Generalized Additive Modeling for Learning Trajectories in E-Learning Environments

Adaptive E-learning is growing in popularity as it personalizes recommendations in response to learners’ learning needs. An a priori expectation of the learning environment is that the learners’ performance levels may change in real time as they complete a sequence of items and receive feedback. Also, the learners’ learning (performance) trajectories may be irregularly shaped over time. Therefore, a modeling approach that flexibly explores the learner’s learning change is desirable. In this study, we demonstrate the applicability of a semi-parametric modeling approach that can estimate learners’ unique learning trajectories in the E-learning environment. We use a generalized additive mixed model that integrates properties of generalized linear mixed models with those of additive models, in which the linear predictor is given by a sum of smooth functions of the covariates as well as a parametric component of the linear predictor. The model we consider explores the effect of time that the learners spend inside and outside the learning environment. We demonstrate its applicability to log data generated by a real-life E-learning environment.