A multilevel logistic hidden Markov model for learning under cognitive diagnosis

Students who wish to learn a specific skill have increasing access to a growing number of online courses and open-source educational repositories of instructional tools, including videos, slides, and exercises. Navigating these tools is time-consuming and the search itself can hinder the learning of the skill. Educators are hence interested in aiding students by selecting the optimal content sequence for individual learners, specifically which skill one should learn next and which material one should use to study. Such adaptive selection would rely on pre-knowledge of how the learners' and the instructional tools' characteristics jointly affect the probability of acquiring a certain skill. Building upon previous research on Latent Transition Analysis and Learning Trajectories, we propose a multilevel logistic hidden Markov model for learning based on cognitive diagnosis models, where the probability that a learner acquires the target skill depends not only on the general difficulty of the skill and the learner's mastery of other skills in the curriculum but also on the effectiveness of the particular learning tool and its interaction with mastery of other skills, captured by random slopes and intercepts for each learning tool. A Bayesian modeling framework and an MCMC algorithm for parameter estimation are proposed and evaluated using a simulation study.