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Abstract
Diagnostic classification models (DCMs) are statistical models designed to provide feedback about students understandings of multiple latent knowledge components, termed attributes. Compared to traditional measurement models that place students abilities on a unidimensional continuous scale, DCMs classify students into levels of attribute mastery and can achieve high reliability with shorter assessments than those required by continuous measurement. To this point, however, DCMs have been used to provide dichotomous feedback about students mastery and non-mastery levels. In educational contexts, further delineating mastery categories may be useful for meaningfully grouping students to provide tailored instruction or interventions. To identify additional mastery levels, we extended the current DCM framework by developing a polytomous DCM (PDCM) that classifies students into more than two mastery levels for each attribute. In the PDCM, we defined a polytomous attribute as an ordinal latent variable, and we allowed the item response probabilities to vary differentially between different mastery levels. A constrained PDCM was proposed in this dissertation by constraining some item parameters to be equal to reduce the number of item parameters and required fewer items and smaller sample size compare to the PDCM.Two simulation studies were conducted to investigate the model estimation and model misspecification. The first study examined the attribute classification accuracies and the item parameter estimation across various conditions. The results shown the PDCM required longer test lengths to yield accurate classification for the attributes and item parameter estimation. The second study evaluated model misspecification. When the attribute mastery levels were under-specified, examinees in the intermediate mastery groups were forced to be classified into other mastery groups and thus the feedback provided was less detailed. When the attribute mastery levels were over-specified, most examinees were still classified into original mastery level groups. An empirical study was conducted to illustrate the application of the PDCM using data from an assessment designed for special education students which measured four mathematics problem-solving skills. We compared PDCM results with a dichotomous DCM framework which shown the PDCM provided improved model-data fit. The more detailed attribute classification also illustrated the utility of PDCM feedback for education practitioners.