Random Parameter Tobit Model Research Articles

Traffic conflict assessment using macroscopic traffic flow variables: A novel framework for real-time applications

The present study develops a comprehensive traffic conflict assessment framework using macroscopic traffic state variables. To this end, vehicular trajectories extracted for a midblock section of a ten-lane divided Western Urban Expressway in India are used. A macroscopic indicator termed “time spent in conflict (TSC)” is adopted to evaluate traffic conflicts. The proportion of Stopping distance (PSD) is adopted as a suitable traffic conflict indicator. Vehicle-to-vehicle interactions in a traffic stream are two-dimensional, highlighting that the vehicles interact simultaneously in lateral and longitudinal dimensions. Therefore, a two-dimensional framework based on the influence zone of the subject vehicle is proposed and employed to evaluate TSCs. The TSCs are modeled as a function of macroscopic traffic flow variables, namely, traffic density, speed, the standard deviation in speed, and traffic composition, under a two-step modeling framework. In the first step, the TSCs are modeled using a grouped random parameter Tobit (GRP-Tobit) model. In the second step, data-driven machine learning models are employed to model TSCs. The results revealed that intermediately congested traffic flow conditions are critical for traffic safety. Furthermore, macroscopic traffic variables positively influence the value of TSC, highlighting that the TSC increases with an increase in the value of any independent variable. Among different machine learning models, the random forest (RF) model was observed as the best-fitted model to predict TSC based on macroscopic traffic variables. The developed machine learning model facilitates traffic safety monitoring in real-time.

An empirical analysis of factors contributing to roadway infrastructure damage from expressway accidents: A Bayesian random parameters Tobit approach

This paper presents an empirical analysis of factors contributing to roadway infrastructure damage from expressway accidents, using a Bayesian random parameters Tobit model. The accident data collected from Kaiyang Expressway, China in 2014 and 2015 are used for the empirical analysis. The results of parameter estimation in the proposed model indicate that: the effects of vehicle types are significantly heterogeneous across observations, and that the effects of horizontal curvature, time of day, vehicle registered province, and accident type are also significant but homogeneous across observations. The marginal effects of these contributing factors are calculated to explicitly quantify their impacts on road infrastructure damage. According to the analysis results, some strategies pertaining to safety education, traffic enforcement, roadway design, and intelligence transportation technology are advocated to reduce road infrastructure damage from expressway accidents.

Analysing the main and interaction effects of commercial vehicle mix and roadway attributes on crash rates using a Bayesian random-parameter Tobit model

In previous research, the effects of commercial vehicle proportions (CVP) on overall crash propensity have been found to be significant, but the results have been varied in terms of the effect direction. In addition, the mediating or moderating effects of roadway attributes on the CVP-vs-safety relationships, have not been investigated. In addressing this gap in the literature, this study integrates databases on crashes, traffic, and inventory for Hong Kong road segments spanning 2014–2017. The classes of commercial vehicles considered are public buses, taxi, and light-, medium- and heavy-goods vehicles. Random-parameter Tobit models were estimated using the crash rates. The results suggest that the CVP of each class show credible effects on the crash rates, for the various crash severity levels. The results also suggest that the interaction between CVP and roadway attributes is credible enough to mediate the effect of CVP on crash rates, and the magnitude and direction of such mediation varies across the vehicle classes, crash severity levels, and roadway attribute type in four ways. First, the increasing effect of taxi proportion on slight-injury crash rate is magnified at road segments with high intersection density. Second, the increasing effect of light-goods vehicle proportion on slight-injury crash rate is magnified at road segments with on-street parking. Third, the association between the medium- and heavy-goods vehicle proportion and killed/severe injury (KSI) crash rate, is moderated by the roadway width (number of traffic lanes). Finally, a higher proportion of medium- and heavy-goods vehicles generally contributes to increased KSI crash rate at road segments with high intersection density. Overall, the findings of this research are expected not only to help guide commercial vehicle enforcement strategy, licensing policy, and lane control measures, but also to review existing urban roadway designs to enhance safety.

Modeling bicycle crash costs using big data: A grid-cell-based Tobit model with random parameters

Bicyclists are among the most vulnerable road users in the urban transportation system. It is critical to investigate the contributing factors to bicycle-related crashes and to identify the hotspots for efficient allocation of treatment resources. A grid-cell-based modeling framework was used to incorporate heterogeneous data sources and to explore the overall safety patterns of bicyclists in Manhattan, New York City. A random parameters (RP) Tobit model was developed in the Bayesian framework to correlate transportation, land use, and sociodemographic data with bicycle crash costs. It is worth mentioning that a new algorithm was proposed to estimate bicyclist-involved crash exposure using large-scale bicycle ridership data from 2014 to 2016 obtained from Citi Bike, which is the largest bicycle sharing program in the United States. The proposed RP Tobit model could deal with left-censored crash cost data and was found to outperform the Tobit model by accounting for the unobserved heterogeneity across neighborhoods. Results indicated that bicycle ridership, bicycle rack density, subway ridership, taxi trips, bus stop density, population, and ratio of population under 14 were positively associated with bicycle crash cost, whereas residential ratio and median age had a negative impact on bicycle crash cost. The RP Tobit model was used to estimate the cell-specific potential for safety improvement (PSI) for hotspot ranking. The advantages of using the RP Tobit crash cost model to capture PSI are that injury severity is considered by being converted into unit costs, and varying effects of certain explanatory variables are accounted for by incorporating random parameters. The cell-based hotspot identification method can provide a complete risk map for bicyclists with high resolution. Most locations with high PSIs either had unprotected bicycle lanes or were close to the access points to protected bicycle routes.

A random parameters regional quantile analysis for the varying effect of road-level risk factors on crash rates

Many studies have been devoted to investigate the spatial variations (heterogeneities) in the effects of risk factors on crash likelihood. However, investigations mainly target the safety effects on the mean of the crash data (distribution). Less attention was paid to investigate the spatial nonstationary effects on the different quantiles of the crash data distribution. In this study, a conditional quantile-based Bayesian hierarchical random parameter Tobit model is proposed to investigate the regional varying effects of road-related factors on crash rate at different quantiles of the crash rate distribution. A specific roadway facility type, urban two-lane two-way roadway segments in Florida, with crash and road related data for a three-year period is used for a case study. The results show that: 1) the regression coefficients of all of the selected risk factors vary over a wide range among 34 counties on every investigated quantiles of crash rate distribution; 2) in each county, the regression coefficients of all of the factors vary over investigated quantiles of the crash rate distribution, and for the same factor, the coefficients present different ranges of the variation in different counties; 3) the 50th-quantile conditional quantile-based Bayesian hierarchical random parameter Tobit model outperforms the conditional mean-based Bayesian hierarchical random parameter Tobit model, Bayesian quantile Tobit model and Bayesian Tobit model in terms of the prediction accuracy measured by the MAE, and 75th-quantile conditional quantile-based Bayesian hierarchical random parameter Tobit model is outstanding in terms of the goodness-of-fit measured by the DIC. These findings suggest the importance of investigating the regional nonstationary effects of risk factors for different quantiles of the crash rate distribution. The practical implications of the proposed conditional quantile-based Bayesian hierarchical random parameter Tobit model in terms of data prediction, parameters interpretation and safety effects explanation are highlighted at the end of this paper.

Real-time conflict-based Bayesian Tobit models for safety evaluation of signalized intersections

The safety of signalized intersections has traditionally been evaluated at an aggregate level by relating historical collision records for several years to the annual traffic volume and the geometric characteristics of the intersection. This is a reactive and macroscopic approach that gives little insight into how important dynamic signal cycle-related variables can affect intersection safety such as the arrival type and the shock wave characteristics. The objective of this study is to develop traffic conflict-based real-time safety models for signalized intersections using several state-of-the-art techniques. Traffic conflicts were measured by multiple indicators including time-to-collision (TTC), modified time-to-collision (MTTC), and deceleration rate to avoid collision (DRAC). Traffic conflict rate was employed as independent variable while traffic volume, queue length, shock wave area, shock wave speed, and platoon ratio of each cycle were used as covariates in the safety models. Four candidate Tobit models were developed and compared under the Bayesian framework: conventional Tobit model, grouped random parameters Tobit (GRP-Tobit) model, random intercept Tobit (RI-Tobit) model, and random parameters Tobit (RP-Tobit) model. The results showed that the GRP-Tobit model performs best with lowest Deviance Information Criteria (DIC), indicating that accounting for the unobserved heterogeneity across sites can significantly improve the model fit. The model estimation results showed that higher conflict rates were associated with various shock wave characteristics (positive sign for shock wave area, shock wave speed, and queue length) and higher traffic volume. Lower conflict rates were related with higher platoon ratio (favorable arrival patterns). The developed models can have potential applications in real-time safety evaluation, real-time optimization of signal control, and connected and autonomous vehicles (CAV) trajectories planning.

Comparison and analysis of crash frequency and rate in cross-river tunnels using random-parameter models

Underground road systems are becoming popular in cites because they can overcome urban space constraints and increase capacity and accessibility for urban transport systems. In cities with rivers and seas, the construction of cross-river tunnels can preserve land resources and reduce traffic congestion without affecting navigation. However, tunnel traffic safety has become an increasing concern due to frequent and serious tunnel traffic crashes. The severity of crashes and the difficulty of rescue in tunnels are higher than those of other road sections. To improve the safety of tunnel operation, this paper analyzes the crash data of 14 river-crossing tunnels in Shanghai from 2015 to 2016. A negative binomial (NB) model is employed for crash frequency, and a tobit model is employed for crash rate. With respect to possible spatial and temporal correlations in accident data and unobserved heterogeneity across observations, random-effect (RE) and random-parameter (RP) regression models are utilized. The tunnel geometry characteristics, traffic conditions and crash location are considered as independent variables. The results of the crash frequency show that annual average daily traffic (AADT), speed limit, grade, grade differences and the ratio of the vertical grade to the curve radius (RGR) are likely to increase the crash frequency in cross-river tunnels while horizontal curve radius, vertical curve radius and long tunnel are associated with fewer crashes. This study also explored the use of crash rate instead of crash frequency as a dependent variable by using a random-parameter tobit model. The results indicate that the significance of most independent variables is consistent with the results obtained from the random-parameter negative binomial model based on crash frequency.

Modelling braking behaviour and accident probability of drivers under increasing time pressure conditions

Drivers apply brakes to reduce the speed of a vehicle based on the perceived risk while approaching a certain event. Inadequate or excessive braking can lead to serious consequences. The current study analyses the braking behaviour and accident probability of the drivers under increasing time pressure conditions. Two perilous events (pedestrian crossing and obstacle overtaking) were designed to examine Brake Pedal Force (BPF) and Brake-To-Maximum Brake (BTMB) transition time on a driving simulator. Eighty-five Indian licensed drivers drove the simulator in three different time pressure conditions: No Time Pressure (NTP) (baseline), Low Time Pressure (LTP), and High Time Pressure (HTP). Random parameters Tobit model was used for analysing BPF and duration analysis approach was considered for BTMB analysis. Further, generalized linear mixed model with logit link function was used to study the effect of BPF and BTMB on accident probability of the drivers. The model results showed that gender, driving profession, approach speed, age, driving history, and driving condition significantly affected braking behaviour of the drivers. It was observed that in pedestrian crossing event, LTP and HTP driving conditions resulted in 42.31 % and 87.28 % increase in BPF and 13 % and 23 % reduction in BTMB respectively with respect to NTP driving condition and the corresponding changes were slightly lower in case of obstacle overtaking event. The accident probability model showed that female drivers needed 119.70 % and 186.08 % more BPF and 37.55 % and 58.51 % less BTMB in LTP and HTP driving conditions respectively to have equivalent risk levels as observed for male drivers. Further, non-professional drivers had to increase their BPF by 166.83 % in LTP and 219.93 % in HTP to offset their increased accident risk as compared to professional drivers under time pressure conditions.

A correlated random parameters tobit model to analyze the safety effects and temporal instability of factors affecting crash rates

Numerous studies have previously used a variety of count-data models to investigate factors that affect the number of crashes over a certain period of time on roadway segments. Unlike past studies which deal with crash frequency, this study views the crash rates directly as a continuous variable left-censored at zero and explores the application of an alternate approach based on tobit regression. To thoroughly investigate the factors affecting freeway crash rates and the potentially temporal instability in the effects of crash factors involving traffic volume, freeway geometries and pavement conditions, a classic uncorrelated random parameters tobit (URPT) model and a correlated random parameters tobit (CRPT) model were estimated, along with a conventional fixed parameters tobit (FPT) model. The analysis revealed a large number of safety factors, including several appealing and interesting factors rarely studied in the past, such as the safety effects of climbing lanes and distance along composite descending grade. The results also showed that the CRPT model was not only able to reflect the heterogeneous effects of various factors, but also able to estimate the underlying interactions among unobserved characteristics, and therefore provide better statistical fit and offer more insights into factors contributing to freeway crashes than its model counterparts. Additionally, the results showed significant temporal instability in CRPT models across the studied time periods indicating that crash factors (including unobserved characteristics and the underlying interactions among them) and their effects on crash rates varied over time, and more attentions should be paid when interpreting crash data-analysis findings and making safety policies.The modeling technique in this study demonstrates the potential of CRPT model as an effective approach to gain new insights into safety factors, particularly when the heterogeneous effects of factors on safety are interactive. Additionally, findings from this study are also expected to assist in developing more effective countermeasures by better understanding the safety effects of factors associated with freeway design characteristics and pavement conditions.

Jointly modeling area-level crash rates by severity: a Bayesian multivariate random-parameters spatio-temporal Tobit regression

ABSTRACTThis study investigates the inclusion of spatio-temporal correlation and interaction in a multivariate random-parameters Tobit model and their influence on fitting areal crash rates with different severity outcomes. The spatial correlation is specified via a multivariate conditional autoregressiv (MCAR) prior, whereas the temporal correlation is specified by a linear time trend. A spatio-temporal interaction is formulated as the product of a time trend and a spatial term with an MCAR prior. A multivariate random-parameters spatio-temporal Tobit model is developed for slight injury and killed or serious injury crash rates using one year of crash data from 131 traffic analysis zones in Hong Kong. The proposed model is estimated and assessed in the Bayesian context. The model estimation results show that spatial and temporal effects and their interactive effects are significant and that the spatial and interactive effects have strong correlations across injury severities. The proposed model outperforms a multivariate random-parameters Tobit model and a multivariate random-parameters spatial Tobit model in terms of model fit. These findings highlight the importance of appropriately accommodating spatio-temporal correlation and interaction for the joint analysis of areal crash rates by severity.

Examining correlations between motorcyclist’s conspicuity, apparel related factors and injury severity score: Evidence from new motorcycle crash causation study

Motorcyclists are vulnerable road users at a particularly high risk of serious injury or death when involved in a crash. In order to evaluate key risk factors in motorcycle crashes, this study quantifies how different “policy-sensitive” factors correlate with injury severity, while controlling for rider and crash specific factors as well as other observed/unobserved factors. The study analyzes data from 321 motorcycle injury crashes from a comprehensive US DOT FHWA’s Motorcycle Crash Causation Study (MCCS). These were all non-fatal injury crashes that are representative of the vast majority (82%) of motorcycle crashes. An anatomical injury severity scoring system, termed as Injury Severity Score (ISS), is analyzed providing an overall score by accounting for the possibility of multiple injuries to different body parts of a rider. An ISS ranges from 1 to 75, averaging at 10.32 for this sample (above 9 is considered serious injury), with a spike at 1 (very minor injury). Preliminary cross-tabulation analysis mapped ISS to the Abbreviated Injury Scale (AIS) injury classification and examined the strength of associations between the two. While the study finds a strong correlation between AIS and ISS classification (Kendall’s tau of 0.911), significant contrasts are observed in that, when compared to ISS, AIS tends to underestimate the severity of an injury sustained by a rider. For modeling, fixed and random parameter Tobit modeling frameworks were used in a corner-solution setting to account for the left-tail spike in the distribution of ISS and to account for unobserved heterogeneity. The developed random parameters Tobit framework additionally accounts for the interactive effects of key risk factors, allowing for possible correlations among random parameters. A correlated random parameter Tobit model significantly out-performed the uncorrelated random parameter Tobit and fixed parameter Tobit models. While controlling for various other factors, we found that motorcycle-specific shoes and retroreflective upper body clothing correlate with lower ISS on-average by 5.94 and 1.88 units respectively. Riders with only partial helmet coverage on-average sustained more severe injuries, whereas, riders with acceptable helmet fit had lower ISS Methodologically, not only do the individual effects of several key risk factors vary significantly across observations in the form of random parameters, but the interactions between unobserved factors characterizing random parameters significantly influence the injury severity score as well. The implications of the findings are discussed.

Analysis of Crash Rates at Freeway Diverge Areas using Bayesian Tobit Modeling Framework

The goal of this study is to evaluate the impact of various risk factors on crash rates at freeway diverge areas. Crash rates data for a three-year period from 367 freeway diverge areas were used for analysis. Four candidate Tobit models were developed and compared under the Bayesian framework: a traditional Tobit model; a random parameters Tobit (RP-Tobit) model; a grouped random parameters Tobit (GRP-Tobit) model; and a random intercept Tobit (RI-Tobit). The results showed that the RP-Tobit model performs best with highest value of Rd2 as well as lowest Mean Absolute Deviance (MAD) and Deviance Information Criteria (DIC), indicating the importance of accounting for unobserved heterogeneity to improve the model fit. Both the GRP-Tobit and the RI-Tobit models provide better performance than the traditional Tobit model. The model results showed that crash rates at freeway diverge areas were positively associated with mainline annual average daily traffic (AADT) and negatively associated with ramp AADT, indicating the different mechanisms of the impact of traffic volume on crash rates at freeway diverge areas. Lane-balanced design and high speed limits at freeway diverge areas have a negative effect on crash rates. The number of lanes on mainline and ramp length have significant heterogeneous effects on crash rates across observations. The RP-Tobit model provides a more comprehensive understanding of the heterogeneous effects of risk factors on crash rates across observations.

Multivariate random parameter Tobit modeling of crashes involving aging drivers, passengers, bicyclists, and pedestrians: Spatiotemporal variations

The increase in 65 years and older population in the United States compels the investigation of the crashes involving all aging (65+) roadway users (drivers, passengers, bicyclists, and pedestrians) in order to ensure their safety. As such, the objective of this research is to provide a spatiotemporal comparative investigation of the crashes involving these aging roadway users in Florida via concurrently using the same set of predictors in order to obtain comparable findings among them. First, a new metric, namely Crash Rate Difference (CRD) approach is developed, which enables one to capture potential spatial and temporal (e.g., weekend and weekday) variations in crash rates of aging user-involved crashes. Second, a multivariate random parameter Tobit model is utilized to determine the factors that drive both the crash occurrence probability and the crash rate of 65+ roadway users, accounting for the unobserved heterogeneity. Findings show that there are statistically significant heterogeneous effects of predictors on the crash rates of different roadway users, which evidences the unobserved heterogeneity across observations. Results also indicate that the presence of facilities such as hospitals, religious facilities, or supermarkets is very influential on crash rates of 65+ roadway users, advocating that roadways around these facilities should be particularly scrutinized by road safety stakeholders. Interestingly, the effect of these facilities on crashes also differs significantly between weekdays and weekends. Moreover, the roadway segments with high crash rates vary temporally depending on whether it is a weekday or a weekend. These findings regarding the spatiotemporal variations clearly indicate the need to develop and design better traffic safety measures and plans addressing these specific roadway segments, which can be tailored to alleviate traffic safety problems for 65+ roadway users.

Incorporating temporal correlation into a multivariate random parameters Tobit model for modeling crash rate by injury severity

ABSTRACTThis study develops three temporal multivariate random parameters Tobit models to analyze crash rate by injury severity; these models simultaneously accommodate temporal correlation and unobserved heterogeneity across observations and correlations across injury severity. The three models are estimated and compared in the Bayesian context with a crash dataset collected from Hong Kong’s Traffic Information System, which contains crash, road geometry, traffic, and environmental information on 194 directional road segments over a five-year period (2002–2006). Significant temporal effects are found in all of the temporal models, and the inclusion of temporal correlation considerably improves the goodness of fit of the multivariate random parameters Tobit regression, according to the results of deviance information criteria (DIC) and Bayesian R2, indicating the strength of considering cross-period temporal correlation. Moreover, after accounting for temporal effects, the magnitude of the correlation between the crash rates at various injury degrees decreases, probably because a portion of the correlation may be attributed to unobserved or unobservable factors with time-dependent or autoregressive safety effects. Among the three candidate temporal models, the one with independent temporal effects has lower DIC and R2 values, which suggests better model-fit performance than the two with constant or correlated temporal effects. This finding supports the model with independent temporal effects as a good alternative for traffic safety analysis.

A Bayesian spatial random parameters Tobit model for analyzing crash rates on roadway segments

This study develops a Bayesian spatial random parameters Tobit model to analyze crash rates on road segments, in which both spatial correlation between adjacent sites and unobserved heterogeneity across observations are accounted for. The crash-rate data for a three-year period on road segments within a road network in Florida, are collected to compare the performance of the proposed model with that of a (fixed parameters) Tobit model and a spatial (fixed parameters) Tobit model in the Bayesian context. Significant spatial effect is found in both spatial models and the results of Deviance Information Criteria (DIC) show that the inclusion of spatial correlation in the Tobit regression considerably improves model fit, which indicates the reasonableness of considering cross-segment spatial correlation. The spatial random parameters Tobit regression has lower DIC value than does the spatial Tobit regression, suggesting that accommodating the unobserved heterogeneity is able to further improve model fit when the spatial correlation has been considered. Moreover, the random parameters Tobit model provides a more comprehensive understanding of the effect of speed limit on crash rates than does its fixed parameters counterpart, which suggests that it could be considered as a good alternative for crash rate analysis.

Analysis of Severe Injury Accident Rates on Interstate Highways Using a Random Parameter Tobit Model

In this study, a random parameter Tobit regression model approach was used to account for the distinct censoring problem and unobserved heterogeneity in accident data. We used accident rate data (continuous data) instead of accident frequency data (discrete count data) to address the zero cell problems from data where roadway segments do not have any recorded accidents over the observed time period. The unobserved heterogeneity problem is also considered by using random parameters, which are parameter estimates that vary across observations instead of fixed parameters, which are parameter estimates that are fixed/constant over observations. Nine years (1999–2007) of panel data related to severe injury accidents in Washington State, USA, were used to develop the random parameter Tobit model. The results showed that the Tobit regression model with random parameters is a better approach to explore factors influencing severe injury accident rates on roadway segments under consideration of unobserved heterogeneity problems.

A multivariate random-parameters Tobit model for analyzing highway crash rates by injury severity

In this study, a multivariate random-parameters Tobit model is proposed for the analysis of crash rates by injury severity. In the model, both correlation across injury severity and unobserved heterogeneity across road-segment observations are accommodated. The proposed model is compared with a multivariate (fixed-parameters) Tobit model in the Bayesian context, by using a crash dataset collected from the Traffic Information System of Hong Kong. The dataset contains crash, road geometric and traffic information on 224 directional road segments for a five-year period (2002–2006). The multivariate random-parameters Tobit model provides a much better fit than its fixed-parameters counterpart, according to the deviance information criteria and Bayesian R2, while it reveals a higher correlation between crash rates at different severity levels. The parameter estimates show that a few risk factors (bus stop, lane changing opportunity and lane width) have heterogeneous effects on crash-injury-severity rates. For the other factors, the variances of their random parameters are insignificant at the 95% credibility level, then the random parameters are set to be fixed across observations. Nevertheless, most of these fixed coefficients are estimated with higher precisions (i.e., smaller variances) in the random-parameters model. Thus, the random-parameters Tobit model, which provides a more comprehensive understanding of the factors’ effects on crash rates by injury severity, is superior to the multivariate Tobit model and should be considered a good alternative for traffic safety analysis.

Modeling the equivalent property damage only crash rate for road segments using the hurdle regression framework

The understanding of the distributional characteristics of the equivalent property damage only (EPDO) crash rate is limited in the existing literature. Models without a proper distribution of EPDO rate could result in biased estimations and misinterpretations of factors. The importance of prediction accuracy and modeling performance for the EPDO rate should be acknowledged since they directly affect the allocation of limited public funds to safety management for road networks. The general objective of this study is to investigate the distributional characteristics of the EPDO rate and accordingly develop proper econometric models for connecting the EPDO rate to explanatory variables. A hurdle framework was proposed in order to accommodate the zero-positive mixed domain of the EPDO rate. For the positive part of the EPDO rate, three representative distributions (lognormal, gamma and normal) were tested and then the three hurdle models were compared against the Tobit model and the random-parameters Tobit model. The empirical results illustrate the lognormal hurdle model's superior modeling performance in comparison to the other four models, and more importantly that conclusion also holds for several different definitions of the EPDO rate under different combinations of property damage only (PDO) equivalency factors.

Modeling Crash Rates for a Mountainous Highway by Using Refined-Scale Panel Data

Traditional traffic safety analyses on crash frequency or crash rate usually focus on highly aggregated cross-sectional data. The adoption of aggregated data ignores the time-varying nature of some critical factors, and their effects on traffic safety may be masked through data aggregation. For mountainous highways, weather- and environment-related variables become critical as a result of complex time- and spatial-varying characteristics as well as interactions with mountainous terrain. Therefore, refined-scale models are often desired to appropriately model crash safety risks on mountainous highways and disclose the inherent crash mechanism. An advanced random parameter Tobit model with panel data (time series cross-sectional data) in refined temporal scale was developed. This is so far the first reported effort on integrating random parameter Tobit model and refined-scale panel data to develop crash rate models. A random parameter model was adopted not only to handle unobserved heterogeneity explicitly, but also to account for serial correlations across observations in panel data. Refined-scale weather and traffic data in a panel formation were adopted to accommodate the varying nature of complex driving conditions. Interstate 70 (I-70) in Colorado is well known for its typical mountainous terrain, critical role for local and national traffic, and inclement weather. As a demonstration of the modeling techniques, crash rates for a segment of I-70 were investigated in refined temporal scale. Results showed that a random parameter Tobit model outperformed a fixed-parameter Tobit model, and factors related to traffic, weather, and surface conditions were found to play significant roles in an accident rate model.

A correlated random parameter approach to investigate the effects of weather conditions on crash risk for a mountainous freeway

Freeway crashes are highly influenced by weather conditions, especially for a mountainous freeway affected by adverse weather conditions. In order to reduce crash occurrence, a variety of weather monitoring systems and Intelligent Transportation Systems (ITS) have been introduced to address the weather impact. However, the effects of weather conditions on crash occurrence have not been fully investigated and understood. With detailed weather information from weather monitoring stations, this study seeks to investigate the complex effects of weather factors, such as visibility and precipitation, on crash occurrence based on safety performance functions. Unlike conventional traffic safety studies which deal with crash frequency, crash rates per 100million vehicle miles travelled were adopted as the dependent variable in this study. Three years of weather related crash data from a 15mile mountainous freeway on I-70 in Colorado were utilized. First, a fixed parameter Tobit model was estimated to unveil the effects of explanatory variables on crash rates. Then, in order to characterize the heterogeneous effects of weather conditions across the homogeneous segments, a traditional random parameter Tobit model was developed. Furthermore, for the purpose of monitoring the intricate interactions between weather conditions and geometric characteristics, a multivariate structure for the distribution of random parameters was introduced; which result in a correlated random parameter Tobit model. Likelihood ratio test results demonstrated that the correlated random parameter Tobit model was superior to the uncorrelated random parameter and fixed parameter Tobit models. Moreover, visibility and precipitation variables were found to have substantial correlations with geometric characteristics like steep downgrade slopes and curve segments. Results from the models will shed lights on future applications of weather warning systems to improve traffic safety.