A model that combines diagnostic classification assessment with mixture item response theory models

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 diagnostic classification mixture Rasch model (DCMixRM). The motivation for the development of the DCMixRM is twofold. First, the DCMixRM is designed to provide rigorous explanation as to 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. The measurement component includes specification of item responses through simultaneously taking into account three sets of latent variables, such as a general ability, latent class membership, and mastery profiles of attributes. In the structural component, characteristics of three latent variables are specified, including distributions of ability, latent class, and mastery 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 in the 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 the Q-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 the simulation 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 reading and a statewide mathematics tests to give an illustration of how the model can be used. Further research directions were discussed as well. Index words: Latent covariate, Local dependence, Multidimensionality, Latent class model (LCM), Mixture Rasch Model (MixRM), Log-linear Cognitive Diagnosis Model (LCDM), Diagnostic Classification Mixture Rasch Model (DCMixRM) A Model That Combines Diagnostic Classification Assessment with Mixture Item Response Theory Models