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Abstract
The educational measurement field has seen prosperous development of longitudinal diagnostic classification models (DCMs) in recent years. These psychometric models shoulder two critical tasks: (1) the model should provide reliable, fine-grained diagnostic feedback about what students know and can do to test users at every measurement occasion, and (2) the model should offer some measures regarding students’ growth for its application over time in scenarios such as throughout an extended lesson, curricular unit, school year, or other period of time. This dissertation introduced a version of the first-order hidden Markov model that is modified to reflect students’ real learning trajectories which may include student forgetting. We utilized the work from Chen et al.’s (2018) where they theoretically laid out the foundation of an unconstrained model but did not manifest and evaluate. We labeled the modified model the unconstrained first-order hidden Markov model (UC-FOHM). The UC-FOHM addressed the absence in the literature that there is currently no available longitudinal DCM that can simultaneously satisfy three conditions: 1) the model does not contain any higher structures or multiple levels in its transition component, 2) the model can evaluate the effect of forgetting, which is omnipresent in student learning, and 3) the model can and has been evaluated within more than two timepoints. This dissertation provided two studies with a multitude of analyses to offer evidence for the usefulness of the UC-FOHM. We conducted the first simulation study to examine the performance of the UC-FOHM in a variety of scenarios regarding sample size, attributes, forgetting rate, and item quality. We further conducted the second simulation study to investigate how well the UC-FOHM performed under three different types of simulated missing data that mimicked examinees dropping out of a longitudinal assessment over time.