The Ordered artition Model: An Extension of the Partial Credit Model

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Abstract
An item response model, called the ordered partition model, is designed for a measurement context in which the categories of response to an item cannot be completely ordered. For example, two different solution strategies may lead to an equivalent degree of success because both strategies may result in the same score, but an examiner may want to maintain the distinction between the strategies. Thus, the data would not be nominal nor completely ordered, so may not be suitable for other polytomous item response models such as the partial credit or the graded response models. The ordered partition model is described as an extension of the partial credit model, its relationship to other models is discussed, and two examples are presented. Index terms: ordered partition model, partial credit model, partial order model, polytomous IRT model, Rasch model