The confirmatory multidimensional generalized graded unfolding model

Most of existing unfolding IRT (item response theory) models for Likert items are unidimensional. When there are multiple tests of Likert items, or when a Likert item measures more than one latent trait simultaneously, unidimensional unfolding models become inefficient or inappropriate. To resolve this problem, we developed the confirmatory multidimensional generalized graded unfolding model, which is a multidimensional extension of the generalized graded unfolding model (Roberts, Donoghue, & Laughlin, 2000), and conducted a series of simulations to evaluate its parameter recovery. The simulation study demonstrated that the parameters of the new model can be recovered fairly well with the R package R2WinBUGS and computer program WinBUGS. The Tattoo Attitude Questionnaires with 3 scales of Likert items were analyzed to demonstrate the advantages of the multidimensional model over the unidimensional model. The results showed that the multidimensional model had a better fit than the unidimensional one (log PsBF = 27.2); the multidimensional model yielded higher reliability estimates (.92, .89, .83) for the 3 latent traits than the unidimensional one (.84, .85, .83); and the multidimensional model yielded higher correlation estimates among the 3 latent traits (.20 ~ .84) than the unidimensional model (.04 ~ .30).