A Multivariate Probit Model for Learning Trajectories: A Fine-Grained Evaluation of an Educational Intervention

Advances in educational technology provide teachers and schools with a wealth of information about student performance. A critical direction for educational research is to harvest the available longitudinal data to provide teachers with real-time diagnoses about students’ skill mastery. Cognitive diagnosis models (CDMs) offer educational researchers, policy makers, and practitioners a psychometric framework for designing instructionally relevant assessments and diagnoses about students’ skill profiles. In this article, the authors contribute to the literature on the development of longitudinal CDMs, by proposing a multivariate latent growth curve model to describe student learning trajectories over time. The model offers several advantages. First, the learning trajectory space is high-dimensional and previously developed models may not be applicable to educational studies that have a modest sample size. In contrast, the method offers a lower dimensional approximation and is more applicable for typical educational studies. Second, practitioners and researchers are interested in identifying factors that cause or relate to student skill acquisition. The framework can easily incorporate covariates to assess theoretical questions about factors that promote learning. The authors demonstrate the utility of their approach with an application to a pre- or post-test educational intervention study and show how the longitudinal CDM framework can provide fine-grained assessment of experimental effects.