Probability Models and Statistical Analyses for Ranking Data

1. Front Matter

   Pages i-xxiii

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2. Ranking Models with Item Covariates

   1. Ranking Models with Item Covariates

      • Douglas E. Critchlow, Michael A. Fligner

      Pages 1-19

3. Nonparametric Methods of Ranking from Paired Comparisons

   1. Nonparametric Methods of Ranking from Paired Comparisons

      • H. A. David, D. M. Andrews

      Pages 20-36

4. On the Babington Smith Class of Models for Rankings

   1. On the Babington Smith Class of Models for Rankings

      • Harry Joe, Joseph S. Verducci

      Pages 37-52

5. Latent Structure Models for Ranking Data

   1. Latent Structure Models for Ranking Data

      • M. A. Croon, R. Luijkx

      Pages 53-74

6. Modelling and Analysing Paired Ranking Data

   1. Modelling and Analysing Paired Ranking Data

      • Paul D. Feigin

      Pages 75-91

7. Maximum Likelihood Estimation in Mallows’s Model Using Partially Ranked Data

   1. Maximum Likelihood Estimation in Mallows’s Model Using Partially Ranked Data

      • Laurel A. Beckett

      Pages 92-107

8. Extensions of Mallows’ ϕ Model

   1. Extensions of Mallows’ ϕ Model

      • Lyinn Chung, John I. Marden

      Pages 108-139

9. Rank Correlations and the Analysis of Rank-Based Experimental Designs

   1. Rank Correlations and the Analysis of Rank-Based Experimental Designs

      • M. Alvo, P. Cabilio

      Pages 140-156

10. Applications of Thurstonian Models to Ranking Data

    1. Applications of Thurstonian Models to Ranking Data

       • Ulf Böckenholt

       Pages 157-172

11. Probability Models on Rankings and the Electoral Process

    1. Probability Models on Rankings and the Electoral Process

       • Hal Stern

       Pages 173-195

12. Permutations and Regression Models

    1. Permutations and Regression Models

       • Peter McCullagh

       Pages 196-215

13. Aggregation Theorems and the Combination of Probabilistic Rank Orders

    1. Aggregation Theorems and the Combination of Probabilistic Rank Orders

       • A. A. J. Marley

       Pages 216-240

14. A Nonparametric Distance Model for Unidimensional Unfolding

    1. A Nonparametric Distance Model for Unidimensional Unfolding

       • Rian van Blokland-Vogelesang

       Pages 241-276

15. Miscellanea

    1. Front Matter

       Pages 277-277

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    2. Models on Spheres and Models for Permutations

       • Peter McCullagh

       Pages 278-283

    3. Complete Consensus and Order Independence: Relating Ranking and Choice

       • Hans Colonius

       Pages 284-288

    4. Ranking From Paired Comparisons by Minimizing Inconsistency

       • Edwin L. Crow

       Pages 289-293

    5. Graphical Techniques for Ranked Data

       • G. L. Thompson

       Pages 294-298

    6. Matched Pairs and Ranked Data

       • Peter McCullagh, Jianming Ye

       Pages 299-306

In June of 1990, a conference was held on Probablity Models and Statisti­ cal Analyses for Ranking Data, under the joint auspices of the American Mathematical Society, the Institute for Mathematical Statistics, and the Society of Industrial and Applied Mathematicians. The conference took place at the University of Massachusetts, Amherst, and was attended by 36 participants, including statisticians, mathematicians, psychologists and sociologists from the United States, Canada, Israel, Italy, and The Nether­ lands. There were 18 presentations on a wide variety of topics involving ranking data. This volume is a collection of 14 of these presentations, as well as 5 miscellaneous papers that were contributed by conference participants. We would like to thank Carole Kohanski, summer program coordinator for the American Mathematical Society, for her assistance in arranging the conference; M. Steigerwald for preparing the manuscripts for publication; Martin Gilchrist at Springer-Verlag for editorial advice; and Persi Diaconis for contributing the Foreword. Special thanks go to the anonymous referees for their careful readings and constructive comments. Finally, we thank the National Science Foundation for their sponsorship of the AMS-IMS-SIAM Joint Summer Programs. Contents Preface vii Conference Participants xiii Foreword xvii 1 Ranking Models with Item Covariates 1 D. E. Critchlow and M. A. Fligner 1. 1 Introduction. . . . . . . . . . . . . . . 1 1. 2 Basic Ranking Models and Their Parameters 2 1. 3 Ranking Models with Covariates 8 1. 4 Estimation 9 1. 5 Example. 11 1. 6 Discussion. 14 1. 7 Appendix . 15 1. 8 References.

• ANOVA
• Likelihood
• Random variable
• correlation
• data analysis
• expectation–maximization algorithm
• matching
• permutations
• ranking data

• Department of Statistics, The Ohio State University, Columbus, USA

  Michael A. Fligner, Joseph S. Verducci

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