Learning meets Assessment: On the relation between Item Response Theory and Bayesian Knowledge Tracing

Abstract: Few models have been more ubiquitous in their respective fields than Bayesian knowledge tracing and item response theory. Both of these models were developed to analyze data on learners. However, the study designs that these models are designed for differ; Bayesian knowledge tracing is designed to analyze longitudinal data while item response theory is built for cross-sectional data. This paper illustrates a fundamental connection between these two models. Specifically, the stationary distribution of the latent variable and the observed response variable in Bayesian knowledge Tracing are related to an item response theory model. This connection between these two models highlights a key missing component: the role of education in these models. A research agenda is outlined which answers how to move forward with modeling learner data. %Furthermore, recent advances in network psychometrics demonstrate how this relationship can be exploited and generalized to a network model.