Browsing by Author "Waters, Andrew"

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    Bayesian Methods for Learning Analytics
    (2014-06-30) Waters, Andrew; Baraniuk, Richard G.; Kemere, Caleb T.; Vannucci, Marina
    Learning Analytics (LA) is a broad umbrella term used to describe statistical models and algorithms for understanding the relationship be- tween a set of learners and a set of questions. The end goal of LA is to understand the dynamics of the responses provided by each learner. LA models serve to answer important questions concerning learners and questions, such as which educational concepts a learner understands well, which ones they do not, and how these concepts relate to the individual question. LA models additionally predict future learning outcomes based on learner performance to date. This information can then be used to adapt learning to achieve specific educational goals. In this thesis, we adopt a fully Bayesian approach to LA, which allows us both to have superior flexibility in modeling as well as achieve superior performance over methods based on convex optimization. We first develop novel models and algorithms for LA. We showcase the performance of these methods on both synthetic as well as real-world educational datasets. Second, we apply our LA framework to the problem of collaboration– type detection in educational data sets. Collaboration amongst learners in educational settings is problematic for two reasons. First, such collaboration may be prohibited and considered a form of cheating. Detecting this form of collaboration is essential for maintaining fairness and academic integrity in a course. Finally, collaboration inhibits the ability of LA methods to accurately model learners. We develop several novel techniques for collaboration–type detection where we not only identify collaboration in a statistically principled way, but also classify the type of collaborative behavior.
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    A Bayesian nonparametric approach for the analysis of multiple categorical item responses
    (Elsevier, 2015) Waters, Andrew; Fronczyk, Kassandra; Guindani, Michele; Baraniuk, Richard G.; Vannucci, Marina
    We develop a modeling framework for joint factor and cluster analysis of datasets where multiple categorical response items are collected on a heterogeneous population of individuals. We introduce a latent factor multinomial probit model and employ prior constructions that allow inference on the number of factors as well as clustering of the subjects into homogeneous groups according to their relevant factors. Clustering, in particular, allows us to borrow strength across subjects, therefore helping in the estimation of the model parameters, particularly when the number of observations is small. We employ Markov chain Monte Carlo techniques and obtain tractable posterior inference for our objectives, including sampling of missing data. We demonstrate the effectiveness of our method on simulated data. We also analyze two real-world educational datasets and show that our method outperforms state-of-the-art methods. In the analysis of the real-world data, we uncover hidden relationships between the questions and the underlying educational concepts, while simultaneously partitioning the students into groups of similar educational mastery.