  This paper adapts topic models to the psychometric testing of MOOC students
based on their online forum postings. Measurement theory from education and
psychology provides statistical models for quantifying a person's attainment of
intangible attributes such as attitudes, abilities or intelligence. Such models
infer latent skill levels by relating them to individuals' observed responses
on a series of items such as quiz questions. The set of items can be used to
measure a latent skill if individuals' responses on them conform to a Guttman
scale. Such well-scaled items differentiate between individuals and inferred
levels span the entire range from most basic to the advanced. In practice,
education researchers manually devise items (quiz questions) while optimising
well-scaled conformance. Due to the costly nature and expert requirements of
this process, psychometric testing has found limited use in everyday teaching.
We aim to develop usable measurement models for highly-instrumented MOOC
delivery platforms, by using participation in automatically-extracted online
forum topics as items. The challenge is to formalise the Guttman scale
educational constraint and incorporate it into topic models. To favour topics
that automatically conform to a Guttman scale, we introduce a novel
regularisation into non-negative matrix factorisation-based topic modelling. We
demonstrate the suitability of our approach with both quantitative experiments
on three Coursera MOOCs, and with a qualitative survey of topic
interpretability on two MOOCs by domain expert interviews.
