Item preference parameters from grouped ranking observations

Abstract

Given a set of rating data for a set of items, determining the values of items is a matter of importance. Various probability models have been proposed to solve this task. The Plackett-Luce model is one of such models, which parametrizes the value of each item by a real valued preference parameter. In this paper, the Plackett-Luce model is generalized to cope with the grouped ranking observations such as movies or restaurants ratings. Since the maximization of the likelihood of the proposed model is computationally intractable, the lower bound of the likelihood which is easy to evaluate is derived, and the em algorithm is adopted to the maximization of the lower bound. © Springer-Verlag Berlin Heidelberg 2009.