.Google Scholar
  62. Roberts, J. H. (1989). A grounded model of consideration set size and composition. In Thomas K. Shrull (Ed.),Advances in consumer research (pp. 749–757). Provo, UT: Association for Consumer Research.Google Scholar
  63. Roberts, J. H., & Lattin, J. M. (1991). Development and testing of a model of consideration set composition.Journal of Marketing Research, 28, 429–440.Google Scholar
  64. Rosenberg, M. J. (1956). Cognitive structures and attitudinal affect.Journal of Abnormal and Social Psychology, 53, 367–372.Google Scholar
  65. Schwarz, G. (1978). Estimating the dimension of a model.Annals of Statistics, 6, 461–464.Google Scholar
  66. Sclove, S. L. (1987). Application of model selection criteria to some problems in multivariate analysis.Psychometrika, 52, 333–343.Google Scholar
  67. Shocker, A. D., Ben-Akiva, M., Boccara, B., & Nedungadi, P. (1991). Consideration set influences on customer decision-making and choice: Issues, models, and suggestions.Marketing letters, 2, 181–198.Google Scholar
  68. Shugan, S. M. (1980). The cost of thinking.Journal of Consumer Research, 7, 99–111.Google Scholar
  69. Silk, A. J., & Urban, G. L. (1978). Pre-test market evaluation of new packaged goods: A model and measurement methodology.Journal of Marketing Research, 15, 171–191.Google Scholar
  70. Simon, H. (1957).Models of man. New York: Wiley and Sons.Google Scholar
  71. Simonson, I., & Tversky, A. (1992). Choice in context: Trade-off contrast and extremism aversion.Journal of Marketing Research, 29, 281–295.Google Scholar
  72. Sneath, P. H., & Sneath, R. R. (1973).Numerical taxonomy. San Francisco: W. H. Freeman.Google Scholar
  73. Spiggle, S., & Sewall, M. A. (1987). A choice sets model of retail selection.Journal of Marketing, 51, 97–111.Google Scholar
  74. Swait, J. (1984).Probabilistic choice set formation in transportation demand models. Unpublished doctoral dissertation, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
  75. Takane, Y. (1981). Multidimensional successive categories scaling: A maximum likelihood method.Psychometrika, 46, 9–28.Google Scholar
  76. Takane, Y., & Carroll, J. D. (1981). Nonmetric maximum likelihood scaling from directional rankings of similarities.Psychometrika, 46, 389–405.Google Scholar
  77. Troye, S. V. (1984) Evoked set formation as a categorization process. In T. C. Kinnear (Ed.),Advances in consumer research (Vol. 11, pp. 180–186). Provo, UT: ACR.Google Scholar
  78. Tversky, A. (1972). Elimination by aspects: A theory of choice.Psychological Review, 79(4), 281–289.Google Scholar
  79. Tversky, A., & Sattath, S. (1979). Preference Trees.Psychological Review, 86, 542–573.Google Scholar
  80. Urban, G. L., & Hauser, J. R. (1993).Design and marketing of new products (2nd ed.). Clifton Heights, NJ: Prentice Hall.Google Scholar
  81. Urban, G. L., Hulland, J. S., & Weinberg, B. D. (1993). Premarket forecasting for new consumer durable goods: Modeling categorization, elimination, and consideration phenomena.Journal of Marketing, 57, 47–63.Google Scholar
  82. Wilkie, W. L., & Pessemier, E. A. (1973). Issues in marketing's use of multi-attribute models.Journal of Marketing Research, 10, 428–441.Google Scholar
  83. Wright, P. (1975). Consumer choice strategies: Simplifying vs. optimizing.Journal of Marketing Research, 12, 60–67.Google Scholar
  84. Wright, P., & Barbour, F. (1977). Phased decision strategies: Sequels to initial screening. In Marting Starr & Milan Zeleny (Eds.),Multiple criteria decision making (pp. 91–109, North Holland TIMS Studies in Management Science). Amsterdam: North Holland.Google Scholar

Copyright information

© The Psychometric Society 1996

Authors and Affiliations

  • Wayne S. DeSarbo
    • 4
  • Donald R. Lehmann
    • 1
  • Gregory Carpenter
    • 2
  • Indrajit Sinha
    • 3
  1. 1.Marketing DepartmentColumbia UniversityUSA
  2. 2.Marketing DepartmentNorthwestern UniversityUSA
  3. 3.Marketing DepartmentTemple UniversityUSA
  4. 4.Department of Marketing, Smeal School of BusinessPennsylvania State UniversityUniversity Park

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