This research in statistical methods involves probability models for the rankings that result when a group of subjects each independently ranks a set of items from first place to last place. These include Thurstone order statistics models, ranking models induced by paired comparisons and models based on distances between rankings. In many practical problems the probability of observing any particular ranking is affected by the values of one or more independent variables, or subject covariates, associated with the subjects performing the ranking. In a different but related situation, covariates associated with the items can be used to describe the probability distribution of the ranking. A principal goal of the proposed research is to investigate the consequences of different methods of incorporating the information contained in both item and subject covariates. The performance of the methods, which allow for the development of formal inferential and graphical techniques for studying the effects of the covariates, will be evaluated. A semi-parametric approach will be described to detect systematic differences between rankings which arise in pairs, such as pre- and post-treatment rankings produced by the same subject. Residual spectral analytic techniques will be applied to ranking models in general and covariate models in particular. Diagnostics based on the distributional properties of the residuals will be developed.
