Marketing Letters

, 19:255

Sequential sampling models of choice: Some recent advances

  • Thomas Otter
  • Joe Johnson
  • Jörg Rieskamp
  • Greg M. Allenby
  • Jeff D. Brazell
  • Adele Diederich
  • J. Wesley Hutchinson
  • Steven MacEachern
  • Shiling Ruan
  • Jim Townsend
Article

Abstract

Choice models in marketing and economics are generally derived without specifying the underlying cognitive process of decision making. This approach has been successfully used to predict choice behavior. However, it has not much to say about such aspects of decision making as deliberation, attention, conflict, and cognitive limitations and how these influence choices. In contrast, sequential sampling models developed in cognitive psychology explain observed choices based on assumptions about cognitive processes that return the observed choice as the terminal state. We illustrate three advantages of this perspective. First, making explicit assumptions about underlying cognitive processes results in measures of deliberation, attention, conflict, and cognitive limitation. Second, the mathematical representations of underlying cognitive processes imply well documented departures from Luce’s Choice Axiom such as the similarity, compromise, and attraction effects. Third, the process perspective predicts response time and thus allows for inference based on observed choices and response times. Finally, we briefly discuss the relationship between these cognitive models and rules for statistically optimal decisions in sequential designs.

Keywords

Luce’s Axiom Choice models Diffusion models Race models Human information processing Response time Optimal decision making Likelihood based inference 

References

  1. Adamowicz, V., Bunch, D., Cameron, T. A., Dellaert, B. G. C., Hanneman, M., Keane, M., et al. (2008). Behavioral frontiers in choice modeling. Marketing Letters doi:10.1007/s11002-008-9038-1.
  2. Ashby, F. G. (1983). A biased random-walk model for 2 choice reaction-times. Journal of Mathematical Psychology, 27, 277–297.CrossRefGoogle Scholar
  3. Ashby, F. G., & Townsend, J. T. (1986). Varieties of perceptual independence. Psychological Review, 93, 154–179.CrossRefGoogle Scholar
  4. Bogacz, R. (2007). Optimal decision-making theories: Linking neurobiology with behaviour. Trends in Cognitive Sciences, 11, 118–125.CrossRefGoogle Scholar
  5. Bogacz, R., Brown, E., Jeff, M., Holmes, J. P., & Cohen, J. D. (2006). The physics of optimal decision making: A formal analysis of models of performance in two-alternative forced-choice tasks. Psychological Review, 113, 700–765.CrossRefGoogle Scholar
  6. Busemeyer, J. R., & Diederich, A. (2002). Survey of decision field theory. Mathematical Social Sciences, 43, 345–370.CrossRefGoogle Scholar
  7. Busemeyer, J. R., & Townsend, J. T. (1993). Decision field theory: A dynamic cognition approach to decision making. Psychological Review, 100, 432–459.CrossRefGoogle Scholar
  8. Diederich, A. (1997). Dynamic stochastic model for decision making under time constraints. Journal of Mathematical Psychology, 41, 260–274.CrossRefGoogle Scholar
  9. Diederich, A. (2003a). MDFT account of decision making under time pressure. Psychonomic Bulletin and Review, 10, 157–166.Google Scholar
  10. Diederich, A. (2003b). Decision making under conflict: Decision time as a measure of conflict strength. Psychonomic Bulletin and Review, 10, 167–176.Google Scholar
  11. Diederich, A., & Busemeyer, J. R. (1999). Conflict and the stochastic dominance principle of decision making. Psychological Science, 10, 353–359.CrossRefGoogle Scholar
  12. Diederich, A., & Busemeyer, J. R. (2003). Simple matrix methods for analyzing diffusion models of choice probability, choice response time and simple response time. Journal of Mathematical Psychology, 47, 304–322.CrossRefGoogle Scholar
  13. Gilbride, T., & Allenby, G. (2006). Estimating heterogeneous EBA and economic screening rule choice models. Marketing Science, 25, 494–509.CrossRefGoogle Scholar
  14. Huang, Y., & Hutchinson, J. W. (2008). Counting every thought: Implicit measures of cognitive responses to advertising. Journal of Consumer Research, 35(1), 98–118.CrossRefGoogle Scholar
  15. Huber, J., Payne, J. W., & Puto, C. (1982). Adding asymmetrically dominated alternatives: Violations of regularity and the similarity hypothesis. Journal of Consumer Research, 9, 90–98.CrossRefGoogle Scholar
  16. Huber, J., & Puto, C. (1983). Market boundaries and product choice: Illustrating attraction and substitution effects. Journal of Consumer Research, 10, 31–44.CrossRefGoogle Scholar
  17. Johnson, J. G., & Busemeyer, J. R. (2005). A dynamic, computational model of preference reversal phenomena. Psychological Review, 112, 841–861.CrossRefGoogle Scholar
  18. Kivetz, R., Netzer, O., & Srinivasan, V. (2004). Alternative models for capturing the compromise effect. Journal of Marketing Research, 41, 237–57.CrossRefGoogle Scholar
  19. LaBerge, D. (1962). A recruitment theory of simple behavior. Psychometrika, 27, 375–396.CrossRefGoogle Scholar
  20. McMillen, T., & Holmes, P. (2005). The dynamics of choice among multiple alternatives. Journal of Mathematical Psychology, 50, 30–57.CrossRefGoogle Scholar
  21. Otter, T., Allenby, G., & van Zandt, T. (2007). An integrated model of choice and response time. Journal of Marketing Research (forthcoming).Google Scholar
  22. Rieskamp, J., Busemeyer, J. R., & Mellers, B. A. (2006). Extending the bounds of rationality: Evidence and theories of preferential choice. Journal of Economic Literature, 44, 631–661.CrossRefGoogle Scholar
  23. Roe, R. M., Busemeyer, J. R., & Townsend, J. T. (2001). Multialternative decision field theory: A dynamic connectionist model of decision making. Psychological Review, 108, 370–392.CrossRefGoogle Scholar
  24. Ruan, S. (2007). Poisson race models for conjoint choice analysis: Theory and applications. Unpublished Ph.D. dissertation. Department of Statistics, The Ohio State University.Google Scholar
  25. Ruan, S., MacEachern, S., Otter, T., & Dean, A. (2007). Dependent Poisson race models and modeling dependence in conjoint choice experiments. Psychometrika (forthcoming).Google Scholar
  26. Simonson, I. (1989). Choice based on reasons: The case of attraction and compromise effects. Journal of Consumer Research, 16, 158–174.CrossRefGoogle Scholar
  27. Smith, P. L. (2000). Stochastic dynamic models of response time and accuracy: A foundational primer. Journal of Mathematical Psychology, 44, 408–436.CrossRefGoogle Scholar
  28. Stone, M. (1960). Models for choice-reaction time. Psychometrika, 25, 251–260.CrossRefGoogle Scholar
  29. Tanner, M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82, 528–540.CrossRefGoogle Scholar
  30. Townsend, J. T. (1972). Some results concerning the identifiability of parallel and serial processes. British Journal of Mathematical and Statistical Psychology, 25, 168–199.Google Scholar
  31. Townsend, J. T., & Ashby, F. G. (1983). Stochastic modeling of elementary psychological processes. Cambridge: Cambridge University Press.Google Scholar
  32. Townsend, J. T., & Nozawa, G. (1995). Spatio-temporal properties of elementary perception: An investigation of parallel, serial and coactive theories. Journal of Mathematical Psychology, 39, 321–360.CrossRefGoogle Scholar
  33. Townsend, J. T., & Schweickert, R. (1989). Toward the trichotomy method: Laying the foundation of stochastic mental networks. Journal of Mathematical Psychology, 33, 309–327.CrossRefGoogle Scholar
  34. Townsend, J. T., & Wenger, M. J. (2004). A theory of interactive parallel processing: New capacity measures and predictions for a response time inequality series. Psychological Review, 111, 1003–1035.CrossRefGoogle Scholar
  35. Tversky, A. (1972a). Elimination by aspects: A theory of choice. Psychological Review, 79, 281–299.CrossRefGoogle Scholar
  36. Tversky, A. (1972b). Choice by elimination. Journal of Mathematical Psychology, 9(4), 341–367.CrossRefGoogle Scholar
  37. Tversky, A., & Simonson, I. (1993). Context dependent preferences. Management Science, 39, 1179–1189.CrossRefGoogle Scholar
  38. Usher, M., & McClelland, J. L. (2004). Loss aversion and inhibition in dynamical models of multialternative choice. Psychological Review, 111, 757–769.CrossRefGoogle Scholar
  39. Vickers, D. (1970). Evidence for an accumulator of psychophysical discrimination. Ergonomics, 13, 37–58.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Thomas Otter
    • 1
  • Joe Johnson
    • 2
  • Jörg Rieskamp
    • 3
  • Greg M. Allenby
    • 4
  • Jeff D. Brazell
    • 5
  • Adele Diederich
    • 6
  • J. Wesley Hutchinson
    • 7
  • Steven MacEachern
    • 8
  • Shiling Ruan
    • 8
  • Jim Townsend
    • 9
  1. 1.J. W. Goethe Universität (Marketing)FrankfurtGermany
  2. 2.Miami University (Psychology)OxfordUSA
  3. 3.University Basel (Psychology)BaselSwitzerland
  4. 4.Ohio State University (Marketing)ColumbusUSA
  5. 5.The Modellers, LLC (Marketing)Salt Lake CityUSA
  6. 6.Jacobs University Bremen (Psychology)BremenGermany
  7. 7.University of Pennsylvania (Marketing)PhiladelphiaUSA
  8. 8.Ohio State University (Statistics)ColumbusUSA
  9. 9.Indiana University (Psychology)BloomingtonUSA

Personalised recommendations