Ranking Models with Item Covariates

Two parametric classes of ranking models are investigated: the Thurstone order statistics models and the Babington Smith models. Both families are natural extensions of commonly used paired comparison models. The concept of an “item parameter” is introduced and studied in the context of each of these classes of models. This distinction between the item parameters and the remaining parameters in a ranking model is useful not only for the general interpretation of model parameters, but also for the specific problem of introducing covariates in these models. Estimation schemes are described for these models, both with and without covariates, and are implemented in an example.