Ties in one block comparison experiments: a generalization of the Mallows–Bradley–Terry ranking model

ABSTRACT

This study is concerned with the extension of the Mallows–Bradley–Terry ranking model for one block comparison consisting of all the items of interest to situations which allow an expression of no preference. We consider a modification of the Mallows–Bradley–Terry ranking model by introducing an additional parameter, called an index of discrimination, in the model. This permits ties in the model. The maximum likelihood estimates of the parameters are found using a Maximization–Minimization algorithm: the evaluation of the mathematical expectations involved in the log-likelihood equation is obtained by generating samples of Monte Carlo Markov chain from the stationary distribution. In addition, a simulation study for asymptotic properties assessment has been made. The proposed method is applied to analyze data election.

KEYWORDS:

• Babington Smith model
• Mallows–Bradley–Terry model
• rank data
• maximum likelihood estimation
• MM algorithm
• MCMC

Acknowledgements

The authors are grateful to the referees.

Disclosure statement

No potential conflict of interest was reported by the authors.