Diagnostic measurement from a standardized math achievement test using multidimensional latent trait models
Jun, Hea Won
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The present study compares applications of continuous multidimensional item response theory (MIRT) models for their diagnostic potential. Typically, MIRT models have not been used for diagnosing the possession of skills or attributes by students, but several researchers have suggested that they can potentially be used for this purpose (e.g., Stout, 2007; Wainer, Vevea, Camacho, Reeve, Rosa, Nelson, Swygert, & Thissen, 2001). This study applies MIRT models to a standardized eighth grade mathematics achievement test that was constructed based on a hierarchically-structured blueprint consisting of standards, benchmarks, and indicators. Only the highest level, consisting of four standards, was used to define the dimensions. The confirmatory models were defined using the standards that had been scored for involvement in each item. For the current study, the exploratory MIRT (EMIRT) model was interpreted with respect to the dimensions. Then, the compensatory and confirmatory MIRT (CMIRT) models and the full information bifactor model were fitted. The interpretation of dimensions, empirical reliabilities of person estimates, and test- and item-fit were examined. Also, dimension and pattern probabilities were obtained for determining their diagnostic potential. Last, a noncompensatory MIRT model (MLTM-D; Embretson & Yang, 2011) and the DINA model (Haertel, 1989; Junker & Sijtsma, 2001) in use as diagnostic models were analyzed to compare pattern probabilities with the compensatory CMIRT model.