Modeling the endogeneity of lane-mean speeds and lane-speed deviations using a Bayesian structural equations approach with spatial correlation

Abstract

This study focused on the development of speed prediction models for a multilane highway which incorporate the potential endogenous relationship between adjacent lane speeds and speed deviations while considering geometric design, traffic flow, and other variables in the model specification and accounting for the correlation structures due to multilevel nature of data. The Full Bayesian framework was employed to build the hierarchical models which accounted for three correlation structures at multiple levels: the correlation between speeds of adjoining lanes due to multivariate nature; spatially structured correlations between the adjacent segments, and spatially unstructured correlations among segments.The model estimates which influence the lane-mean speed indicated the directional variation of exogenous factors. For the westbound traffic, the afternoon and night hours were observed to be influential while eastbound traffic was more sensitive to the morning period. The segment length revealed a lane-varying correlation where longer segments influenced a speed reduction for the three lanes closer to the median while the speed in outermost lane exhibited a reverse trend as it increased with longer segments. Both models, with mean speed and speed deviations, demonstrated the significant presence of endogeneity due to mean speeds and speed deviations of adjacent lanes, respectively. This study also assessed the accuracy of predicted mean speed and speed deviations by calculating the measures of discrepancy between the observed and model predicted speeds. The Bayesian residuals, which incorporated the normal, multivariate, and spatial correlation structures, exhibited significant superiority at the prediction accuracy than the Normal ones. This discrepancy in prediction performance reflected the impact of consideration or exclusion of random effects.