Abstract
In this paper, we consider different score functions in order summarize certain characteristics for one and two sample ranking data sets. Our approach is flexible and is based on embedding the nonparametric problem in a parametric framework. We make use of the von Mises-Fisher distribution to approximate the normalizing constant in our model. In order to gain further insight in the data, we make use of penalized likelihood to narrow down the number of items where the rankers differ. We applied our method on various real life data sets and we conclude that our methodology is consistent with the data.
Highlights
Ranking data occur quite frequently in practice
For convenience we only show the number of judges who rank the top and the lowest but giving other rankings involves in determining the value of θ
A negative value of γi means that group 1 shows more preference for Item i compared to population 2
Summary
Ranking data occur quite frequently in practice. There are examples in sport competitions (Deng, Han, Li, and Liu 2014), in the selection of candidates in political elections (Croon 1989; Lee and Philip 2012), in the arrangement of web-pages when using search engines (Aslam and Montague 2001) and in flagging disease related gene in bioinformatics (DeConde, Hawley, Falcon, Clegg, Knudsen, and Etzioni 2006) just to name a few. We first introduce a parametric model for the one sample case which incorporates an arbitrary score function. Such score functions include both the Spearman and Kendal scores. Score Functions and Penalized Likelihood for Ranking Data is usually very large. For this reason, we may apply penalized likelihood methods to focus on those items that are preferred by the rankers.
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