Complex sentence: 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.
Split into simpler sentences: In other words, in IRT models where the discrimination parameter is controlled, the item response curves of different items can cross. This means that the relative difficulties of items are not invariant across the sample of persons, in violation of the assumptions of invariant measurement.