Estimation of speed differentials on rural highways using hierarchical linear regression models

Abstract

Large speed differentials between highway segments are associated with an increase in the number of accidents. Traditional speed differential measures, derived from single-level linear regression models, suffer from serious deficiencies, namely underestimating the speed differential (due to intracorrelated data) and inflating the adequacy of the model’s explanation (due to aggregate data). High-quality speed differential predictions are highly desirable right from the initial design phase, but the estimation process is not straightforward, and decision makers must recognize that speed differential predictions are subject to considerable uncertainty. This paper compares four models: two single-level models, a conventional multilevel model, and a Bayes multilevel model. The results show empirically that multilevel models increase the accuracy and precision of estimates of speed differentials, possibly with fewer data. The paper introduces a new, easy to interpret speed consistency measure that simply represents the probability that a vehicle exceeds a certain speed differential. This measure is calculated using a multilevel model and takes into account the uncertainty in the estimates of speed differentials. Overall, we show that a multilevel modeling approach can improve the quality of decision making that makes use of speed differential information in road design and road safety.