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A Thurstonian Ranking Model with Rank-Induced Dependencies

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  • Daniel Ennis
  • John Ennis

Abstract

A Thurstonian model for ranks is introduced in which rank-induced dependencies are specified through correlation coefficients among ranked objects that are determined by a vector of rank-induced parameters. The ranking model can be expressed in terms of univariate normal distribution functions, thus simplifying a previously computationally intensive problem. A theorem is proven that shows that the specification given in the paper for the dependencies is the only way that this simplification can be achieved under the process assumptions of the model. The model depends on certain conditional probabilities that arise from item orders considered by subjects as they make ranking decisions. Examples involving a complete set of ranks and a set with missing values are used to illustrate recovery of the objects’ scale values and the rank dependency parameters. Application of the model to ranks for gift items presented singly or as composite items is also discussed. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Daniel Ennis & John Ennis, 2013. "A Thurstonian Ranking Model with Rank-Induced Dependencies," Journal of Classification, Springer;The Classification Society, vol. 30(1), pages 124-147, April.
    • Handle: RePEc:spr:jclass:v:30:y:2013:i:1:p:124-147
    DOI: 10.1007/s00357-013-9125-8
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    References listed on IDEAS

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    1. Daniel Ennis & Norman Johnson, 1994. "A general model for preferential and triadic choice in terms of centralF distribution functions," Psychometrika, Springer;The Psychometric Society, vol. 59(1), pages 91-96, March.
    2. David B. MacKay & Bryan Lilly, 2004. "Percept Variance, Subadditivity and the Metric Classification of Similarity, and Dissimilarity Data," Journal of Classification, Springer;The Classification Society, vol. 21(2), pages 185-206, September.
    3. Daniel Ennis & F. Ashby, 1993. "The relative sensitivities of same-different and identification judgment models to perceptual dependence," Psychometrika, Springer;The Psychometric Society, vol. 58(2), pages 257-279, June.
    4. Kenneth Mullen & Daniel Ennis, 1987. "Mathematical formulation of multivariate euclidean models for discrimination methods," Psychometrika, Springer;The Psychometric Society, vol. 52(2), pages 235-249, June.
    5. Kenneth Mullen & Daniel Ennis, 1991. "A simple multivariate probabilistic model for preferential and triadic choices," Psychometrika, Springer;The Psychometric Society, vol. 56(1), pages 69-75, March.
    6. Joseph Zinnes & David MacKay, 1983. "Probabilistic multidimensional scaling: Complete and incomplete data," Psychometrika, Springer;The Psychometric Society, vol. 48(1), pages 27-48, March.
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