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On a Common Misconception Concerning the Partial Credit and Generalized Partial Credit Polytomous IRT Models NCES IRT

Donoghue, John R.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
National Center for Education Statistics (NCES), Item Response Theory (IRT), Models, Psychometrics, Scaling, Scoring, Test Theory


Recent years have seen a growing use of items which yield responses which can be scored as ordered categories. Masters' partial credit and Muraki's generalized partial credit item response theory models are commonly used to scale such items. A common misconception about these models is that the item category response functions (ICRFs, which describe the probability that an examinee of given ability will receive a particular categorical score) must be symmetric. This paper demonstrates that ICRFs need not be symmetric; indeed, for certain common situations, ICRFs cannot be symmetric. Origins of this misunderstanding are discussed, and the special cases of three- and four-category items are considered.

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