Developing a Common Scale for Testlet Model Parameter Estimates under the Common-item Nonequivalent Groups Design

An important advantage of item response theory (IRT) is increased flexibility for methods of test equating. Several methods of IRT scaling have been developed, but under the assumption of local independence of item responses, such as Haebara's linking procedure. A recent development in IRT has been the introduction of Testlet Response Theory (TRT) models, in which local dependence among related sets of items is accounted for by the incorporation of "testlet effect" parameters in the model. This study extended Haebara's item characteristic curve scale linking method to the three-parameter logistic (3-PL) testlet model. Quadrature points and weights were used to approximate the estimated distribution of the testlet effect parameters so that the expected score of each item given theta can be computed and the scale linking parameters can be estimated. A simulation study was conducted to examine the performance of the proposed scale linking procedure by comparing it with the scale linking procedures that are based on the 3-PL IRT model and the graded response model. An operational data analysis was also performed to illustrate the application of the proposed scale linking method with real data.