Fitting Bradley Terry Models Using a Multiplicative Algorithm

Ben Torsney ()
Additional contact information
Ben Torsney: University of Glasgow, Department of Statistics

A chapter in COMPSTAT 2004 — Proceedings in Computational Statistics, 2004, pp 513-526 from Springer

Abstract: Abstract We consider the problem of estimating the parameters of a Bradley Terry Model by the method of maximum likelihood, given data from a paired comparisons experiment. The parameters of a basic model can be taken to be weights which are positive and sum to one. Hence they correspond to design weights and optimality theorems and numerical techniques developed in the optimal design arena can be transported to this estimation problem. Furthermore extensions of the basic model to allow for a factorial structure in the treatments leads to an optimisation problem with respect to several sets of weights or distributions. We can extend techniques to this case. In section 1 we introduce the notion of paired comparisons experiments and the Bradley Terry Model. In section 2 the parameter estimation problem is outlined with optimality results and a general class of multiplicative algorithms outlined in sections 3 and 4 respectively. A specific algorithm is applied to the Bradley Terry log-likelihood in section 5 and treatments with a factorial structure are considered in section 6. Finally in section 7 extensions to triple comparisons and to extended rankings are briefly outlined.

Keywords: Bradley Terry model; discrete data; factorial structure; general equivalence theorem; maximum likelihood estimation; multiplicative algorithm; optimal design theory; paired comparisons (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2656-2_42

Ordering information: This item can be ordered from
http://www.springer.com/9783790826562

DOI: 10.1007/978-3-7908-2656-2_42

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().