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.