Driver speed dynamics in pedestrian crossing warnings: A multilevel functional regression approach

This is the authors' abstract. We don't add key points for this paper.

Despite the critical role of vehicle-to-everything pedestrian warning systems in mitigating collision risks, current research inadequately captures how drivers’ continuous behavioral trajectories are dynamically modulated by the interplay of crossing infrastructure (CI) type, warning lead time (WLT), and warning form (WF). To address this gap, we propose a multilevel functional data analysis framework that integrates functional representation with multilevel principal component analysis to separate between-driver and within-driver variance. A nonparametric functional variable-coefficient linear mixed-effects model is then constructed to capture the temporal evolution of driver speed and pedal operations while accounting for inter-individual heterogeneity. Using high-fidelity simulated driving data from 52 drivers across a fully factorial design (3 CI types × 3 WLTs × 5 WFs), we analyze the dynamic effects of WLT and WF on speed and pedal application. Bootstrap-based hypothesis testing evaluates parameter significance across three distinct phases: braking adjustment, sustained braking, and speed recovery. Results show that incorporating multilevel principal component analysis and accounting for driving style significantly improves predictive accuracy. 4.5 s warning triggers faster reactions but often leads to a brake-then-release pattern and abrupt compensatory acceleration. The multimodal warning combining image with voice command proves most robust overall. Interaction analyses reveal context-specific optima: a 5.5 s voice warning excels in unmarked areas, whereas a 4.5 s multimodal warning induces decisive deceleration at crosswalks with yellow flashing lights. By proposing infrastructure-adaptive warning strategies and differentiated interventions, this study provides a theoretical and practical framework to optimize human-machine interaction and connected-vehicle safety.