Analysis of Ordinal Paired Comparison Data

SUMMARY Two types of model are discussed for paired comparisons of several treatments using ordinal scales such as (A <≪ B, A ≪ B, A < B, A = B, A > B, A » B, A ⋙ B), where A ≪ B denotes strong preference for treatment B over treatment A, A ≪ B denotes moderate preference for B, A < B denotes weak preference for B, A = B denotes no preference, and so forth. For the binary scale (A < B, A > B), special cases of the models using logit transforms simplify to the Bradley‐Terry model. When the same raters compare each pair of treatments, one can allow within‐rater dependence by fitting the models with constrained maximum likelihood.