Empirical Bayes method in the study of traffic safety via heterogeneous negative multinomial model

In the study of traffic safety, expected crash frequencies across sites are generally estimated via the negative binomial model, assuming time invariant safety. Since the time invariant safety assumption may be invalid, Hauer (1997) proposed a modified empirical Bayes (EB) method. Despite the modification, no attempts have been made to examine the generalisable form of the marginal distribution resulting from the modified EB framework. Because the hyper-parameters needed to apply the modified EB method are not readily available, an assessment is lacking on how accurately the modified EB method estimates safety in the presence of the time variant safety and regression-to-the-mean (RTM) effects. This study derives the closed form marginal distribution, and reveals that the marginal distribution in the modified EB method is equivalent to the negative multinomial (NM) distribution, which is essentially the same as the likelihood function used in the random effects Poisson model. As a result, this study shows that the gamma posterior distribution from the multivariate Poisson-gamma mixture can be estimated using the NM model or the random effects Poisson model. This study also shows that the estimation errors from the modified EB method are systematically smaller than those from the comparison group method by simultaneously accounting for the RTM and time variant safety effects. Hence, the modified EB method via the NM model is a generalisable method for estimating safety in the presence of the time variant safety and the RTM effects.

Forecasting crashes at the planning level: Simultaneous negative binomial crash model applied in Tucson, Arizona

At least two important transportation planning activities rely on planning-level crash prediction models. One is motivated by the Transportation Equity Act for the 21st Century, which requires departments of transportation and metropolitan planning organizations to consider safety explicitly in the transportation planning process. The second could arise from a need for state agencies to establish incentive programs to reduce injuries and save lives. Both applications require a forecast of safety for a future period. Planning-level crash prediction models for the Tucson, Arizona, metropolitan region are presented to demonstrate the feasibility of such models. Data were separated into fatal, injury, and property-damage crashes. To accommodate overdispersion in the data, negative binomial regression models were applied. To accommodate the simultaneity of fatality and injury crash outcomes, simultaneous estimation of the models was conducted. All models produce crash forecasts at the traffic analysis zone level. Statistically significant (p-values < 0.05) and theoretically meaningful variables for the fatal crash model included population density, persons 17 years old or younger as a percentage of the total population, and intersection density. Significant variables for the injury and property-damage crash models were population density, number of employees, intersections density, percentage of miles of principal arterial, percentage of miles of minor arterials, and percentage of miles of urban collectors. Among several conclusions it is suggested that planning-level safety models are feasible and may play a role in future planning activities. However, caution must be exercised with such models.

Modeling random effect and excess zeros in road traffic accident prediction

Poisson distribution has often been used for count like accident data. Negative Binomial (NB) distribution has been adopted in the count data to take care of the over-dispersion problem. However, Poisson and NB distributions are incapable of taking into account some unobserved heterogeneities due to spatial and temporal effects of accident data. To overcome this problem, Random Effect models have been developed. Again another challenge with existing traffic accident prediction models is the distribution of excess zero accident observations in some accident data. Although Zero-Inflated Poisson (ZIP) model is capable of handling the dual-state system in accident data with excess zero observations, it does not accommodate the within-location correlation and between-location correlation heterogeneities which are the basic motivations for the need of the Random Effect models. This paper proposes an effective way of fitting ZIP model with location specific random effects and for model calibration and assessment the Bayesian analysis is recommended.

L’internationalisation des jeunes entreprises de hautes technologies : Le rôle des compétences internationales des fondateurs [The internationalization of new technology based firms : the role of the international skills of founding teams]

Extending recent research on the importance of specific resources and skills for the internationalization of start-ups, this article tests a negative binomial model on a sample of 520 recently created high technology firms from the UK and Germany. The results show that previous international experience of entrepreneurs facilitates the rapid penetration of foreign markets, especially when the company features a clear and deliberate strategic intent of internationalization from the outset. This research provides one of the first empirical studies linking the influence of entrepreneurial teams to a high probability of success in the internationalization of high-technology ventures.

Sampling stored-product insect pests : a comparison of four statistical sampling models for probability of pest detection

Background: Developing sampling strategies to target biological pests such as insects in stored grain is inherently difficult owing to species biology and behavioural characteristics. The design of robust sampling programmes should be based on an underlying statistical distribution that is sufficiently flexible to capture variations in the spatial distribution of the target species. Results: Comparisons are made of the accuracy of four probability-of-detection sampling models - the negative binomial model,1 the Poisson model,1 the double logarithmic model2 and the compound model3 - for detection of insects over a broad range of insect densities. Although the double log and negative binomial models performed well under specific conditions, it is shown that, of the four models examined, the compound model performed the best over a broad range of insect spatial distributions and densities. In particular, this model predicted well the number of samples required when insect density was high and clumped within experimental storages. Conclusions: This paper reinforces the need for effective sampling programs designed to detect insects over a broad range of spatial distributions. The compound model is robust over a broad range of insect densities and leads to substantial improvement in detection probabilities within highly variable systems such as grain storage.

Investigation of pedestrian crashes on two-way two-lane rural roads in Ethiopia

Understanding pedestrian crash causes and contributing factors in developing countries is critically important as they account for about 55% of all traffic crashes. Not surprisingly, considerable attention in the literature has been paid to road traffic crash prediction models and methodologies in developing countries of late. Despite this interest, there are significant challenges confronting safety managers in developing countries. For example, in spite of the prominence of pedestrian crashes occurring on two-way two-lane rural roads, it has proven difficult to develop pedestrian crash prediction models due to a lack of both traffic and pedestrian exposure data. This general lack of available data has further hampered identification of pedestrian crash causes and subsequent estimation of pedestrian safety performance functions. The challenges are similar across developing nations, where little is known about the relationship between pedestrian crashes, traffic flow, and road environment variables on rural two-way roads, and where unique predictor variables may be needed to capture the unique crash risk circumstances. This paper describes pedestrian crash safety performance functions for two-way two-lane rural roads in Ethiopia as a function of traffic flow, pedestrian flows, and road geometry characteristics. In particular, random parameter negative binomial model was used to investigate pedestrian crashes. The models and their interpretations make important contributions to road crash analysis and prevention in developing countries. They also assist in the identification of the contributing factors to pedestrian crashes, with the intent to identify potential design and operational improvements.

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.

Visual impairment, postural stability and falls among older adults with glaucoma

Purpose: To investigate the impact of glaucomatous visual impairment on postural sway and falls among older adults.Methods: The sample comprised 72 community-dwelling older adults with open-angle glaucoma, aged 74.0 5.8 years (range 62 to 90 years). Measures of visual function included binocular visual acuity (high-contrast), binocular contrast sensitivity (Pelli- Robson) and binocular visual fields (merged monocular HFA 24-2 SITA-Std). Postural stability was assessed under four conditions: eyes open and closed, on a firm and on a foam surface. Falls were monitored for six months with prospective falls diaries. Regression models, adjusting for age and gender, examined the association between vision measures and postural stability (linear regression) and the number of falls (negative binomial regression). Results: Greater visual field loss was significantly associated with poorer postural stability with eyes open, both on firm (r = 0.34, p < 0.01) and foam (r = 0.45, p < 0.001) surfaces. Eighteen (25 per cent) participants experienced at least one fall: 12 (17 per cent) participants fell only once and six (eight per cent) participants fell two or more times (up to five falls). Visual field loss was significantly associated with falling; the rate of falls doubled for every 10 dB reduction in field sensitivity (rate ratio = 1.08, 95% CI = 1.02–1.13). Importantly, in a model comprising upper and lower field sensitivity, only lower field loss was significantly associated with the number of falls (rate ratio = 1.17, 95% CI = 1.04–1.33). Conclusions: Binocular visual field loss was significantly associated with postural instability and falls among older adults with glaucoma. These findings provide valuable directions for developing falls risk assessment and falls prevention strategies for this population.

Important omitted spatial variables in safety models: Understanding contributing crash causes at intersections

Advances in safety research—trying to improve the collective understanding of motor vehicle crash causation—rests upon the pursuit of numerous lines of inquiry. The research community has focused on analytical methods development (negative binomial specifications, simultaneous equations, etc.), on better experimental designs (before-after studies, comparison sites, etc.), on improving exposure measures, and on model specification improvements (additive terms, non-linear relations, etc.). One might think of different lines of inquiry in terms of ‘low lying fruit’—areas of inquiry that might provide significant improvements in understanding crash causation. It is the contention of this research that omitted variable bias caused by the exclusion of important variables is an important line of inquiry in safety research. In particular, spatially related variables are often difficult to collect and omitted from crash models—but offer significant ability to better understand contributing factors to crashes. This study—believed to represent a unique contribution to the safety literature—develops and examines the role of a sizeable set of spatial variables in intersection crash occurrence. In addition to commonly considered traffic and geometric variables, examined spatial factors include local influences of weather, sun glare, proximity to drinking establishments, and proximity to schools. The results indicate that inclusion of these factors results in significant improvement in model explanatory power, and the results also generally agree with expectation. The research illuminates the importance of spatial variables in safety research and also the negative consequences of their omissions.

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

Modeling crash outcome probabilities at rural intersections: Application of hierarchical binomial logistic models

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.

Further notes on the application of zero-inflated models in highway safety

The intent of this note is to succinctly articulate additional points that were not provided in the original paper (Lord et al., 2005) and to help clarify a collective reluctance to adopt zero-inflated (ZI) models for modeling highway safety data. A dialogue on this important issue, just one of many important safety modeling issues, is healthy discourse on the path towards improved safety modeling. This note first provides a summary of prior findings and conclusions of the original paper. It then presents two critical and relevant issues: the maximizing statistical fit fallacy and logic problems with the ZI model in highway safety modeling. Finally, we provide brief conclusions.

Identifying large truck hot spots using crash counts and PDOEs

Large trucks are involved in a disproportionately small fraction of the total crashes but a disproportionately large fraction of fatal crashes. Large truck crashes often result in significant congestion due to their large physical dimensions and from difficulties in clearing crash scenes. Consequently, preventing large truck crashes is critical to improving highway safety and operations. This study identifies high risk sites (hot spots) for large truck crashes in Arizona and examines potential risk factors related to the design and operation of the high risk sites. High risk sites were identified using both state of the practice methods (accident reduction potential using negative binomial regression with long crash histories) and a newly proposed method using Property Damage Only Equivalents (PDOE). The hot spots identified via the count model generally exhibited low fatalities and major injuries but large minor injuries and PDOs, while the opposite trend was observed using the PDOE methodology. The hot spots based on the count model exhibited large AADTs, whereas those based on the PDOE showed relatively small AADTs but large fractions of trucks and high posted speed limits. Documented site investigations of hot spots revealed numerous potential risk factors, including weaving activities near freeway junctions and ramps, absence of acceleration lanes near on-ramps, small shoulders to accommodate large trucks, narrow lane widths, inadequate signage, and poor lighting conditions within a tunnel.

Inferior field loss increases rate of falls in older adults with glaucoma

PURPOSE: To examine the visual predictors of falls and injurious falls among older adults with glaucoma. METHODS: Prospective falls data were collected for 71 community-dwelling adults with primary open-angle glaucoma, mean age 73.9 ± 5.7 years, for one year using monthly falls diaries. Baseline assessment of central visual function included high-contrast visual acuity and Pelli-Robson contrast sensitivity. Binocular integrated visual fields were derived from monocular Humphrey Field Analyser plots. Rate ratios (RR) for falls and injurious falls with 95% confidence intervals (CIs) were based on negative binomial regression models. RESULTS: During the one year follow-up, 31 (44%) participants experienced at least one fall and 22 (31%) experienced falls that resulted in an injury. Greater visual impairment was associated with increased falls rate, independent of age and gender. In a multivariate model, more extensive field loss in the inferior region was associated with higher rate of falls (RR 1.57, 95%CI 1.06, 2.32) and falls with injury (RR 1.80, 95%CI 1.12, 2.98), adjusted for all other vision measures and potential confounding factors. Visual acuity, contrast sensitivity, and superior field loss were not associated with the rate of falls; topical beta-blocker use was also not associated with increased falls risk. CONCLUSIONS: Falls are common among older adults with glaucoma and occur more frequently in those with greater visual impairment, particularly in the inferior field region. This finding highlights the importance of the inferior visual field region in falls risk and assists in identifying older adults with glaucoma at risk of future falls, for whom potential interventions should be targeted. KEY WORDS: glaucoma, visual field, visual impairment, falls, injury