  Learning and understanding car-following (CF) behaviors are crucial for
microscopic traffic simulation. Traditional CF models, though simple, often
lack generalization capabilities, while many data-driven methods, despite their
robustness, operate as "black boxes" with limited interpretability. To bridge
this gap, this work introduces a Bayesian Matrix Normal Mixture Regression
(MNMR) model that simultaneously captures feature correlations and temporal
dynamics inherent in CF behaviors. This approach is distinguished by its
separate learning of row and column covariance matrices within the model
framework, offering an insightful perspective into the human driver
decision-making processes. Through extensive experiments, we assess the model's
performance across various historical steps of inputs, predictive steps of
outputs, and model complexities. The results consistently demonstrate our
model's adeptness in effectively capturing the intricate correlations and
temporal dynamics present during CF. A focused case study further illustrates
the model's outperforming interpretability of identifying distinct operational
conditions through the learned mean and covariance matrices. This not only
underlines our model's effectiveness in understanding complex human driving
behaviors in CF scenarios but also highlights its potential as a tool for
enhancing the interpretability of CF behaviors in traffic simulations and
autonomous driving systems.
