Multi-dimensional unobserved heterogeneities: Modeling likelihood of speeding behaviors in different patterns for taxi speeders with mixed distributions, multivariate errors, and jointly correlated random parameters

Speeding behaviors can be classified into different patterns according to both speeding-range and speeding-distance. Among the speeding patterns, some are more frequently observed in specific traffic scenarios, implying that the likelihood of speeding behaviors may vary across the speeding patterns due to the inconsistent impact of temporal, road, environmental, and other traffic factors. Additionally, the trigger of speeding is a complex process so the researchers may not have access to all the critical information associated with the speeding behaviors. This issue may bring about not only independent heterogeneity but also multi-dimensional heterogeneities that are mutually correlated when modeling speeding behaviors by patterns. However, the joint solution to the above challenges is rarely seen in past studies. To fill the knowledge gaps, this study uses taxi GPS trajectories to extract speeding behaviors and classify them into four patterns. The speeder's percent of speeding distance for each speeding pattern is respectively measured to represent the likelihood of speeding behaviors by patterns. Afterwards, we compare the data-fitting between the models combined with different beta-gamma mixture distributions and a multivariate Gaussian error in modeling the four patterns of speeding likelihood. The combination with the best fitness is used to incorporate jointly correlated random parameters. The results show that the model with beta-gamma-gamma-gamma mixed distributions performs better than other combinations. The model with jointly correlated random parameters outperforms models with other random parameters. The factor analysis reveals that percent of driving at night, percent of driving on roads with a low-speed limit (≤30 km/h), average delays in junctions along the trips, and hourly income have consistent effects on the likelihood of speeding behaviors in all patterns, while the effects of the remaining factors are inconsistent across the speeding patterns. Furthermore, the heterogeneity unveiled by the model parameters is discussed. The study highlights the necessity of considering mixed distributions and multi-dimensional heterogeneities in modeling speeding likelihood by different patterns.