TopicResponse: A Marriage of Topic Modelling and Rasch Modelling for Automatic Measurement in MOOCs

Abstract: This paper explores the suitability of using automatically discovered topics from MOOC discussion forums for modelling students' academic abilities. The Rasch model from psychometrics is a popular generative probabilistic model that relates latent student skill, latent item difficulty, and observed student-item responses within a principled, unified framework. According to scholarly educational theory, discovered topics can be regarded as appropriate measurement items if (1) students' participation across the discovered topics is well fit by the Rasch model, and if (2) the topics are interpretable to subject-matter experts as being educationally meaningful. Such Rasch-scaled topics, with associated difficulty levels, could be of potential benefit to curriculum refinement, student assessment and personalised feedback. The technical challenge that remains, is to discover meaningful topics that simultaneously achieve good statistical fit with the Rasch model. To address this challenge, we combine the Rasch model with non-negative matrix factorisation based topic modelling, jointly fitting both models. We demonstrate the suitability of our approach with quantitative experiments on data from three Coursera MOOCs, and with qualitative survey results on topic interpretability on a Discrete Optimisation MOOC.