Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory

There has been considerable research conducted over the last 20 years focused on predicting motor vehicle crashes on transportation facilities. The range of statistical models commonly applied includes binomial, Poisson, Poisson-gamma (or negative binomial), zero-inflated Poisson and negative binomial models (ZIP and ZINB), and multinomial probability models. Given the range of possible modeling approaches and the host of assumptions with each modeling approach, making an intelligent choice for modeling motor vehicle crash data is difficult. There is little discussion in the literature comparing different statistical modeling approaches, identifying which statistical models are most appropriate for modeling crash data, and providing a strong justification from basic crash principles. In the recent literature, it has been suggested that the motor vehicle crash process can successfully be modeled by assuming a dual-state data-generating process, which implies that entities (e.g., intersections, road segments, pedestrian crossings, etc.) exist in one of two states—perfectly safe and unsafe. As a result, the ZIP and ZINB are two models that have been applied to account for the preponderance of “excess” zeros frequently observed in crash count data. The objective of this study is to provide defensible guidance on how to appropriate model crash data. We first examine the motor vehicle crash process using theoretical principles and a basic understanding of the crash process. It is shown that the fundamental crash process follows a Bernoulli trial with unequal probability of independent events, also known as Poisson trials. We examine the evolution of statistical models as they apply to the motor vehicle crash process, and indicate how well they statistically approximate the crash process. We also present the theory behind dual-state process count models, and note why they have become popular for modeling crash data. A simulation experiment is then conducted to demonstrate how crash data give rise to “excess” zeros frequently observed in crash data. It is shown that the Poisson and other mixed probabilistic structures are approximations assumed for modeling the motor vehicle crash process. Furthermore, it is demonstrated that under certain (fairly common) circumstances excess zeros are observed—and that these circumstances arise from low exposure and/or inappropriate selection of time/space scales and not an underlying dual state process. In conclusion, carefully selecting the time/space scales for analysis, including an improved set of explanatory variables and/or unobserved heterogeneity effects in count regression models, or applying small-area statistical methods (observations with low exposure) represent the most defensible modeling approaches for datasets with a preponderance of zeros

Accident prediction model for railway-highway interfaces

Considerable past research has explored relationships between vehicle accidents and geometric design and operation of road sections, but relatively little research has examined factors that contribute to accidents at railway-highway crossings. Between 1998 and 2002 in Korea, about 95% of railway accidents occurred at highway-rail grade crossings, resulting in 402 accidents, of which about 20% resulted in fatalities. These statistics suggest that efforts to reduce crashes at these locations may significantly reduce crash costs. The objective of this paper is to examine factors associated with railroad crossing crashes. Various statistical models are used to examine the relationships between crossing accidents and features of crossings. The paper also compares accident models developed in the United States and the safety effects of crossing elements obtained using Korea data. Crashes were observed to increase with total traffic volume and average daily train volumes. The proximity of crossings to commercial areas and the distance of the train detector from crossings are associated with larger numbers of accidents, as is the time duration between the activation of warning signals and gates. The unique contributions of the paper are the application of the gamma probability model to deal with underdispersion and the insights obtained regarding railroad crossing related vehicle crashes. Considerable past research has explored relationships between vehicle accidents and geometric design and operation of road sections, but relatively little research has examined factors that contribute to accidents at railway-highway crossings. Between 1998 and 2002 in Korea, about 95% of railway accidents occurred at highway-rail grade crossings, resulting in 402 accidents, of which about 20% resulted in fatalities. These statistics suggest that efforts to reduce crashes at these locations may significantly reduce crash costs. The objective of this paper is to examine factors associated with railroad crossing crashes. Various statistical models are used to examine the relationships between crossing accidents and features of crossings. The paper also compares accident models developed in the United States and the safety effects of crossing elements obtained using Korea data. Crashes were observed to increase with total traffic volume and average daily train volumes. The proximity of crossings to commercial areas and the distance of the train detector from crossings are associated with larger numbers of accidents, as is the time duration between the activation of warning signals and gates. The unique contributions of the paper are the application of the gamma probability model to deal with underdispersion and the insights obtained regarding railroad crossing related vehicle crashes.

Governors highway safety associations and transportation planning: Exploratory factor analysis and structural equation modeling

The Intermodal Surface Transportation Efficiency Act (ISTEA) of 1991 mandated the consideration of safety in the regional transportation planning process. As part of National Cooperative Highway Research Program Project 8-44, "Incorporating Safety into the Transportation Planning Process," we conducted a telephone survey to assess safety-related activities and expertise at Governors Highway Safety Associations (GHSAs), and GHSA relationships with metropolitan planning organizations (MPOs) and state departments of transportation (DOTs). The survey results were combined with statewide crash data to enable exploratory modeling of the relationship between GHSA policies and programs and statewide safety. The modeling objective was to illuminate current hurdles to ISTEA implementation, so that appropriate institutional, analytical, and personnel improvements can be made. The study revealed that coordination of transportation safety across DOTs, MPOs, GHSAs, and departments of public safety is generally beneficial to the implementation of safety. In addition, better coordination is characterized by more positive and constructive attitudes toward incorporating safety into planning.

Development of accident prediction models for rural highway intersections

A study was done to develop macrolevel crash prediction models that can be used to understand and identify effective countermeasures for improving signalized highway intersections and multilane stop-controlled highway intersections in rural areas. Poisson and negative binomial regression models were fit to intersection crash data from Georgia, California, and Michigan. To assess the suitability of the models, several goodness-of-fit measures were computed. The statistical models were then used to shed light on the relationships between crash occurrence and traffic and geometric features of the rural signalized intersections. The results revealed that traffic flow variables significantly affected the overall safety performance of the intersections regardless of intersection type and that the geometric features of intersections varied across intersection type and also influenced crash type.

Evaluation of the Scottsdale Loop 101 automated speed enforcement demonstration program

Speeding is recognized as a major contributing factor in traffic crashes. In order to reduce speed-related crashes, the city of Scottsdale, Arizona implemented the first fixed-camera photo speed enforcement program (SEP) on a limited access freeway in the US. The 9-month demonstration program spanning from January 2006 to October 2006 was implemented on a 6.5 mile urban freeway segment of Arizona State Route 101 running through Scottsdale. This paper presents the results of a comprehensive analysis of the impact of the SEP on speeding behavior, crashes, and the economic impact of crashes. The impact on speeding behavior was estimated using generalized least square estimation, in which the observed speeds and the speeding frequencies during the program period were compared to those during other periods. The impact of the SEP on crashes was estimated using 3 evaluation methods: a before-and-after (BA) analysis using a comparison group, a BA analysis with traffic flow correction, and an empirical Bayes BA analysis with time-variant safety. The analysis results reveal that speeding detection frequencies (speeds> or =76 mph) increased by a factor of 10.5 after the SEP was (temporarily) terminated. Average speeds in the enforcement zone were reduced by about 9 mph when the SEP was implemented, after accounting for the influence of traffic flow. All crash types were reduced except rear-end crashes, although the estimated magnitude of impact varies across estimation methods (and their corresponding assumptions). When considering Arizona-specific crash related injury costs, the SEP is estimated to yield about $17 million in annual safety benefits.

Experimental evaluation of hotspot identification methods

Identifying crash “hotspots”, “blackspots”, “sites with promise”, or “high risk” locations is standard practice in departments of transportation throughout the US. The literature is replete with the development and discussion of statistical methods for hotspot identification (HSID). Theoretical derivations and empirical studies have been used to weigh the benefits of various HSID methods; however, a small number of studies have used controlled experiments to systematically assess various methods. Using experimentally derived simulated data—which are argued to be superior to empirical data, three hot spot identification methods observed in practice are evaluated: simple ranking, confidence interval, and Empirical Bayes. Using simulated data, sites with promise are known a priori, in contrast to empirical data where high risk sites are not known for certain. To conduct the evaluation, properties of observed crash data are used to generate simulated crash frequency distributions at hypothetical sites. A variety of factors is manipulated to simulate a host of ‘real world’ conditions. Various levels of confidence are explored, and false positives (identifying a safe site as high risk) and false negatives (identifying a high risk site as safe) are compared across methods. Finally, the effects of crash history duration in the three HSID approaches are assessed. The results illustrate that the Empirical Bayes technique significantly outperforms ranking and confidence interval techniques (with certain caveats). As found by others, false positives and negatives are inversely related. Three years of crash history appears, in general, to provide an appropriate crash history duration.

Bayesian multinomial logit: Theory and route choice example

Statisticians along with other scientists have made significant computational advances that enable the estimation of formerly complex statistical models. The Bayesian inference framework combined with Markov chain Monte Carlo estimation methods such as the Gibbs sampler enable the estimation of discrete choice models such as the multinomial logit (MNL) model. MNL models are frequently applied in transportation research to model choice outcomes such as mode, destination, or route choices or to model categorical outcomes such as crash outcomes. Recent developments allow for the modification of the potentially limiting assumptions of MNL such as the independence from irrelevant alternatives (IIA) property. However, relatively little transportation-related research has focused on Bayesian MNL models, the tractability of which is of great value to researchers and practitioners alike. This paper addresses MNL model specification issues in the Bayesian framework, such as the value of including prior information on parameters, allowing for nonlinear covariate effects, and extensions to random parameter models, so changing the usual limiting IIA assumption. This paper also provides an example that demonstrates, using route-choice data, the considerable potential of the Bayesian MNL approach with many transportation applications. This paper then concludes with a discussion of the pros and cons of this Bayesian approach and identifies when its application is worthwhile

Developing risk assessment tools for fleet settings : where to from here?

The costs of work-related crashes In Australia and overseas, fleet safety or work-related road safety is an issue gaining increased attention from researchers, organisations, road safety practitioners and the general community. This attention is primarily in response to the substantial physical, emotional and economic costs associated with work-related road crashes. The increased risk factors and subsequent costs of work-related driving are also now well documented in the literature. For example, it is noteworthy that research has demonstrated that work-related drivers on average report a higher level of crash involvement compared to personal car drivers (Downs et al., 1999; Kweon and Kockelman, 2003) and in particular within Australia, road crashes are the most common form of work-related fatalities (Haworth et al., 2000).

Assessing wet crashes for the skid resistance management of road assets

Australia, road crash trauma costs the nation A$15 billion annually whilst the US estimates an economic impact of around US$ 230 billion on its network. Worldwide economic cost of road crashes is estimated to be around US$ 518 billion each year. Road accidents occur due to a number of factors including driver behaviour, geometric alignment, vehicle characteristics, environmental impacts, and the type and condition of the road surfacing. Skid resistance is considered one of the most important road surface characteristics because it has a direct effect on traffic safety. In 2005, Austroads (the Association of Australian and New Zealand Road Transport and Traffic Authorities) published a guideline for the management of skid resistance and Queensland Department of Main Roads (QDMR) developed a skid resistance management plan (SRMP). The current QDMR strategy is based on rationale analytical methodology supported by field inspection with related asset management decision tools. The Austroads’s guideline and QDMR's skid resistance management plan have prompted QDMR to review its skid resistance management practice. As a result, a joint research project involving QDMR, Queensland University of Technology (QUT) and the Corporative Research Centre for Integrated Engineering Asset Management (CRC CIEAM) was formed. The research project aims at investigating whether there is significant relationship between road crashes and skid resistance on Queensland’s road networks. If there is, the current skid resistance management practice of QDMR will be reviewed and appropriate skid resistance investigatory levels will be recommended. This paper presents analysis results in assessing the relationship between wet crashes and skid resistance on Queensland roads. Attributes considered in the analysis include surface types, annual average daily traffic (AADT), speed and seal age.

Visual assessment of pedestrian crashes

Of the numerous factors that play a role in fatal pedestrian collisions, the time of day, day of the week, and time of year can be significant determinants. More than 60% of all pedestrian collisions in 2007 occurred at night, despite the presumed decrease in both pedestrian and automobile exposure during the night. Although this trend is partially explained by factors such as fatigue and alcohol consumption, prior analysis of the Fatality Analysis Reporting System database suggests that pedestrian fatalities increase as light decreases after controlling for other factors. This study applies graphical cross-tabulation, a novel visual assessment approach, to explore the relationships among collision variables. The results reveal that twilight and the first hour of darkness typically observe the greatest frequency of pedestrian fatal collisions. These hours are not necessarily the most risky on a per mile travelled basis, however, because pedestrian volumes are often still high. Additional analysis is needed to quantify the extent to which pedestrian exposure (walking/crossing activity) in these time periods plays a role in pedestrian crash involvement. Weekly patterns of pedestrian fatal collisions vary by time of year due to the seasonal changes in sunset time. In December, collisions are concentrated around twilight and the first hour of darkness throughout the week while, in June, collisions are most heavily concentrated around twilight and the first hours of darkness on Friday and Saturday. Friday and Saturday nights in June may be the most dangerous times for pedestrians. Knowing when pedestrian risk is highest is critically important for formulating effective mitigation strategies and for efficiently investing safety funds. This applied visual approach is a helpful tool for researchers intending to communicate with policy-makers and to identify relationships that can then be tested with more sophisticated statistical tools.

Nonprofit organizational and work unit identification and the occupational stress process

Research investigating the transactional approach to the work stressor-employee adjustment relationship has described many negative main effects between perceived stressors in the workplace and employee outcomes. A considerable amount of literature, theoretical and empirical, also describes potential moderators of this relationship. Organizational identification has been established as a significant predictor of employee job-related attitudes. To date, research has neglected investigation of the potential moderating effect of organizational identification in the work stressor-employee adjustment relationship. On the basis of identity, subjective fit and sense of belonging literature it was predicted that higher perceptions of identification at multiple levels of the organization would mitigate the negative effect of work stressors on employee adjustment. It was expected, further, that more proximal, lower order identifications would be more prevalent and potent as buffers of stressors on strain. Predictions were tested with an employee sample from five organizations (N = 267). Hierarchical moderated multiple regression analyses revealed some support for the stress-buffering effects of identification in the prediction of job satisfaction and organizational commitment, particularly for more proximal (i.e., work unit) identification. These positive stress-buffering effects, however, were present for low identifiers in some situations. The present study represents an extension of the application of organizational identity theory by identifying the effects of organizational and workgroup identification on employee outcomes in the nonprofit context. Our findings will contribute to a better understanding of the dynamics in nonprofit organizations and therefore contribute to the development of strategy and interventions to deal with identity-based issues in nonprofits.

Mathematically defined tissue engineering scaffold architectures prepared by stereolithography

The technologies employed for the preparation of conventional tissue engineering scaffolds restrict the materials choice and the extent to which the architecture can be designed. Here we show the versatility of stereolithography with respect to materials and freedom of design. Porous scaffolds are designed with computer software and built with either a poly(d,l-lactide)-based resin or a poly(d,l-lactide-co-ε-caprolactone)-based resin. Characterisation of the scaffolds by micro-computed tomography shows excellent reproduction of the designs. The mechanical properties are evaluated in compression, and show good agreement with finite element predictions. The mechanical properties of scaffolds can be controlled by the combination of material and scaffold pore architecture. The presented technology and materials enable an accurate preparation of tissue engineering scaffolds with a large freedom of design, and properties ranging from rigid and strong to highly flexible and elastic.

Cell invasion with proliferation mechanisms motivated by time-lapse data

Cell invasion involves a population of cells which are motile and proliferative. Traditional discrete models of proliferation involve agents depositing daughter agents on nearest- neighbor lattice sites. Motivated by time-lapse images of cell invasion, we propose and analyze two new discrete proliferation models in the context of an exclusion process with an undirected motility mechanism. These discrete models are related to a family of reaction- diffusion equations and can be used to make predictions over a range of scales appropriate for interpreting experimental data. The new proliferation mechanisms are biologically relevant and mathematically convenient as the continuum-discrete relationship is more robust for the new proliferation mechanisms relative to traditional approaches.

Response of tall buildings with symmetric setbacks under blast loading

This study explores three-dimensional nonlineardynamic responses of typical tall buildings with and without setbacks under blast loading. These 20 storey reinforced concrete buildings have been designed for normal (dead, live and wind)loads. The influence of the setbacks on the lateral load response due to blasts in terms of peak deflections, accelerations, inter-storey drift and bending moments at critical locations (including hinge formation) were investigated. Structural response predictions were performed with a commercially available three-dimensional finite element analysis programme using non-linear direct integration time history analyses. Results obtained for buildings with different setbacks were compared and conclusions made. The comparisons revealed that buildings have setbacks that protect the tower part above the setback level from blast loading show considerably better response in terms of peak displacement and interstorey drift, when compared to buildings without setbacks. Rotational accelerations were found to depend on the periods of the rotational modes. Abrupt changes in moments and shears are experienced near the levels of the setbacks. Typical twenty storey tall buildings with shear walls and frames that are designed for only normaln loads perform reasonably well, without catastrophic collapse, when subjected to a blast that is equivalent to 500 kg TNT at a standoff distance of 10 m.

Driver distractions: Characteristics underlying drivers' risk perceptions

Driver distraction is a research area that continues to receive considerable research interest but the drivers’ perspective is less well documented. The current research focuses on how drivers perceive the risks associated with a range of driver distractions with the aim of identifying features that contribute to their risk perception judgements. Multidimensional scaling analysis was employed to better understand drivers’ risk perceptions for 15 in-vehicle and external distractions. Results identify both salient qualitative characteristics that underpin drivers’ risk perceptions, such as the probability of a crash, as well as identify other features inherent in the distractions that may also contribute to risk perceptions. The implications of the results are discussed for better understanding drivers’ perceptions of distractions and the potential for improving road safety messages related to distracted driving.