A Taxonomy of Polytomous Item Response Models

Abstract: A common framework is provided that comprises classical ordinal item response models as the cumulative, sequential and adjacent categories models as well as nominal response models and item response tree models. The taxonomy is based on the ways binary models can be seen as building blocks of the various models. In particular one can distinguish between conditional and unconditional model components. Conditional models are by far the larger class of models containing the adjacent categories model and the whole class of hierarchically structured models. The latter is introduced as a class of models that comprises binary trees and hierarchically structured models that use ordinal models conditionally. The study of the binary models contained in latent trait models clarifies the relation between models and the interpretation of item parameters. It is also used to distinguish between ordinal and nominal models by giving a conceptualization of ordinal models. The taxonomy differs from previous taxonomies by focusing on the structured use of dichotomizations instead of the role of parameterizations.