Thurstone’s Case V Model: A Structural Equations Modeling Perspective

  • Albert Maydeu-Olivares
Part of the Mathematical Modelling: Theory and Applications book series (MMTA, volume 19)


Modeling how we choose among alternatives, or more generally, modeling preferences, is one of the core topics of study in Psychology. Preferences can be studied experimentally using a variety of procedures, one of the oldest being the method of paired comparisons. This method remains quite popular in areas such as psychophysics and consumer psychology. For a good overview of the method of paired comparisons see David (1988).


Factor Model Paired Comparison Ranking Data Tetrachoric Correlation Ranking Experiment 
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  1. Arminger, G., Wittenberg, J. & Schepers, A. (1996). MECOSA 3. User guide. Friedrichsdorf: Additive GmbH.Google Scholar
  2. Bock, R.D. & Jones, L.V. (1968). The measurement and prediction of judgment and choice. San Francisco: Holden-Day.Google Scholar
  3. Bockenholt, U. (1990). Multivariate Thurstonian models. Psychometrika, 55, 391–403.CrossRefGoogle Scholar
  4. Bockenholt, U. (1993). Applications of Thurstonian models to ranking data. In M.A. Fligner and J.S. Verducci (Eds). Probability models and statistical analyses for ranking data. New York: Springer-Verlag.Google Scholar
  5. Bockenholt, U. (2001). Hierarchical modeling of paired comparison data. Psychological Methods, 6,49–66.PubMedCrossRefGoogle Scholar
  6. Brady, H.E. (1989). Factor and ideal point analysis for interpersonally incomparable data. Psychometrika, 54,181–202.CrossRefGoogle Scholar
  7. Chan, W. & Bentler, P.M. (1998). Co variance structure analysis of ordinal ipsative data. Psychometrika, 63, 360–369.CrossRefGoogle Scholar
  8. David, H.A. (1988). The method of paired comparisons. London: Griffin.Google Scholar
  9. Joreskog, K.G. & Goldberger, A.S. (1975). Estimation of a model with multiple indicators and multiple causes of a single latent variable. Journal of the American Statistical Association, 69, 631–639.Google Scholar
  10. Luce, R.D. (1959). Individual choice behavior. New York: Wiley.Google Scholar
  11. Maydeu-Olivares, A. (1998). Structural equation modeling of binary preference data. Dissertation Abstracts International: Section B: The Sciences and Engineering, 58, 5694.Google Scholar
  12. Maydeu-Olivares, A. (1999). Thurstonian modeling of ranking data via mean and covariance structure analysis. Psychometrika, 64, 325–340.CrossRefGoogle Scholar
  13. Maydeu-Olivares, A. (2001). Limited information estimation and testing of Thurstonian models for paired comparison data under multiple judgment sampling. Psychometrika, 66, 209–228.CrossRefGoogle Scholar
  14. Maydeu-Olivares, A. (2002). Limited information estimation and testing of Thurstonian models for preference data. Mathematical Social Sciences, 43,467–483.CrossRefGoogle Scholar
  15. Maydeu-Olivares, A. (2003). On Thurstone’s model for paired comparisons and ranking data. In Yanai, H., Okada, A., Shigematu, K., Kano, Y., Meulman, J.J. (Eds.). New Developments in Psychometrics(pp. 519–526) Tokyo: Springer.CrossRefGoogle Scholar
  16. Mosteller, F. (1951a). Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations. Psychometrika, 16, 3–9.CrossRefGoogle Scholar
  17. Mosteller, F. (1951b). Remarks on the method of paired comparisons: III. A test of significance for paired comparisons when equal standard deviations and equal correlations are assumed. Psychometrika, 16, 207–218.PubMedCrossRefGoogle Scholar
  18. Muthen, B. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika, 43, 551–560.CrossRefGoogle Scholar
  19. Muthen, B. (1979). A structural probit model with latent variables. Journal of the American Statistical Association, 74, 807–811.Google Scholar
  20. Muthen, B. (1982). Some categorical response models with continuous latent variables. In K.G. Joreskog & H. Wold (Eds.). Systems under indirect observation. (Vol 1) (pp. 65–79). Amsterdam: North Holland.Google Scholar
  21. Muthen, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49, 115–132.CrossRefGoogle Scholar
  22. Muthen, B. (1993). Goodness of fit with categorical and other non normal variables. In K.A. Bollen & J.S. Long [Eds.]. Testing structural equation models(pp. 205–234). Newbury Park, CA: Sage.Google Scholar
  23. Muthen, B., du Toit, S.H.C. & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes. Paper accepted for publication in Psychometrika. Google Scholar
  24. Muthen, L. & Muthen, B. (1998). Mplus. Los Angeles, CA: Muthen & Muthen.Google Scholar
  25. Satorra, A. & Bentler, P.M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye and C.C. Clogg (Eds.). Latent variable analysis Applications to developmental research(pp. 399–419). Thousand Oaks, CA: Sage.Google Scholar
  26. Takane, Y. (1987). Analysis of covariance structures and probabilistic binary choice data. Communication and Cognition,20,45–62.Google Scholar
  27. Torgerson, W.S. (1958). Theory and methods of scaling. New York: Wiley.Google Scholar
  28. Thurstone, L.L. (1927). A law of comparative judgment. Psychological Review, 79, 281–299.Google Scholar
  29. Thurstone, L.L. (1931). Rank order as a psychological method. Journal of Experimental Psychology, 14, 187–201.CrossRefGoogle Scholar
  30. Tsai, R.C. & Bockenholt, U. (2001). Maximum likelihood estimation of factor and ideal point models for paired comparison data. Journal of Mathematical Psychology, 45, 795–811.CrossRefGoogle Scholar
  31. Tsai, R.C. & Yao, G. (2000). Testing Thurstonian Case V ranking models using posterior predictive checks. British Journal of Mathematical and Statistical Psychology, 53, 275–292.PubMedCrossRefGoogle Scholar
  32. Yao, G. & Bockenholt, 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
  33. Yu, P.L.H. (2000). Bayesian analysis of order-statistics models for ranking data. Psychometrika, 65,281–299.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Albert Maydeu-Olivares
    • 1
    • 2
  1. 1.Faculty of PsychologyUniversity of BarcelonaBarcelonaSpain
  2. 2.Marketing DepartmentInstituto de EmpresaMadridSpain

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