Nonparametric Models for Polytomous Responses

Mokken (this volume) has argued that his nonparametric IRT model for dichotomous responses can be used to order persons with respect to total score on a monotone homogeneous (MH) set of n items, such that apart from measurement error, this reflects the order of these persons on the property measured by the item set (ability, attitude, capacity, achievement, etc.). If the stronger model of double monotonicity (DM) holds, one can also order the items with respect to popularity. In a majority of cases, the respondents giving a positive reply to a difficult item will also answer positively to all more easy items. It has been explained how Loevinger’s H-coefficient per item pair, per item and for the scale can be used to express the extent to which this Guttman pattern holds true, and to search for homogeneous scales from a larger pool of items.

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