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The first part of this paper describes a series of loglinear preference models based on paired comparisons, a method of measurement whose aim is to order a set of objects according to an attribute of interest by asking subjects to compare pairs of objects. Based on the basic Bradley-Terry specification, two types of models, the loglinear Bradley-Terry model and a pattern approach are presented. Both methods are extended to include subject and object-specific covariates and some further structural effects. In addition, models for derived paired comparisons (based on rankings and ratings) are also included. Latent classes and missing values can be included. The second part of the paper describes the package prefmod that implements the above models in R. Illustrational applications are provided in the last part of the paper.