Rasch analysis of rank-ordered data

Theoretical and practical aspects of several methods for the construction of linear measures from rank-ordered data are presented. The final partial-rankings of 356 professional golfers participating in 47 stroke-play tournaments are used for illustration. The methods include decomposing the rankings into independent paired comparisons without ties, into dependent paired comparisons without ties and into independent paired comparisons with ties. A further method, which is easier to implement, entails modeling each tournament as a partial-credit item in which the rank of each golfer is treated as the observation of a category on a partial-credit rating scale. For the golf data, the partial-credit method yields measures with greater face validity than the paired comparison methods. The methods are implemented with the computer programs FACETS and WINSTEPS.