In other words, in IRT models where the discrimination parameter is controlled, the item response curves of different items can cross, meaning that the relative difficulties of items are not invariant across the sample of persons, in violation of the assumptions of invariant measurement.
The item response curves of different items can cross, meaning that the relative difficulties of items are not invariant across the sample of persons. This is in violation of the assumptions of invariant measurement. This is in other words. This is in IRT models. The discrimination parameter is controlled.