A Bayesian Infinite Factor Model for Learning and Content Analytics

• Activity Number: 187
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Kassie Fronczyk*+
• Keywords: factor analysis ; Indian buffet process

Abstract

Personalized learning systems (PLS) that leverage modern technology and flexible modeling tools afford the opportunity to revolutionize education by tailoring the educational experience of each learner to their background, learning goals, and performance to date. Two key aspects of such a PLS are learning analytics, which estimates the level of mastery that each learner has attained with respect to course concepts, and content analytics, which estimates the relations between test items (homework questions, exam problems, etc.) and course concepts.

We develop a probit factor analysis model to enable data-driven decision making through content and learning analytics. Under a fully Bayesian setting, we gain insight on the learner's grasp of the latent concepts and how each question relates to these concepts. Moreover, the number of latent concepts in many cases is unknown a priori. To account for this uncertainty, our method utilizes a nonparametric prior to allow the number of latent concepts to be inferred. We validate our approach on both synthetic and real-world educational datasets.