Abstract
Some theoretical relations are established between the score on a polytomous item and the total score on a set of Guttman dependent binary items. Conditions are derived under which these two scores are identically distributed. Application of the theoretical results to three well‐known models for polytomous data yields, among others, the result that the score on a graded response item (Samejima, 1969) is never distributed as the total score on a set of independent binary Rasch items (Rasch, 1969).
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