Parameter importance and global sensitivity analysis of a continuous-state probabilistic cellular automata model of peer instruction in heterogeneous classrooms

Abstract

We present a continuous-state probabilistic cellular automata model of peer instruction in heterogeneous classrooms. Building on a previous binary-state model, we incorporate co-construction and transmission learning with a similarity effect, and model student aptitude as a mixture of two logit-normal distributions to represent bimodal ability distributions common in mixed-aptitude settings. Using a comprehensive parameter sweep, we assess parameter importance via Random Forest feature importance and Sobol sensitivity indices. We find that co-construction learning rate η and initial mean aptitude μ are the most influential parameters across all performance metrics, with η dominating at later learning stages and μ at earlier ones. Modal separation and low-aptitude proportion — both controllable through student sectioning — also show notable importance, particularly for lower-aptitude groups. These results suggest that instructional design choices affecting co-construction and class composition have the greatest impact on peer learning outcomes in heterogeneous classrooms.