Rasch dichotomous items are modeled to have the same (or known) discrimination. The inter-adjacent-category discrimination of polytomous Rasch items is also modeled to be the same (or known), but the overall discrimination of polytomous items depends on the distance between its Rasch-Andrich thresholds and so can vary across items and instruments..
Consider a five category rating scale, modeled by a set of 4 equally spaced Rasch-Andrich thresholds. Then the overall item discrimination can vary from very steep to almost flat depending on the distance between the threshold values.
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The plot shows the relationship between uniform threshold spacing, x, and the item-discrimination slope, a, of an equivalent logistic ogive with the range y = 0-4 score points given by
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A discrimination of a ≥ 1.0 implies that the polytomy is equivalent to summing 4 independent dichotomous 0-1 items. When a = 1.0 the items are of equal difficulty. When the inter-threshold distance is negative, the Rasch-Andrich threshold are “disordered”.
It can be seen that one advantage of using Rasch polytomies over independent dichotomous items is that a polytomy can provide higher item discrimination while maintaining the desirable measurement properties of a Rasch model. This is useful for items targeting pass-fail decisions and computer-adaptive testing. This is also one situation in which disordered thresholds can be advantageous.
John Michael Linacre
Item Discrimination and Rasch-Andrich Thresholds, Linacre J.M. Linacre J.M. … Rasch Measurement Transactions, 2006, 20:1 p. 1054
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