Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-14T21:16:26.984Z Has data issue: false hasContentIssue false
  • English
  • Français

Modeling Viewpoint Shifts in Probabilistic Choice

Published online by Cambridge University Press:  01 January 2025

Tomoya Okubo and
Shin-ichi Mayekawa
Tomoya Okubo*
Affiliation:
The National Center for University Entrance Examinations
Shin-ichi Mayekawa
Affiliation:
Tokyo Institute of Technology
*
Requests for reprints should be sent to Tomoya Okubo, The National Center for University Entrance Examinations, 2-19-23 Komaba, Meguro-ku, Tokyo, 153-8501, Japan. E-mail: okubo@rd.dnc.ac.jp
Get accessRights & Permissions [Opens in a new window]

Abstract

A number of mathematical models for overcoming intransitive choice have been proposed and tested in the literature of decision theory. This article presents the development of a new stochastic choice model based on multidimensional scaling. This allows decision-makers to have multiple viewpoints, whereas current multidimensional scaling models are based on the assumption that a subject or group of subjects has only one viewpoint. The implication of our model is that subjects make an intransitive choice because they are able to shift their viewpoint. This paper also presents the maximum likelihood estimation of the proposed model, and reanalyzes Tversky’s gamble experiment data.

Keywords

viewpoint shiftvector modellatent class modelmultidimensional scaling modeldecision theory

Information

Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 2 , June 2015, pp. 412 - 427
Copyright
Copyright © 2013 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Agresti, A. (2002). Categorical data analysis. Hoboken: Wiley.CrossRefGoogle Scholar
Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. Proc. 2nd international symposium on information theory, 267–281.Google Scholar
Anderson, E.B. (1973). Conditional inference for multiple-choice questionnaires. British Journal of Mathematical & Statistical Psychology, 26, 31–44.CrossRefGoogle Scholar
Anderson, E.B. (1980). Discrete statistical models with social science applications. Amsterdam: North-Holland.Google Scholar
Bennett, J.F., & Hays, W.L. (1960). Multidimensional unfolding: determining the dimensionality of ranked preference data. Psychometrika, 25, 27–43.CrossRefGoogle Scholar
Birnbaum, M.H., & Gutierrez, R.J. (2007). Testing for intransitivity of preferences predicted by a lexicographic semi-order. Organizational Behavior and Human Decision Processes, 104, 96–112.CrossRefGoogle Scholar
Birnbaum, M.H., Patton, J.N., & Lott, M.K. (1999). Evidence against rank-dependent utility theories: tests of cumulative independence, interval independence stochastic dominance, and transitivity. Organizational Behavior and Human Decision Processes, 77, 44–83.CrossRefGoogle ScholarPubMed
Böckenholt, U., & Böckenholt, I. (1991). Constrained latent class analysis: simultaneous classification and scaling of discrete choice data. Psychometrika, 56, 699–716.CrossRefGoogle Scholar
Böckenholt, I., & Gaul, W. (1986). Analysis of choice behavior via probabilistic ideal point and vector models. Applied Stochastic Models and Data Analysis, 2, 202–226.CrossRefGoogle Scholar
Budescu, D.V., & Weiss, W. (1987). Reflection and transitive and intransitive preferences: a test of prospect theory. Organizational Behavior and Human Decision Processes, 39, 184–202.CrossRefGoogle Scholar
Busemeyer, J.R., & Townsend, J.T. (1993). Decision field theory: a dynamic-cognitive approach to decision making in an uncertain environment. Psychological Review, 100, 432–459.CrossRefGoogle Scholar
Carroll, J.D. (1972). Individual differences and multidimensional scaling. In Shepard, R.N., Romney, A.K., & Nerlove, S.B. (Eds.), Multidimensional scaling, Vol. I (pp. 105–155). New York: Seminar Press.Google Scholar
Chintagunta, P.K. (1994). Heterogeneous logit model implications for brand positioning. Journal of Marketing Research, 31, 304–311.CrossRefGoogle Scholar
Davis-Stober, C.P. (2012). A lexicographic semiorder polytope and probabilistic representations of choice. Journal of Mathematical Psychology, 56, 86–94.CrossRefGoogle Scholar
Dempster, A.P., Laired, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39, 1–38.CrossRefGoogle Scholar
DeSarbo, W.S., Atalay, A.S., & Blanchard, S.J. (2009). A three-way clusterwise multidimensional unfolding procedure for the spatial representation of context dependent preferences. Computational Statistics & Data Analysis, 53, 3217–3230.CrossRefGoogle Scholar
DeSarbo, W.S., & Cho, J. (1989). A stochastic multidimensional scaling vector threshold model for the spatial representation of “pick any/n” data. Psychometrika, 54, 105–129.CrossRefGoogle Scholar
DeSarbo, W.S., Howard, D.J., & Jedidi, K. (1991). Multiclus: a new method for simultaneously performing multidimensional scaling and cluster analysis. Psychometrika, 56, 121–136.CrossRefGoogle Scholar
DeSarbo, W.S., Oliver, R.L., & De Soete, G. (1986). A probabilistic multidimensional scaling vector model. Applied Psychological Measurement, 10, 79–98.CrossRefGoogle Scholar
De Soete, G., & Heiser, W. (1993). A latent class unfolding model for analyzing single stimulus preference ratings. Psychometrika, 58, 545–565.CrossRefGoogle Scholar
De Soete, G., & Winsberg, S. (1993). A latent class vector model for preference ratings. Journal of Classification, 10, 195–218.CrossRefGoogle Scholar
Goodman, L.A. (1979). On the estimation of parameters in latent structure analysis. Psychometrika, 44, 123–128.CrossRefGoogle Scholar
Harless, D.W., & Camerer, C.F. (1994). The predictive utility of generalized expected utility theories. Econometrica, 62, 1251–1289.CrossRefGoogle Scholar
Hey, J.D., & Orme, C. (1994). Investigating generalizations of expected utility theory using experimental data. Econometrica, 62, 1291–1326.CrossRefGoogle Scholar
Iverson, G., & Falmagne, J.C. (1985). Statistical issues in measurement. Mathematical Social Sciences, 10, 131–153.CrossRefGoogle Scholar
Loomes, G., Moffatt, P.G., & Sugden, R. (2002). A microeconometric test of alternative stochastic theories of risky choice. Journal of Risk and Uncertainty, 24, 103–130.CrossRefGoogle Scholar
Loomes, G., & Sugden, R. (1995). Incorporating a stochastic element into decision theories. European Economic Review, 39, 641–648.CrossRefGoogle Scholar
Loomes, G., & Sugden, R. (1998). Testing different stochastic specifications of risky choice. Economica, 65, 581–598.CrossRefGoogle Scholar
Montgomery, H. (1977). A study of intransitive preferences using a think aloud procedure. In Jungerman, H., & de Zeeuw, G. (Eds.), Decision making and change in human affairs (pp. 347–362). Hoboken: Wiley.CrossRefGoogle Scholar
Regenwetter, M., Dana, J., & Davis-Stober, C.P. (2010). Testing transitivity of preferences on two-alternative forced choice data. Frontiers in Psychology, 1, 148.CrossRefGoogle ScholarPubMed
Regenwetter, M., Dana, J., & Davis-Stober, C.P. (2011). Transitivity of preferences. Psychological Review, 118, 42–56.CrossRefGoogle ScholarPubMed
Regenwetter, M., & Davis-Stober, C.P. (2012). Behavioral variability of choices versus structural inconsistency of preferences. Psychological Review, 119, 408–416.CrossRefGoogle ScholarPubMed
Scheffé, H. (1952). An analysis of variance for paired comparisons. Journal of the American Statistical Association, 47, 381–400.Google Scholar
Slater, P. (1960). The analysis of personal preferences. British Journal of Statistical Psychology, 13, 119–135.CrossRefGoogle Scholar
Takane, Y. (1980). Maximum likelihood estimation in the generalized case of Thurstone’s model of comparative judgment. Japanese Psychological Research, 22, 188–196.CrossRefGoogle Scholar
Takane, Y. (1998). Choice model analysis of the “pick any/n” type of binary data. Japanese Psychological Research, 40, 31–39.CrossRefGoogle Scholar
Takane, Y., van der Heijden, P.G.M., & Browne, M.W. (2003). On likelihood ratio tests for dimensionality selection. In Higuchi, T., Iba, Y., & Ishiguro, M. (Eds.), Proceedings of science of modeling: the 30th anniversary meeting of the information criterion (AIC) (pp. 348–349). Tokyo: The Institute of Statistical Mathematics.Google Scholar
Thurstone, L.L. (1927). A law of comparative judgment. Psychological Review, 34, 273–286.CrossRefGoogle Scholar
Tsai, R., & Böckenholt, U. (2006). Modelling intransitive preferences: a random-effects approach. Journal of Mathematical Psychology, 50, 1–14.CrossRefGoogle Scholar
Tsai, R., & Böckenholt, U. (2008). On the importance of distinguishing between within- and between-subject effects in intransitive intertemporal choice. Journal of Mathematical Psychology, 52, 10–20.CrossRefGoogle Scholar
Tucker, L.R. (1960). Intra-individual and inter-individual multidimensionality. In Gulliksen, H., & Messick, S. (Eds.), Psychological scaling: theory and applications (pp. 155–167). New York: Wiley.Google Scholar
Tversky, A. (1969). Intransitivity of preference. Psychological Review, 76, 31–48.CrossRefGoogle Scholar
Winsberg, S., & De Soete, G. (2002). A bootstrap procedure for mixture models: applied to multidimensional scaling latent class models. Applied Stochastic Models in Business and Industry, 18, 391–406.CrossRefGoogle Scholar