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Abstract
Diagnostic classification models (DCMs) are psychometric models that classify examinees according to a specified set of categorical latent traits, or attributes. These classifications can be used to indicate the multifaceted psychological status or multidimensional knowledge state of each examinee. In educational contexts, DCM estimates can identify specific areas for further remediation or instruction where needed. Research on DCMs has been relatively sparse until the past decade or so. As a result, there are fundamental topics related to their application that have not been explored. One such area is the analysis of pre-test/post-test designed experiments. In a pre-test/post-test designed experiment, examinees are administered an assessment before an intervention, then take the same or a parallel form of the assessment after the intervention. In this type of study, the primary objective is to measure growth in examinees, individually and collectively. This dissertation is comprised of two studies, both focusing on developing and examining novel methodology related to the analysis of pre-test/post-test designs in a DCM framework. The first study focuses on the development and application of the Latent Transition Diagnostic Model (LTDM) as a longitudinal and general diagnostic classification model for assessing growth in attribute mastery from pre-test to post-test. The second study extends the LTDM to form the multiple-group LTDM (MG LTDM). In a randomized controlled trial with a control group and an intervention group, the MG LTDM can be used to assess group-differential growth in attribute mastery (i.e., intervention effects). To statistically assess growth and group-differential growth in the LTDM and MG LTDM, respectively, a Wald test was employed. Results of simulation studies show that both models provide highly accurate and reliable classifications, and that the Wald test has appropriate Type I error and is powerful in the detection of growth, even with small effect sizes and less than ideal sample sizes. To demonstrate their practical utility, both models are applied to analyze pre-test/post-test data from a diagnostic test measuring middle school students problem solving abilities in mathematics.