Abstract
A class of exponential-family models on the set of permutations of k objects or items is described. The null or uniform model gives probability 1/k! to each of the k! possible permutations. The first-order inversion model has as sufficient statistic the k × k matrix listing the number of times that each pair of candidates was ranked in that order, i.e. the number of times that candidate a was preferred over candidate b for all ordered pairs a and b. In the second-order inversion model the sufficient statistic is a similar listing for each ordered triplet of three candidates. Interesting sub-models are identified and used to help in the analysis of the APA election data.
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© 1993 Springer-Verlag New York, Inc.
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McCullagh, P. (1993). Permutations and Regression Models. In: Fligner, M.A., Verducci, J.S. (eds) Probability Models and Statistical Analyses for Ranking Data. Lecture Notes in Statistics, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2738-0_11
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DOI: https://doi.org/10.1007/978-1-4612-2738-0_11
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