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Deterministic Evolution of Strength in Multiple Comparisons Models: Who is the Greatest Golfer?
Author(s) -
Baker Rose D.,
McHale Ian G.
Publication year - 2015
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12101
Subject(s) - mathematics , barycentric coordinate system , tournament , function (biology) , set (abstract data type) , interpolation (computer graphics) , econometrics , statistics , mathematical optimization , computer science , artificial intelligence , motion (physics) , combinatorics , geometry , evolutionary biology , biology , programming language
We present a statistical methodology for fitting time‐varying rankings, by estimating the strength parameters of the Plackett–Luce multiple comparisons model at regularly spaced times for each ranked item. We use the little‐known method of barycentric rational interpolation to interpolate between the strength parameters so that a competitor's strength can be evaluated at any time. We chose the time‐varying strengths to evolve deterministically rather than stochastically, a preference that we reason often has merit. There are many statistical and computational problems to overcome on fitting anything beyond ‘toy’ data sets. The methodological innovations here include a method for maximizing a likelihood function for many parameters, approximations for modelling tied data and an approach to the elimination of secular drift of the estimated ‘strengths’. The methodology has obvious applications to fields such as marketing, although we demonstrate our approach by analysing a large data set of golf tournament results, in search of an answer to the question ‘who is the greatest golfer of all time?’