Previous studies have mainly focused on investigating one source of local item dependence (LID). However, in some cases, such as scenario-based science assessments, LID might be caused by two possible sources simultaneously. In this study, such kind of LID that is caused by two factors simultaneously is named as dual local item dependence (DLID).

This study proposed a cross-classified model to account for DLID. Two simulation studies were conducted with the primary purpose of evaluating the performance of the proposed cross-classified model. Data sets with DLID were simulated with both testlet effects and content clustering effects. The second purpose of this study was to investigate the potential factors affecting the need to use the more complex cross-classified modeling of DLID over the simplified multilevel modeling of LID by ignoring cross-classification structure. For both simulation studies, five factors were manipulated, including sample size, number of testlets, testlet length, magnitude of the testlet effects represented by standard deviations (SDs), and magnitude of the content clustering effects represented by SDs. The difference between the two simulation studies was that, simulation study 1 constrained the SDs of the testlet effects and content clustering effects as the same across testlets and content areas, respectively; simulation study 2 released this constraint by having mixed SDs of the testlet effects and mixed SDs of the content clustering effects.

Results of both simulation studies indicated that the proposed cross-classified model yielded more accurate parameter recovery, including item difficulty, persons' ability, and random effects' SD parameters with smaller estimation errors than the two multilevel models and the Rasch model which ignored one or both item clustering effects. The two manipulated variables, the magnitude of the testlet effects and the magnitude of the content clustering effects, determined the necessity of using the more complex cross-classified model over the simplified multilevel models and the Rasch model: the larger the magnitude of the testlet effects and the content clustering effects, the more necessary to use the proposed cross-classified model. Limitations are discussed and suggestions for future research are presented at the end.