Identifiability: A Fundamental Problem of Student Modeling

In this paper we show how model identifiability is an issue for student modeling: observed student performance corresponds to an infinite family of possible model parameter estimates, all of which make identical predictions about student performance. However, these parameter estimates make different claims, some of which are clearly incorrect, about the student’s unobservable internal knowledge. We propose methods for evaluating these models to find ones that are more plausible. Specifically, we present an approach using Dirichlet priors to bias model search that results in a statistically reliable improvement in predictive accuracy (AUC of 0.620 ± 0.002 vs. 0.614 ± 0.002). Furthermore, the parameters associated with this model provide more plausible estimates of student learning, and better track with known properties of students’ background knowledge. The main conclusion is that prior beliefs are necessary to bias the student modeling search, and even large quantities of performance data alone are insufficient to properly estimate the model.