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Abstract
The purpose of this dissertation is to present a new psychometric model that combines a Mixture Rasch model with a diagnostic model. We refer to this model as a diagnosticclassification mixture Rasch model (DCMixRM). The motivation for the development of theDCMixRM is twofold. First, the DCMixRM is designed to provide rigorous explanation asto factors that are potentially causing the latent classes to form. In doing so, this model uses attribute mastery states as covariates. Second, the DCMixRM is also designed to connect assessment to instruction by furnishing diagnostic information along with a general ability level.This model consists of two components: measurement and structural components. Themeasurement component includes specification of item responses through simultaneouslytaking into account three sets of latent variables, such as a general ability, latent classmembership, and mastery profiles of attributes. In the structural component, characteristicsof three latent variables are specified, including distributions of ability, latent class, andmastery profile. Further, in this model, we specify the relationship among these variables,particulary the association between latent class and mastery profile.The DCMixRM has several advantages: it provides a way to detect heterogeneity inthe population; it yields more accurate classification of latent classes; it provides a rigorous explanation about features of latent classes; it allows us to examine incompleteness of theQ-matrix; and it allows us to make inferences on a global ability as well as on mastery profiles formed over the set of attributes.A series of simulation studies were conducted to evaluate the quality of estimation process for the DCMixRM in terms of convergence and recovery of model parameters. For thesimulation study, two sets of tests were designed: 30 items involving 3 attributes (A3I30), 20 items involving 4 attributes (A4I20). Under each condition, sample size, similarity of ability means across latent classes, and strength of relationship between latent class and mastery profile were manipulated. Although for some conditions, convergence appeared problematic, results showed that the model parameters were well recovered enough to lead appropriate inferences on the model parameters. We also applied the model to two empirical data sets, including an international readingand a statewide mathematics tests to give an illustration of how the model can be used.Further research directions were discussed as well.