Summary
We investigate by means of a simulation study whether standard structural equation modeling techniques are suitable for estimating an unrestricted Thurstonian model to: (a) multiple judgment paired comparisons data, and (b) ranking data. We point out that Thurstone’s (1927) original model is not a proper model for multiple judgment paired comparisons data as it assigns zero probability to all intransitive paired comparisons patterns. To fit multiple judgment paired comparisons data one must employ Takane’s (1987) extension of Thurstone’s original model, or alternatively, a Thurstonian correlation structure model, which we introduce. We found that for some models as few as 100 observations suffice to obtain accurate parameter estimates, standard errors and goodness of fit tests when 7 stimuli are modeled (21 binary variables). For other models, however, sample sizes of 1000 observations are needed. All in all, the procedure investigated appears to be an attractive choice to estimate these models.
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References
Bock, R.D. & Jones, L.V. (1968). The measurement and prediction ofjudgment and choice. San Francisco: Holden-Day.
Dansie, B.R. (1986) Normal order statistics as permutation probability models. Applied Statistics, 35, 269–275.
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. (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.
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.
Thurstone, L.L. (1931). Rank order as a psychological method. Journal of Experimental Psychology, 14, 187–201.
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Maydeu-Olivares, A. (2003). On Thurstone’s Model for Paired Comparisons and Ranking Data. In: Yanai, H., Okada, A., Shigemasu, K., Kano, Y., Meulman, J.J. (eds) New Developments in Psychometrics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-66996-8_59
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DOI: https://doi.org/10.1007/978-4-431-66996-8_59
Publisher Name: Springer, Tokyo
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