A Thurstonian Ranking Model with Rank-Induced Dependencies

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.

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