Polytomous item scores and Guttman dependence

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    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).
    Original languageEnglish
    Pages (from-to)39-61
    JournalBritish journal of mathematical & statistical psychology
    Issue number1
    Publication statusPublished - 1999


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