Bayesovské sítě pro e-learning a systémy hodnocení ve vzdělávání

This thesis focuses on modeling students’ knowledge using Bayesian networks and psychometric models. It is based on data from a mathematics test administered as part of the unified entrance examination and investigates how the choice of Q-matrix structure affects the predictive performance of selected models. The main objective of the thesis is to propose and compare two different approaches to constructing a Q-matrix. The expert-based approach, derived from the author’s content analysis of mathematical tasks, defines four basic skills. In contrast, the data-driven approach uses students’ responses and applies Bayesian network structure learning, graph transformations, and hierarchical clustering to identify five latent skills. To evaluate both proposed structures, the Noisy-AND model and logistic regression are applied to binary data, while the Graded Response Model retains information about partial credit scores. The results show that the data-driven Q-matrix improved performance in most of the evaluated metrics. A comparison of the models at the level of individual items also shows differences in the behaviour of compensatory and non-compensatory approaches. Finally, the thesis discusses limitations related to data imbalance and the difficulty of interpreting the content of skills identified directly from data. At the same time, the thesis shows that the proposed data-driven procedure offers an alternative perspective that may be useful in knowledge assessment.