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Types: Preprint
Subjects: Case III model, Case V model, Comparative data, Goodness of fit, Limited information estimation, MPLUS, Personal assessment, Random utility models, Scale invariance, Structural equation models
(WP 04/03 Clave pdf) Thurstone´s (1927) is not a proper model for multiple judgment paired comparison data as it assigns zero probabilities to all intransitive patterns. To obtain a proper model, Takane (1987) extended Thurstone´s model by adding a vector of pair specific random errors. We investigate an unrestricted Thurstone-Takane model when (a) the variances of the paired specific errors are assumed to be equal, and (b) when they are assumed to be unequal. We also consider a new model, an unrestricted Thurstonian mean and correlation structure model.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • David, H.A. (1988). The method of paired comparisons. London: Griffin.
    • Kroeger, K. (1992). Unpublished dataset. University of Illinois, Urbana-Champaign.
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    • Maydeu-Olivares, A. (1999). Thurstonian modeling of ranking data via mean and covariance structure analysis. Psychometrika, 64, 325-340.
    • Maydeu-Olivares, A. (2001). Limited information estimation and testing of Thurstonian models for paired comparison data under multiple judgment sampling. Psychometrika, 66, 209-228.
    • Muthén, B. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika, 43, 551-560.
    • Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49, 115-132.
    • Muthén, 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.
    • Muthén, L. & Muthén, B. (1998). MPLUS. Los Angeles, CA: Muthén & Muthén.
    • Rummelhart, D.L. & Greeno, J.G. (1971). Similarity between stimuli: An experimental test of the Luce and Restle choice models. Journal of Mathematical Psychology, 8, 370- 381.
    • 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.
    • Satorra, A. & Bentler, P.M. (2001). A scaled difference chi-square test statistic for moment structure analysis. Psychometrika, 66,
    • Takane, Y. (1987). Analysis of covariance structures and probabilistic binary choice data. Communication and Cognition, 20, 45-62.
    • Thurstone, L.L. (1927). A law of comparative judgment. Psychological Review, 79, 281-299.
  • No related research data.
  • Discovered through pilot similarity algorithms. Send us your feedback.

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