Abstract
If the Warriors beat the Rockets and the Rockets beat the Spurs, does that mean that the Warriors are better than the Spurs? Sophisticated fans would argue that the Warriors are better by the transitive property, but could Spurs fans make a legitimate argument that their team is better despite this chain of evidence?
We first explore the nature of intransitive (rock-scissors-paper) relationships with a graph theoretic approach to the method of paired comparisons framework popularized by Kendall and Smith (1940). Then, we focus on the setting where all pairs of items, teams, players, or objects have been compared to one another twice (i.e., home and away). We propose a novel linear model (CRSP) whose latent bilinear fixed effect allows us to estimate deviations from our transitive model (C).
Degree Date
Winter 2019
Document Type
Dissertation
Degree Name
Ph.D.
Department
Statistical Science
Advisor
Ian Richard Harris
Second Advisor
Sara Lynne Stokes
Third Advisor
Cornelis Jacobus Potgieter
Fourth Advisor
Paul Xavier Uhlig
Fifth Advisor
Eric Cooper Larson
Sixth Advisor
Daniel Francis Heitjan
Subject Area
Computer Science, Statistics
Number of Pages
177
Format
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Recommended Citation
McShane, Ryan Patrick Alexander, "Modeling Stochastically Intransitive Relationships in Paired Comparison Data" (2019). Statistical Science Theses and Dissertations. 13.
https://scholar.smu.edu/hum_sci_statisticalscience_etds/13
Included in
Applied Statistics Commons, Categorical Data Analysis Commons, Discrete Mathematics and Combinatorics Commons, Multivariate Analysis Commons, Numerical Analysis and Scientific Computing Commons, Probability Commons, Statistical Methodology Commons, Statistical Models Commons, Statistical Theory Commons, Theory and Algorithms Commons
