Abstract
This is a short overview of the R add-on package BradleyTerry2, which facilitates the specification and fitting of Bradley-Terry logit, probit or cauchit models to paircomparison data. Included are the standard ‘unstructured’ Bradley-Terry model, structured versions in which the parameters are related through a linear predictor to explanatory variables, and the possibility of an order or ‘home advantage’ effect or other ‘contest-specific’ effects. Model fitting is either by maximum likelihood, by penalized quasi-likelihood (for models which involve a random effect), or by bias-reduced maximum likelihood in which the first-order asymptotic bias of parameter estimates is eliminated. Also provided are a simple and efficient approach to handling missing covariate data, and suitably-defined residuals for diagnostic checking of the linear predictor.
Highlights
The Bradley-Terry model (Bradley and Terry, 1952) assumes that in a ‘contest’ between any two ‘players’, say player i and player j (i, j ∈ {1, . . . , K}), the odds that i beats j is αi/α j, where αi and α j are positive-valued parameters which might be thought of as representing ‘ability’
The primary purpose of the BradleyTerry2 package, implemented in the R statistical computing environment (Ihaka and Gentleman, 1996; R Development Core Team, 2003), is to facilitate the specification and fitting of such models, including special cases in which the ability parameters are related to available explanatory variables through a linear predictor of the form λi =
In order to fit a Bradley-Terry model to these data using BTm from the BradleyTerry2 package, the data must first be converted to binomial frequencies
Summary
The Bradley-Terry model (Bradley and Terry, 1952) assumes that in a ‘contest’ between any two ‘players’, say player i and player j (i, j ∈ {1, . . . , K}), the odds that i beats j is αi/α j, where αi and α j are positive-valued parameters which might be thought of as representing ‘ability’. The Bradley-Terry model (Bradley and Terry, 1952) assumes that in a ‘contest’ between any two ‘players’, say player i and player j The model can alternatively be expressed in the logit-linear form logit[pr(i beats j)] = λi − λ j,. Assuming independence of all contests, the parameters {λi} can be estimated by maximum likelihood using standard software for generalized linear models, with a suitably specified model matrix. The primary purpose of the BradleyTerry package, implemented in the R statistical computing environment (Ihaka and Gentleman, 1996; R Development Core Team, 2003), is to facilitate the specification and fitting of such models, including special cases in which the ability parameters are related to available explanatory variables through a linear predictor of the form λi =. The logit link can be replaced, if required, by a different symmetric link function (probit or cauchit)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
