Pairwise Marginal Likelihood for the Bradley–Terry Model

Abstract

The statistical inference for the Bradley–Terry model with logit link and random effects is often made cumbersome by the high-dimensional intractable integrals involved in the marginal likelihood. An inferential methodology based on the marginal pairwise likelihood approach is proposed. This method belongs to the broad class of composite likelihood and involves marginal pairs probabilities of the responses. These probabilities are derived from the approximation of the logistic distribution function by a normal scale mixture. The sample performance of this approach is evaluated by a simulation study. The main motivation of this work is the lizards data, on which the the proposed approach is illustrated.

Keywords:

• 62F12
• 62H12
• 62J02
• 62J12
• 62J15

Keywords:

• Bradley–Terry model
• Composite likelihood
• Fixed effects
• Lizards data
• Logit link
• Marginal pairwise likelihood
• Marginal maximum likelihood
• Probit link
• Variance component

Acknowledgements

The author would like to thank the two anonymous referees for their valuable comments that led to substantive improvements of the paper.