In the field of education, understanding differences in student performance by content area subdomains, and classifying students based on these differences, is of interest for differentiating instruction. Structured mixture item response theory (IRT) models offer a unique opportunity to achieve these goals within a confirmatory modeling approach. However, to date, there have been no known applications of this type of model to computer adaptive testing (CAT), a common test design in large-scale educational assessments. This thesis fills this gap by demonstrating the application of a particular structured mixture IRT model to early kindergarten geometry data. Results suggest the model is useful in CAT applications for understanding how students differ by domain, but that the test design must follow certain specifications for student classifications.
Performance-targeted interventions, typically based on student test performance, arean important tool in improving educational outcomes. These types of interventions are often applied at the school level, where low-performing schools are selected for participation. However, typical school effects methods for understanding school performance do not directly identify the low-performing schools that would benefit the most from additional support. Additionally, typical school effects methods do not differentiate school performance based on important aspects of the curriculum. This dissertation fills this gap in school effects methods by proposing the Multilevel Diagnostic Item Response (MD-IR) model. The MD-IR model is a multilevel, confirmatory mixture item response theory model that incorporates strategic constraints in order to differentiate schools, and students within schools, based on the aspects of the curriculum that would be most relevant for a performance-targeted intervention. By incorporating latent classes, the MD-IR model classifies schools as high- or low-performing, and as such, identifies schools most in need of support. The formulation of the MD-IR model is presented, along with a detailed empirical example demonstrating its application in the context of international educational development using data from PISA for Development. Results from the empirical example illustrate the utility of this model and its promise in filling this identification gap in the school effects literature.
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