scholarly journals Random-Parameter Multivariate Negative Binomial Regression for Modeling Impacts of Contributing Factors on the Crash Frequency by Crash Types

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Chenzhu Wang ◽  
Fei Chen ◽  
Jianchuan Cheng ◽  
Wu Bo ◽  
Ping Zhang ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Unobserved Heterogeneity ◽  
Random Parameter ◽  
Traffic Volume ◽  
Crash Risk ◽  
Operating Speed ◽  
Contributing Factors ◽  
Road Geometry ◽  
Elasticity Effects

Highways provide the basis for safe and efficient driving. Road geometry plays a critical role in dynamic driving systems. Contributing factors such as plane, longitudinal alignment, and traffic volume, as well as drivers’ sight characteristics, determine the safe operating speed of cars and trucks. In turn, the operating speed influences the frequency and type of crashes on the highways. Methods. Independent negative binomial and Poisson models are considered as the base approaches to modeling in this study. However, random-parameter models reduce unobserved heterogeneity and obtain higher dimensions. Therefore, we propose the random-parameter multivariate negative binomial (RPMNB) model to analyze the influence of the traffic, speed, road geometry, and sight characteristics on the rear-end, bumping-guardrail, other, noncasualty, and casualty crashes. Subsequently, we compute the goodness-of-fit and predictive measures to confirm the superiority of the proposed model. Finally, we also calculate the elasticity effects to augment the comparison. Results. Among the significant variables, black spots, average annual daily traffic volume (AADT), operating speed of cars, speed difference of cars, and length of the present plane curve positively influence the crash risk, whereas the speed difference of trucks, length of the longitudinal slope corresponding to the minimum grade, and stopping sight distance negatively influence the crash risk. Based on the results, several practical and efficient measures can be taken to promote safety during the road design and operating processes. Moreover, the goodness-of-fit and predictive measures clearly highlight the greater performance of the RPMNB model compared to standard models. The elasticity effects across all the models show comparable performance with the RPMNB model. Thus, the RPMNB model reduces the unobserved heterogeneity and yields better performance in terms of precision, with more consistent explanatory power compared to the traditional models.

Factors Affecting Driver Injury Severity in the Wrong-Way Crash: Accounting for Potential Heterogeneity in Means and Variances of Random Parameters

2021 ◽  
pp. 036119812110098
Author(s):  
Miao Yu ◽  
Jinxing Shen ◽  
Changxi Ma
Keyword(s):  
High Speed ◽  
Injury Severity ◽  
Unobserved Heterogeneity ◽  
Research Effort ◽  
Random Parameter ◽  
Policy Implications ◽  
Contributing Factors ◽  
Severe Injuries ◽  
Data Set ◽  
Severity Levels

Because of the high percentage of fatalities and severe injuries in wrong-way driving (WWD) crashes, numerous studies have focused on identifying contributing factors to the occurrence of WWD crashes. However, a limited number of research effort has investigated the factors associated with driver injury-severity in WWD crashes. This study intends to bridge the gap using a random parameter logit model with heterogeneity in means and variances approach that can account for the unobserved heterogeneity in the data set. Police-reported crash data collected from 2014 to 2017 in North Carolina are used. Four injury-severity levels are defined: fatal injury, severe injury, possible injury, and no injury. Explanatory variables, including driver characteristics, roadway characteristics, environmental characteristics, and crash characteristics, are used. Estimation results demonstrate that factors, including the involvement of alcohol, rural area, principal arterial, high speed limit (>60 mph), dark-lighted conditions, run-off-road collision, and head-on collision, significantly increase the severity levels in WWD crashes. Several policy implications are designed and recommended based on findings.

scholarly journals Development of Accident Frequency Models with Random Parameters on Interstate Roadway Segments with and without Lighting Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Minho Park ◽  
Dongmin Lee
Keyword(s):  
Traffic Accidents ◽  
Negative Binomial ◽  
Unobserved Heterogeneity ◽  
Random Parameter ◽  
Random Parameters ◽  
Factors Affecting ◽  
Interstate Highways ◽  
Estimated Parameters ◽  
Fixed Parameter ◽  
Lighting Systems

This study explored factors affecting traffic accidents in roadway segments with and without lighting systems using a random parameter negative binomial model. This study sought to make up for a shortcoming of the fixed parameter model that constrained the estimated parameters to be fixed across observations, by applying random parameters that can take into account unobserved heterogeneity. Three variables had a random parameter among nine significant variables in segments with lighting systems, while seven of the eleven significant variables in a segment without a lighting system had random parameters. The different influence of interstate highway geometrics on vehicle crashes with and without lighting systems found through this study considering unobserved heterogeneity may hopefully help reduce accident frequencies and consider installation of lighting systems on interstate highways in the future.

scholarly journals Distinguishing between Rural and Urban Road Segment Traffic Safety Based on Zero-Inflated Negative Binomial Regression Models

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Xuedong Yan ◽  
Bin Wang ◽  
Meiwu An ◽  
Cuiping Zhang
Keyword(s):  
Regression Models ◽  
Negative Binomial ◽  
Traffic Volume ◽  
Road Segment ◽  
Crash Risk ◽  
Segment Length ◽  
Crash Frequency ◽  
Urban Road ◽  
Fatal Crash ◽  
Rural And Urban

In this study, the traffic crash rate, total crash frequency, and injury and fatal crash frequency were taken into consideration for distinguishing between rural and urban road segment safety. The GIS-based crash data during four and half years in Pikes Peak Area, US were applied for the analyses. The comparative statistical results show that the crash rates in rural segments are consistently lower than urban segments. Further, the regression results based on Zero-Inflated Negative Binomial (ZINB) regression models indicate that the urban areas have a higher crash risk in terms of both total crash frequency and injury and fatal crash frequency, compared to rural areas. Additionally, it is found that crash frequencies increase as traffic volume and segment length increase, though the higher traffic volume lower the likelihood of severe crash occurrence; compared to 2-lane roads, the 4-lane roads have lower crash frequencies but have a higher probability of severe crash occurrence; and better road facilities with higher free flow speed can benefit from high standard design feature thus resulting in a lower total crash frequency, but they cannot mitigate the severe crash risk.

scholarly journals Exploring Unobserved Heterogeneity in Cyclists’ Occupying Motorized Vehicle Lane Behaviors at Different Bike Facility Configurations

2022 ◽  
Vol 19 (2) ◽  
pp. 792
Author(s):  
Lei Zhang ◽  
Shengrui Zhang ◽  
Bei Zhou ◽  
Yan Huang ◽  
Dan Zhao ◽  
...  
Keyword(s):  
Road Traffic ◽  
Unobserved Heterogeneity ◽  
Random Parameter ◽  
Contributing Factors ◽  
Time Intervals ◽  
Recording Time ◽  
Heterogeneous Effects ◽  
Lane Width ◽  
Random Parameter Logit ◽  
Working Day

Cyclists occupying motorized vehicle lanes disrupt road traffic order and increase collisions. Exploring the contributing factors could help develop countermeasures to regulate such behaviors. The purpose of this study is to explore the intrinsic features influencing the behavior of cyclists in occupying motorized vehicle lanes at different bicycle facilities. We investigated a total of 34,631 cycling behavior samples in the urban area of Pingdingshan, China. A Bayesian random parameter logit model was used to account for the unobserved heterogeneous effects. The experimental results of all bike facilities demonstrate that the bike type, dividing strip type, bike lane width, temporary on-street parking, and whether it is a working day significantly affect cyclists’ occupying motorized vehicle lane behaviors. Factors associated with unobserved heterogeneity are age, barriers dividing strip, vehicle lane numbers, bike volume, vehicle volume, and daily recording time intervals. Comparing the estimated model of five type bike lane facilities across different dividing strips, we find that cyclists have a significantly different occupying probability and the heterogeneity factors of the various bike facilities also have their focus. When the non-motorized road conditions become more open, the cyclist behavior becomes more random and the heterogeneity factors become broader.

Analysis of Rural Interstate Fatality Rates in Consideration of Recent Increases in Maximum Statutory Speed Limits

2019 ◽  
Vol 2673 (11) ◽  
pp. 48-58
Author(s):  
Jacob Warner ◽  
Hitesh Chawla ◽  
Chao Zhou ◽  
Peter T. Savolainen
Keyword(s):  
Traffic Safety ◽  
Negative Binomial ◽  
Unobserved Heterogeneity ◽  
State Level ◽  
Random Parameter ◽  
Maximum Speed ◽  
Speed Limit ◽  
Speed Limits ◽  
Fatal Crashes ◽  
Significant Research

The relationship between traffic safety and speed limits has been an area of significant research. Since the repeal of the National Maximum Speed Law in 1995, states have full autonomy in establishing maximum statutory speed limits. Since 2001, at least 25 states have increased their maximum limits to speeds as high as 85 mph. This study examines changes in rural interstate fatalities from 2001 to 2016 in consideration of such increases. Speed limit policy data include the maximum speed limit for each state–year combination, as well as the proportion of rural interstate mileage posted at each speed limit in each state. Random parameter negative binomial models are estimated to control for unobserved heterogeneity, as well as time-invariant effects unique to each state. The results show that increasing the mileage of rural interstates posted at 70, 75, or 80 mph by 1% is associated with fatality increases of 0.2%, 0.5%, and 0.6%, respectively. These increases are more pronounced than when considering only the maximum statutory limits in each state. The study also examines the influence between these higher limits and the frequency of fatal crashes involving speeding and driver distraction. At the highest limits of 75 and 80 mph, the increases among these subsets of crashes are greater than the increases in total fatalities. Ultimately, this study provides important empirical evidence in support of continuing speed limit policy discussions, in addition to identifying salient analytical concerns that should be considered as a part of longitudinal analyses of state-level fatality data.

scholarly journals A comparison of zero-inflated and hurdle models for modeling zero-inflated count data

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Cindy Xin Feng
Keyword(s):  
Health Services ◽  
Count Data ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Simulation Studies ◽  
Final Choice ◽  
Hurdle Models ◽  
Count Distribution ◽  
Careful Assessment

AbstractCounts data with excessive zeros are frequently encountered in practice. For example, the number of health services visits often includes many zeros representing the patients with no utilization during a follow-up time. A common feature of this type of data is that the count measure tends to have excessive zero beyond a common count distribution can accommodate, such as Poisson or negative binomial. Zero-inflated or hurdle models are often used to fit such data. Despite the increasing popularity of ZI and hurdle models, there is still a lack of investigation of the fundamental differences between these two types of models. In this article, we reviewed the zero-inflated and hurdle models and highlighted their differences in terms of their data generating processes. We also conducted simulation studies to evaluate the performances of both types of models. The final choice of regression model should be made after a careful assessment of goodness of fit and should be tailored to a particular data in question.

Does Displaying Safety Messages on Dynamic Message Signs have Measurable Impacts on Crash Risk?

2021 ◽  
pp. 036119812110444
Author(s):  
Megat-Usamah Megat-Johari ◽  
Nusayba Megat-Johari ◽  
Peter T. Savolainen ◽  
Timothy J. Gates ◽  
Eva Kassens-Noor
Keyword(s):  
Negative Binomial ◽  
Driver Behavior ◽  
Field Research ◽  
Crash Risk ◽  
Traffic Crashes ◽  
Crash Data ◽  
Safety Issues ◽  
Dynamic Message Signs ◽  
Safety Message ◽  
Message Signs

Transportation agencies have increasingly been using dynamic message signs (DMS) to communicate safety messages in an effort to both increase awareness of important safety issues and to influence driver behavior. Despite their widespread use, evaluations as to potential impacts on driver behavior, and the resultant impacts on traffic crashes, have been very limited. This study addresses this gap in the extant literature and assesses the relationship between traffic crashes and the frequency with which various types of safety messages are displayed. Safety message data were collected from a total of 202 DMS on freeways across the state of Michigan between 2014 and 2018. These data were integrated with traffic volume, roadway geometry, and crash data for segments that were located downstream of each DMS. A series of random parameters negative binomial models were estimated to examine total, speeding-related, and nighttime crashes based on historical messaging data while controlling for other site-specific factors. The results did not show any significant differences with respect to total crashes. Marginal declines in nighttime crashes were observed at locations with more frequent messages related to impaired driving, though these differences were also not statistically significant. Finally, speeding-related crashes were significantly less frequent near DMS that showed higher numbers of messages related to speeding or tailgating. Important issues are highlighted with respect to methodological concerns that arise in the analysis of such data. Field research is warranted to investigate potential impacts on driving behavior at the level of individual drivers.

Safety Performance Functions for Rural Two-Lane County Road Segments

2018 ◽  
Vol 2672 (52) ◽  
pp. 226-237 ◽  
Author(s):  
Steven Y. Stapleton ◽  
Anthony J. Ingle ◽  
Meghna Chakraborty ◽  
Timothy J. Gates ◽  
Peter T. Savolainen
Keyword(s):  
Negative Binomial ◽  
Unobserved Heterogeneity ◽  
Strong Association ◽  
Random Effect ◽  
Safety Performance ◽  
Federal Aid ◽  
Rural County ◽  
Design Standards ◽  
Safety Performance Functions ◽  
Lane County

Safety performance functions (SPFs) were developed for rural two-lane county roadway segments in Michigan. Five years of crash data (2011 to 2015) were analyzed for greater than 6,500 mi of rural county roadways, covering 29 of Michigan’s 83 counties and representing all regions of the state. Three separate models were developed to estimate annual deer-excluded total and injury crashes on rural county roadways: 1) paved federal-aid segments, 2) paved non-federal-aid segments, and 3) paved and gravel non-federal-aid segments with fewer than 400 vpd. To account for the unobserved heterogeneity associated with differing county design standards, mixed effects negative binomial models with a county-specific random effect were utilized. Not surprisingly, the county segment SPFs generally differed from traditional models generated using data from state-maintained roadways. County federal-aid roadways general showed greater crash occurrence than county non-federal-aid roadways, the Highway Safety Manual (HSM) two-lane rural roadways model, and rural state highways in Michigan. County non-federal-aid paved roadways showed crash occurrence rates that were remarkably similar to the HSM base rural two-lane roadway model, whereas gravel roadways showed greater crash occurrence rates. The presence of horizontal curves with design speeds below 55 mph had a strong association with the occurrence of total and injury crashes across all county road classes. Increasing driveway density was also found to be associated with increased crash occurrence. However, lane width, roadway surface width, and paved shoulder width had little to no impact on total or injury crashes.

scholarly journals On hypergeometric generalized negative binomial distribution

2002 ◽  
Vol 29 (12) ◽  
pp. 727-736 ◽  
Author(s):  
M. E. Ghitany ◽  
S. A. Al-Awadhi ◽  
S. L. Kalla
Keyword(s):  
Recurrence Relation ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Field Data ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Generalized Negative Binomial Distribution ◽  
The Right ◽  
Three Term Recurrence Relation

It is shown that the hypergeometric generalized negative binomial distribution has moments of all positive orders, is overdispersed, skewed to the right, and leptokurtic. Also, a three-term recurrence relation for computing probabilities from the considered distribution is given. Application of the distribution to entomological field data is given and its goodness-of-fit is demonstrated.

scholarly journals Maximum Product of Spacing Parameter Estimation of Gompertz Rayleigh Distribution and Application to Rainfall Datasets

2021 ◽  
pp. 41-59
Author(s):  
Hussein Ahmad Abdulsalam ◽  
Sule Omeiza Bashiru ◽  
Alhaji Modu Isa ◽  
Yunusa Adavi Ojirobe
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Rainfall Data ◽  
Parameter Estimates ◽  
Data Sets ◽  
Unknown Parameters ◽  
Exponentiated Weibull ◽  
Integrated Hazard

Gompertz Rayleigh (GomR) distribution was introduced in an earlier study with few statistical properties derived and parameters estimated using only the most common traditional method, Maximum Likelihood Estimation (MLE). This paper aimed at deriving more statistical properties of the GomR distribution, estimating the three unknown parameters via a competitive method, Maximum Product of Spacing (MPS) and evaluating goodness of fit using rainfall data sets from Nigeria, Malaysia and Argentina. Properties of statistical distributions including distribution of smallest and largest order statistics, cumulative or integrated hazard function, odds function, rth non-central moments, moment generating function, mean, variance and entropy measures for GomR distribution were explicitly derived. The fitted data sets reveal the flexibility of GomR distribution over other distributions been compared with. Simulation study was used to evaluate the consistency, accuracy and unbiasedness of the GomR distribution parameter estimates obtained from the method of MPS. The study found that GomR distribution could not provide a better fit for Argentine rainfall data but it was the best distribution for the rainfall data sets from Nigeria and Malaysia in comparison with the distributions; Generalized Weibull Rayleigh (GWR), Exponentiated Weibull Rayleigh (EWR), Type (II) Topp Leone Generalized Inverse Rayleigh (TIITLGIR), Kumarawamy Exponential Inverse Raylrigh (KEIR), Negative Binomial Marshall-Olkin Rayleigh (NBMOR) and Exponentiated Weibull (EW). Furthermore, the estimates from MPSE were consistent as the sample size increases but not as efficient as those from MLE.

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