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Thurstonian-Based Analyses: Past, Present, and Future Utilities

Published online by Cambridge University Press:  01 January 2025

Ulf Böckenholt
Ulf Böckenholt*
Affiliation:
McGill University
*
Requests for reprints should be sent to: E-mail: ulf.bockenholt@mcgill.ca
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Abstract

Current psychometric models of choice behavior are strongly influenced by Thurstone’s (1927, 1931) experimental and statistical work on measuring and scaling preferences. Aided by advances in computational techniques, choice models can now accommodate a wide range of different data types and sources of preference variability among respondents induced by such diverse factors as person-specific choice sets or different functional forms for the underlying utility representations. At the same time, these models are increasingly challenged by behavioral work demonstrating the prevalence of choice behavior that is not consistent with the underlying assumptions of these models. I discuss new modeling avenues that can account for such seemingly inconsistent choice behavior and conclude by emphasizing the interdisciplinary frontiers in the study of choice behavior and the resulting challenges for psychometricians.

Keywords

consistency conditionsidentifiabilityrandom utility modelssocial dependencies

Information

Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 4 , December 2006 , pp. 615 - 629
Copyright
Copyright © 2007 The Psychometric Society

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Footnotes

The author would like to thank R. Darrell Bock whose work inspired many of the ideas presented here. The paper benefitted from helpful comments by Albert Maydeu-Olivares and Rung-Ching Tsai. The reported research was supported in parts by the Social Sciences and Humanities Research Council of Canada.

References

Allenby, G.M., Lenk, P.J. (1994). Modeling household purchase behavior with logistic normal regression. Journal of the American Statistical Association, 89, 1218–1231.CrossRefGoogle Scholar
Anselin, L. (2002). Under the Hood: Issues in the specification and interpretation of spatial regression models. Agricultural Economics, 17, 247–267.CrossRefGoogle Scholar
Ansari, A., & Iyengar, R. (in press). Semiparametric Thurstonian models for recurrent choices: A Bayesian analyis. Psychometrika, 71.Google Scholar
Ashford, J.R., Sowdon, R.R. (1970). Multivariate probit analysis. Biometrics, 26, 535–546.CrossRefGoogle Scholar
Ben-Akiva, M., McFadden, D., Abe, M., Böckenholt, U., Bolduc, D., Gopinath, D., Morikawa, T., Ramaswamy, V., Rao, V., Revelt, D., Steinberg, D. (1997). Modeling methods for discrete choice analysis. Marketing Letters, 8, 273–286.CrossRefGoogle Scholar
Block, H., Marschak, J.et al. (1960). Random orderings and stochastic theories of response. In Olkin, I.et al. (Eds.), Contributions to probability and statistics (pp. 97–132). Stanford, CA: Stanford University Press.Google Scholar
Bock, R.D. (1958). Remarks on the test of significance for the method of paired comparisons. Psychometrika, 23, 323–334.CrossRefGoogle Scholar
Bock, R.D.et al (1969). Estimating multinomial response relations. In Bose, R.C.et al. (Eds.), Essays in probability and statistics (pp. 111–132). Chapel Hill: University of North Carolina Press.Google Scholar
Bock, R.D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29–51.CrossRefGoogle Scholar
Bock, R.D., Jones, L.V. (1968). The measurement and prediction of judgment and choice, San Francisco: Holden-Day.Google Scholar
Böckenholt, U. (1992). Thurstonian models for partial ranking data. British Journal of Mathematical and Statistical Psychology, 45, 31–49.CrossRefGoogle Scholar
Böckenholt, U. (1996). Analyzing multi-attribute ranking data: Joint and conditional approaches. British Journal of Mathematical and Statistical Psychology, 49, 57–78.CrossRefGoogle Scholar
Böckenholt, U. (1998). Modeling time-dependent preferences: Drifts in ideal points. In Greenacre, M., Blasius, J. (Eds.), Visualization of categorical data (pp. 461–476). Hillsdale, NJ: Erlbaum.CrossRefGoogle Scholar
Böckenholt, U. (2001a). Thresholds and intransitivities in pairwise judgments: A multilevel analysis. Journal of Educational and Behavioral Statistics, 26, 269–282.CrossRefGoogle Scholar
Böckenholt, U. (2001b). Mixed-effects analyses of rank-ordered data. Psychometrika, 66, 45–62.CrossRefGoogle Scholar
Böckenholt, U. (2002). A Thurstonian analysis of preference change. Journal of Mathematical Psychology, 46, 300–314.CrossRefGoogle Scholar
Böckenholt, U. (2004). Comparative judgments as an alternative to ratings: Identifying the scale origin. Psychological Methods, 9, 453–465.CrossRefGoogle Scholar
Böckenholt, U. (2005). A latent Markov model for the analysis of longitudinal data collected in continuous time: States, durations, and transitions. Psychological Methods, 10, 65–83.CrossRefGoogle ScholarPubMed
Böckenholt, U., Dillon, W.R. (1997a). Modeling within-subject dependencies in ordinal paired comparison data. Psychometrika, 62, 414–434.CrossRefGoogle Scholar
Böckenholt, U., Dillon, W.R. (1997b). Some new methods for an old problem: Modeling preference changes and competitive market structures in pre-test market data. Journal of Marketing Research, 34, 130–142.CrossRefGoogle Scholar
Böckenholt, U., Hynan, L. (1994). Caveats on a process-tracing measure and a remedy. Journal of Behavioral Decision Making, 7, 103–118.CrossRefGoogle Scholar
Böckenholt, U., Tsai, R. (2006). Random-effects models for preference data. In Rao, C.R., Sinharay, S. (Eds.), Handbook of statistics (Vol. 26, pp. 447–468). Amsterdam: Elsevier Science.Google Scholar
Böckenholt, U., & Tsai, R. (2007). An unstable preference view of the compromise and asymmetric dominance effects. Manuscript in preparation.Google Scholar
Bradlow, E., Bronnenberg, B., Russell, G., Arora, N., Bell, D.R., Dev Suvvuri, S., Ter Hofstede, F., Sismeiro, C., Thomadsen, R., Yang, S. (2005). Spatial models in marketing. Marketing Letters, 16, 267–278.CrossRefGoogle Scholar
Brady, H.E. (1989). Factor and ideal point analysis for interpersonally incomparable data. Psychometrika, 54, 181–202.CrossRefGoogle Scholar
Brock, W.A., Durlauf, S.N. (2001). Interactions-based models. Handbook of econometrics (Vol. 5, pp. 3297–3380). Amsterdam: North-Holland.CrossRefGoogle Scholar
Caffo, B., Griswold, M. (2006). A user-friendly tutorial on link-probit-normal models. The American Statistician, 60, 139–145.CrossRefGoogle Scholar
Chakravarti, D., Sinha, A., Kim, J. (2005). Choice research: A wealth of perspectives. Marketing Letters, 16, 173–182.CrossRefGoogle Scholar
Chan, W., Bentler, P.M. (1998). Covariance structure analysis of ordinal ipsative data. Psychometrika, 63, 369–399.CrossRefGoogle Scholar
Coombs, C.H. (1964). A theory of data, New York: Wiley.Google Scholar
David, H.A. (1988). The method of paired comparisons, London: Griffin.Google Scholar
Edgeworth, F.Y. (1881). Mathematical physics, London: Kegan Paul.Google Scholar
Falmagne, J.C. (1985). Elements of psychophysical theory, Oxford: Clarendon Press.Google Scholar
Fechner, G.T. (1860). Elemente der Psychophysik, Leipzig: Breitkopf und Härtel.Google Scholar
Georgescu-Roegen, N. (1936). The pure theory of consumer’s behavior. Quarterly Journal of Economics, 50, 545–593.CrossRefGoogle Scholar
Gonzalez-Vallejo, C. (2002). Making trade-offs: A new probabilistic and context sensitive model of choice behavior. Psychological Review, 109, 137–155.CrossRefGoogle Scholar
Gueorguieva, R., Agresti, R. (2001). A correlated probit model for joint modeling of clustered binary and continuous responses. Journal of the American Statistical Association, 96, 1102–1112.CrossRefGoogle Scholar
Guttman, L. (1946). An approach for quantifying paired comparisons and rank order. Annals of Mathematical Statistics, 17, 144–163.CrossRefGoogle Scholar
Hanemann, M. (1984). Discrete continuous models of consumer demand. Econometrica, 52, 541–561.CrossRefGoogle Scholar
Hausman, J., Wise, D. (1978). A conditional probit model for qualitative choice: Discrete decisions recognizing interdependence and heterogeneous preferences. Econometrica, 46, 403–429.CrossRefGoogle Scholar
Hensher, D.A., Rose, J.M., Greene, W.H. (2005). Applied choice analysis: A primer, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Higgins, E.T. (1997). Beyond pleasure and pain. American Psychologist, 52, 1280–1300.CrossRefGoogle ScholarPubMed
Johnson, J.G., Busemeyer, J.R. (2005). A dynamic, stochastic, computational model of preference reversal phenomena. Psychological Review, 112, 841–861.CrossRefGoogle ScholarPubMed
Kahneman, D. (2003). Maps of bounded rationality: Psychology for behavioral economics. American Economic Review, 93, 1449–1475.CrossRefGoogle Scholar
Kahneman, D., Thaler, R.H. (2006). Anomalies: Utility maximization and experienced utilty. Journal of Economic Perspectives, 20, 221–234.CrossRefGoogle Scholar
Leibenstein, H. (1950). Bandwagon, snob, and Veblen effects in the theory of consumer’s demand. The Quarterly Journal of Economics, 64, 183–207.CrossRefGoogle Scholar
Liechty, J., Fong, D.K.H., DeSarbo, W.S. (2005). Dynamic models incorporating individual heterogeneity: Utility evolution in conjoint analysis. Marketing Science, 24, 285–293.CrossRefGoogle Scholar
Louviere, J.J., Hensher, D.A., Swait, J.D. (2000). Stated choice methods, New York: Cambridge University Press.CrossRefGoogle Scholar
Luce, R.D. (1959). Individual choice behavior, New York: Wiley.Google Scholar
Luce, R.D. (2000). Utility of gains and losses: Measurement-theoretical and experimental approaches, Hillsdale, NJ: Erlbaum.Google Scholar
Luce, R.D., Suppes, P. (1965). Preference, utility, and subjective probability. In Luce, R.D., Bush, R.R., Galanter, E. (Eds.), Handbook of mathematical psychology (Vol. III, pp. 235–406). New York: Wiley.Google Scholar
Luce, R.D., Tukey, J. (1964). Simultaneous conjoint measurement: A new type of fundamental measurement. Journal of Mathematical Psychology, 1, 1–27.CrossRefGoogle Scholar
Lynch, J.G., Wood, W. (2006). Helping consumers help themselves. Journal of Public Policy and Marketing, 26, 1–7.CrossRefGoogle Scholar
MacKay, D.B., Easley, R.F., Zinnes, J.L. (1995). A single ideal point model for market structure analysis. Journal of Marketing Research, 32, 433–443.CrossRefGoogle Scholar
Manski, C.F. (1977). The structure of random utility models. Theory and Decision, 8, 229–254.CrossRefGoogle Scholar
Manski, C.F. (2000). Economic analysis of social interactions. Journal of Economic Perspectives, 14, 115–136.CrossRefGoogle Scholar
Manski, C.F. (2004). Measuring expectations. Econometrica, 72, 1329–1376.CrossRefGoogle Scholar
Marschak, J. (1960). Binary choice constraints on random utility indictor. In Arrow, K.I., Karlin, S., Suppes, P. (Eds.), Stanford symposium on mathematical methods in the social sciences (pp. 312–329). Stanford, CA: Stanford University Press.Google Scholar
Marshall, P., Bradlow, E.T. (2002). A unified approach to conjoint analysis models. Journal of the American Statistical Association, 97, 674–682.CrossRefGoogle Scholar
May, K.O. (1954). Intransitivity, utility, and the aggregation of preference patterns. Econometrica, 22, 1–13.CrossRefGoogle Scholar
Maydeu-Olivares, A., Böckenholt, U. (2005). Structural equation modeling of paired comparison and ranking data. Psychological Methods, 10, 285–304.CrossRefGoogle ScholarPubMed
McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In Zarembka, P. (Eds.), Frontiers in econometrics (pp. 105–142). New York: Academic Press.Google Scholar
McFadden, D. (1984). Qualitative choice models. In Griliches, Z., Intriligator, M.D. (Eds.), Handbook of econometrics (pp. 1395–1457). Cambridge, MA: MIT Press.CrossRefGoogle Scholar
McFadden, D. (2001). Economic choices. American Economic Review, 91, 351–378.CrossRefGoogle Scholar
McFadden, D. (2006). Free markets and fettered consumers. American Economic Review, 96, 5–29.CrossRefGoogle Scholar
McFadden, D., Train, K. (2000). Mixed MNL models for discrete response. Journal of Applied Econometrics, 15, 447–470.3.0.CO;2-1>CrossRefGoogle Scholar
Mellers, B.A., Biagini, K. (1994). Similarity and choice. Psychological Review, 101, 505–518.CrossRefGoogle Scholar
Montague, P.R., King-Casas, B., Cohen, J.D. (2006). Imaging valuation models in human choice. Annual Review of Neuroscience, 29, 417–448.CrossRefGoogle ScholarPubMed
Mourali, M., Böckenholt, U., & Laroche, M. (in press). Compromise and attraction effects under prevention and promotion motivations. Journal of Consumer Research.Google Scholar
Pareto, V. (1900). Sunto di alcuni capitoli di un nuovo trattato di economia pura del Prof. Pareto. Giornale degli Economisti, 20, 216–235, 511–49Google Scholar
Rijmen, F., Tuerlinckx, F., De Boeck, P., Kuppens, P. (2003). A nonlinear mixed model framework for item response theory. Psychological Methods, 8, 185–205.CrossRefGoogle ScholarPubMed
Roelofsma, P., Read, D. (2000). Intransitive intertemporal choice. Journal of Behavioral Decision Making, 13, 161–177.3.0.CO;2-P>CrossRefGoogle Scholar
Rudas, T., Clogg, C.C., Lindsay, B.G. (1994). A new index of fit based on mixture methods for the analysis of contingency tables. Journal of the Royal Statistical Society, Series B, 56, 623–639.CrossRefGoogle Scholar
Ryan, M., Netten, A., Skatun, D., Smith, P. (2006). Using discrete choice experiments to estimate a preference-based measure of outcome—An application to social care for older people. Journal of Health Economics, 25, 927–944.CrossRefGoogle ScholarPubMed
Shafir, E., LeBoeuf, R.A. (2002). Rationality. Annual Review of Psychology, 53, 491–517.CrossRefGoogle ScholarPubMed
Shuford, E.H., Jones, L.V., Bock, R.D. (1960). A rational origin obtained by the method of contingent paired comparisons. Psychometrika, 25, 343–356.CrossRefGoogle Scholar
Simonson, I., Tversky, A. (1992). Choice in context: Tradeoff contrast and extremeness aversion. Journal of Marketing Research, 29, 281–295.CrossRefGoogle Scholar
Skrondal, A., Rabe-Hesketh, S. (2003). Multilevel logistic regression for polytomous data and rankings. Psychometrika, 68, 267–287.CrossRefGoogle Scholar
Soetevent, A.R., & Kooreman, P. (in press). A discrete choice model with social interactions: With an application to high school teen behavior. Journal of Applied Econometrics.Google Scholar
Sunstein, C.R., Thaler, R.H. (2003). Libertarian paternalism is not an oxymoron. University of Chicago Law Review, 70, 1159–1202.CrossRefGoogle Scholar
Takane, Y. (1987). Analysis of covariance structures and probabilistic binary choice data. Cognition and Communication, 20, 45–62.Google Scholar
Thurstone, L.L. (1927). A law of comparative judgment. Psychological Review, 34, 273–286.CrossRefGoogle Scholar
Thurstone, L.L. (1931). The indifference function. Journal of Social Psychology, 2, 139–167.CrossRefGoogle Scholar
Thurstone, L.L., Jones, L.V. (1957). The rational origin for measuring subjective values. Journal of the American Statistical Association, 52, 458–471.CrossRefGoogle Scholar
Train, K. (2003). Discrete choice methods with simulations, Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Tsai, R. (2000). Remarks on the identifiability of Thurstonian ranking models: Case V, Case III, or neither. Psychometrika, 65, 233–240.CrossRefGoogle Scholar
Tsai, R. (2003). Remarks on the identifiability of Thurstonian paired comparison models under multiple judgment. Psychometrika, 68, 361–372.CrossRefGoogle Scholar
Tsai, R., Böckenholt, U. (2001). Maximum likelihood estimation of factor and ideal point models for paired comparison data. Journal of Mathematical Psychology, 45, 795–811.CrossRefGoogle Scholar
Tsai, R., Böckenholt, U. (2002). Two-level linear paired comparison models: Estimation and identifiability issues. Mathematical Social Sciences, 43, 429–449.CrossRefGoogle Scholar
Tsai, R., Böckenholt, U. (2006). Modeling intransitive preferences: A random-effects approach. Journal of Mathematical Psychology, 50, 1–14.CrossRefGoogle Scholar
Tsai, R., & Böckenholt, U. (2007). On the importance of distinguishing between within- and between-subject effects in intransitive intertemporal choice. Manuscript submitted for publication.Google Scholar
Tversky, A. (1969). Intransitivity of preference. Psychological Review, 76, 31–48.CrossRefGoogle Scholar
Veblen, T. (1899). The theory of the leisure class, New York: Macmillan.Google Scholar
Wallis, W.A., Friedman, M. (1942). The empirical derivation of indifference functions. In Lange, O. (Eds.), Studies in mathematical economics and econometrics (pp. 175–189). Chicago: University of Chicago Press.Google Scholar
Wedel, M., Kamakura, W.A. (1999). Market segmentation: Conceptual and methodological foundations, Dodrecht: Kluwer Academic.Google Scholar
Winkielman, P., Berridge, K. (2003). Irrational wanting and subrational liking: How rudimentary affective and motivational processes shape preferences and choice. Political Psychology, 24, 657–680.CrossRefGoogle Scholar
Yao, G., Böckenholt, U. (1999). Bayesian estimation of Thurstonian ranking models based on the Gibbs sampler. British Journal of Mathematical and Statistical Psychology, 52, 79–92.CrossRefGoogle Scholar
Yeomans, J. (1992). Statistical mechanics of phase transitions, Oxford: Oxford University Press.CrossRefGoogle Scholar
Yu, P.L.H., Lam, K.F., & Lo, S.M. (1998). Factor analysis for ranking data. Unpublished manuscript. Department of Statistics, The University of Hong Kong.Google Scholar