  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.
