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Abstract: It is important to examine the nature of the relationships between roadway, environmental, and traffic factors and motor vehicle crashes, with the aim to improve the collective understanding of causal mechanisms involved in crashes and to better predict their occurrence. Statistical models of motor vehicle crashes are one path of inquiry often used to gain these initial insights. Recent efforts have focused on the estimation of negative binomial and Poisson regression models (and related deviants) due to their relatively good fit to crash data. Of course analysts constantly seek methods that offer greater consistency with the data generating mechanism (motor vehicle crashes in this case), provide better statistical fit, and provide insight into data structure that was previously unavailable. One such opportunity exists with some types of crash data, in particular crash-level data that are collected across roadway segments, intersections, etc. It is argued in this paper that some crash data possess hierarchical structure that has not routinely been exploited. This paper describes the application of binomial multilevel models of crash types using 548 motor vehicle crashes collected from 91 two-lane rural intersections in the state of Georgia. Crash prediction models are estimated for angle, rear-end, and sideswipe (both same direction and opposite direction) crashes. The contributions of the paper are the realization of hierarchical data structure and the application of a theoretically appealing and suitable analysis approach for multilevel data, yielding insights into intersection-related crashes by crash type. [Copyright &y& Elsevier]

• The Langevin force explains stochastic volatility in the behaviour model. • Anticipation factors define impacts of spacing and speed to adjacent modes. • Stochastic models cover fine fluctuations in speed profiles under varied conditions. The study proposes a mathematical framework to explain the stochastic behavioural patterns of personal mobility (PM) devices under low-carbon heterogeneous traffic conditions in shared lanes. We create a set of anticipation factors in a stochastic PM behaviour model to tackle sensitivities to both space headway and relative speed against intra- and inter-modes. The proposed behaviour model involves a deterministic and a stochastic force. In the deterministic force, the anticipation factors are used in an optimal velocity model and a full velocity difference model. In the stochastic force, the Langevin equation is used to capture PMs' stochastic characteristics against movements of other PMs, pedestrians, and bicycles, and the effect of lateral interactions. We carried out real-world circular experiments of mixed sustainable modes to verify the performance of the proposed models. Five models' performances are compared under four different traffic conditions, including bike-mixed, pedestrian-mixed, low-speed, and high-speed conditions. We confirmed that newly created anticipation factors play a significant role in all models under all conditions to partially influence the following PM devices' behaviour from the leading two different sustainable modes. The validation results illustrate the excellence of the proposed method. Consequently, behavioural uncertainty is well captured by the stochastic PM devices following models under all traffic conditions, although it requires more parameters than the deterministic PM behavioural models. The proposed method paves the way for the stochastic CF model's applicability to describe PM devices' behavioural dynamics under mixed traffic conditions using anticipation factors. Besides, it lays the foundation stone of PM devices' dynamics in a shared lane to construct effective regulations and safety standards. [ABSTRACT FROM AUTHOR]