Abstract
A model for preferential and triadic choice is derived in terms of weighted sums of centralF distribution functions. This model is a probabilistic generalization of Coombs' (1964) unfolding model and special cases, such as the model of Zinnes and Griggs (1974), can be derived easily from it. This new form extends previous work by Mullen and Ennis (1991) and provides more insight into the same problem that they discussed.
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References
Coombs, C. H. (1964).A theory of data. New York: Wiley.
De Soete, G., Carroll, J. D., & DeSarbo, W. S. (1986). The wandering ideal point model: A probabilistic multidimensional unfolding model for paired comparisons data.Journal of Mathematical Psychology, 30, 28–41.
Ennis, D. M., & Mullen, K. (1986a). A multivariate model for discrimination methods.Journal of Mathematical Psychology, 30, 206–219.
Ennis, D. M., & Mullen, K. (1986b). Theoretical aspects of sensory discrimination.Chemical Senses, 11, 513–522.
Ennis, D. M., & Mullen, K. (1992). A general probabilistic model for triad discrimination, preferential choice, and two-alternative identification.In F. G. Ashby (Ed.),Probabilistic multidimensional models of perception and cognition. Hillside, N. J.: Lawrence Erlbaum Associates.
Ennis, D. M., Mullen, K., & Frijters, J. E. R. (1988). Variants of the method of triads: Unidimensional Thurstonian models.British Journal of Mathematical and Statistical Psychology, 41, 25–36.
Imhof, J. P. (1961). Computing the distribution of quadratic forms in normal variables.Biometrika, 48, 419–426.
Johnson, N. L., & Kotz, S. (1970).Distributions in statistics: Continuous univariate distributions—2. New York: Wiley.
Mullen, K., & Ennis, D. M. (1987). Mathematical formulation of multivariate Euclidean models for discrimination methods.Psychometrika, 52, 235–249.
Mullen, K., & Ennis, D. M. (1991). A simple multivariate probabilistic model for preferential and triadic choices.Psychometrika, 56, 69–75.
Mullen, K., Ennis, D. M., de Doncker, E., & Kapenga, J. A. (1988). Multivariate models for the triangular and duo-trio methods.Biometrics, 44, 1169–1175.
Ruben, H. (1962). Probability content of regions under spherical normal distributions, IV.Annals of Mathematical Statistics, 33, 542–570.
Torgerson, W. S. (1958).Theory and methods of scaling. New York: Wiley.
Zinnes, J. L., & Griggs, R. A. (1974). Probabilistic multidimensional unfolding analysis.Psychometrika, 39, 327–350.
Zinnes, J. L., & MacKay, D. B. (1987). Probabilistic multidimensional analysis of preference ratio judgments.Communication and Cognition, 20, 17–44.
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Ennis, D.M., Johnson, N.L. A general model for preferential and triadic choice in terms of centralF distribution functions. Psychometrika 59, 91–96 (1994). https://doi.org/10.1007/BF02294268
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DOI: https://doi.org/10.1007/BF02294268