Random parameter structure and the testlet model: extension of the Rasch testlet model.

The current Rasch testlet model (RT) assumes independence of the testlet effect and the target dimension. This article investigated the impact of the violation of that assumption on RT and the performance of an extended Rasch testlet model (ET) in which the random parameter variance-covariance matrix is estimated without any constraints. Our simulation results showed that ET was the same or superior to RT in its performance. The target dimension variance in RT was the most strongly affected parameter and the bias of the target dimension variance was largest when the testlet effect was large and the correlation between the testlet effect and the target dimension was high. This suggests that in some real data applications, it may be difficult to accurately assess the size of testlet effect relative to the target dimension. RT showed close performance to ET with regard to item and testlet effect parameter estimation.