Testing the actual equivalence of automatically generated items

If the automatic item generation is used for generating test items, the question of how the equivalence among different instances may be tested is fundamental to assure an accurate assessment. In the present research, the question was dealt by using the knowledge space theory framework. Two different ways of considering the equivalence among instances are proposed: The former is at a deterministic level and it requires that all the instances of an item template must belong to exactly the same knowledge states; the latter adds a probabilistic level to the deterministic one. The former type of equivalence can be modeled by using the BLIM with a knowledge structure assuming equally informative instances; the latter can be modeled by a constrained BLIM. This model assumes equality constraints among the error parameters of the equivalent instances. An approach is proposed for testing the equivalence among instances, which is based on a series of model comparisons. A simulation study and an empirical application show the viability of the approach.