Modeling learning in knowledge space theory through bivariate Markov processes

摘要: Abstract Bivariate Markov processes (BMPs) described by Ephraim and Mark (2012) consist of a pair stochastic in the continuous time, one observable other latent, that are jointly Markov. In present article, navigation behavior learning process user web-based tutoring system modeled as BMPs constrained assumptions coherent with concepts competence-based knowledge space theory. Such constraints expressed formal about nature process. Scenarios considered where observed is an individual through pages intelligent system, whereas latent consists transitions among states competence structure. The approach seems to be rather general flexible modeling scenarios different assumptions. As example, BMP models developed for some exemplary scenarios. Maximum likelihood parameter estimation via expectation–maximization algorithm presented. results simulation study showed values well-recovered algorithm. application bivariate model real data students navigating Stat-Knowlab proposed provides useful insight into students’ processes.