Preference Probability Based on Ranks – A New Approach Using Logistic Regression with Zero Intercept

• Activity Number: 43 - SPEED: Statistics in Sports; Physical Activity/Sleep Studies, and Nonparametrics Part 1
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Sports
• Author(s): Oluwagbenga Agboola*
• Companies: University of Northern Colorado
• Keywords: Bradley-Terry Model; pairwise preference; logistic regression; numerical approximation procedures; maximum likelihood estimation; simulated data

Abstract

Many probability models have been proposed to describe rankings. One of these is the Bradley-Terry model, which is based on observed pairwise preferences. For this study, we reverse the case and propose a new approach for estimating pairwise preference probabilities based on observed rankings. The new approach uses logistic regression with zero intercept as the statistical model that fits this situation. In order to implement the model, we first estimate the parameter using maximum likelihood estimation. Then we evaluate this estimation using numerical approximation procedures. We consider three such procedures: bisection method, Newton-Raphson method, and improved Newton's method. Using simulated data, we compare the three procedures based on the number of iterations required for convergence, as well as CPU time. We identify the improved Newton's method as the fastest of the three methods.