THREE MULTIDIMENSIONAL MODELS FOR TESTLET-BASED TESTS: FORMAL RELATIONS AND AN EMPIRICAL COMPARISON

Abstract

Three multidimensional item response theory (IRT) models for testlet-based tests are described. In the bifactor model (Gibbons & Hedeker, 1992), each item measures a general dimension in addition to a testlet-specific dimension. The testlet model (Bradlow, Wainer, & Wang, 1999) is a bifactor model in which the loadings on the specific dimensions are restricted to be proportional to the loadings on the general dimension within each testlet (Li, Bolt, & Fu, 2006). In the second-order model, the items only load on the testlet-specific factors. The correlations between the testlet-specific factors are modeled through a second-order factor. The second-order model is formally equivalent to the testlet model. The models were applied to a testlet-based international English assessment test.