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Probability Models for Ranking Data

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Statistical Methods for Ranking Data

Part of the book series: Frontiers in Probability and the Statistical Sciences ((FROPROSTAS))

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Abstract

Probability modeling for ranking data is an efficient way to understand people’s perception and preference on different objects. Various probability models for ranking data have been developed, particularly in the last decade where many new problems involving a large number of objects emerged. In their review paper on probability models for ranking data, Critchlow et al. (1991) broadly categorized these models into four classes: (1) order statistics models, (2) paired comparison models, (3) distance-based models, and (4) multistage models. Since their publication in 1991, variants of these models and new models have been developed. In this chapter, we will introduce these four classes of models and describe their properties.

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Notes

  1. 1.

    Note \(e^{-\varepsilon }\) follows an exponential distribution with mean 1.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada

    Mayer Alvo

  2. Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, China

    Philip L. H. Yu

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  1. Mayer Alvo
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  2. Philip L. H. Yu
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Chapter Notes

Chapter Notes

In this chapter, we have introduced several important probability models for ranking data. Extension of order statistics models and distance-based models will be discussed in Chaps. 9 and 11, respectively. Other models not considered here are a variety of exponential family models based on marginals (spectral decomposition of Diaconis (1988, 1989)) or pairwise and higher-way comparisons (inversion models of McCullagh (1993b)), nested orthogonal contrast models (Marden 1992), and models based on insertion sorting (Doignon et al. 2004; Biernacki and Jacques 2013).

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Alvo, M., Yu, P.L.H. (2014). Probability Models for Ranking Data. In: Statistical Methods for Ranking Data. Frontiers in Probability and the Statistical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1471-5_8

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