A model for correlated paired comparison data

Abstract

Paired comparison data arise when objects are compared in couples. This type of data occurs in many applications. Traditional models developed for the analysis of paired comparison data assume independence among all observations, but this seems unrealistic because comparisons with a common object are naturally correlated. A model that introduces correlation between comparisons with at least a common object is discussed. The likelihood function of the proposed model involves the approximation of a high dimensional integral. To overcome numerical difficulties a pairwise likelihood approach is adopted. The methodology is illustrated through the analysis of the 2006/2007 Italian men’s volleyball tournament and the 2008/2009 season of the Italian water polo league.