Mixtures of weighted distance-based models for ranking data

Abstract

Ranking data has applications in different fields of studies, like marketing, psychology and politics. Over the years, many models for ranking data have been developed. Among them, distance-based ranking models, which originate from the classical rank correlations, postulate that the probability of observing a ranking of items depends on the distance between the observed ranking and a modal ranking. The closer to the modal ranking, the higher the ranking probability is. However, such a model basically assumes a homogeneous population, and the single dispersion parameter may not be able to describe the data very well. To overcome the limitations, we consider new weighted distance measures which allow different weights for different ranks in formulating more flexible distance-based models. The mixtures of weighted distance-based models are also studied for analyzing heterogeneous data. Simulations results will be included, and we will apply the proposed methodology to analyze a real world ranking dataset.