The sparse Luce model

The Luce model is one of the most popular ranking models used to estimate the ranks of items. In this study, we focus on grouping items with similar abilities and consider a new supervised clustering method by fusing specific parameters used in the Luce model. By modifying the penalty function conventionally used in grouping parameters, we obtain a new method of grouping items in the Luce model without pairwise comparison modeling and develop an efficient algorithm to estimate the parameters. Moreover, we give an application of the proposed algorithm to the Bradley-Terry model with ties. In the real data analysis, we confirm that the proposed estimator provides an easier interpretation of ranks and an improvement in the quality of prediction.