Multivariate Poisson-lognormal Regression Research Articles

Do footbridge and underpass improve pedestrian safety? A Hong Kong case study using three-dimensional digital map of pedestrian network

Hong Kong is a compact city with high activity and travel intensity. In the past decades, many footbridges and underpasses were installed to reduce the pedestrian-vehicle conflicts on urban roads. However, it is rare that the effects of configuration of pedestrian network on pedestrian crashes are investigated. In Hong Kong, many footbridges and underpasses are connected to major transport hubs and commercial building development and become parts of giant elevated and underground walkway systems. It is challenging to characterize such a complicated pedestrian network. In this study, a three-dimensional digital map is applied to estimate the connectivity and accessibility of pedestrian network, and measure the relationship between pedestrian network characteristics and pedestrian safety at the macroscopic level. Hence, the effects of footbridge and underpass on pedestrian safety are examined. For example, comprehensive built environment, pedestrian network, traffic, and crash data are aggregated to 379 grids (0.5 km × 0.5 km). Then, multivariate Poisson lognormal regression approach is applied to model fatal and severe injury (FSI) and slight injury pedestrian crashes, with which the effects of unobserved heterogeneity, spatial correlation, and correlation between crash counts are accounted. Results indicate that population density, traffic volume, walking trip, footpath density, node density, number of vertices per footpath segment, bus stop, metro exit, residential area, commercial area, and government and utility area are positively associated with pedestrian crashes. In contrast, average gradient, accessibility of footbridge, accessibility of underpass, and number of crossings per road segment are negatively associated with pedestrian crashes. In other word, pedestrian safety would be improved when footbridge and underpass are more accessible. Findings have implications for the design and planning of pedestrian network to promote walkability and improve pedestrian safety.

Effects of road network characteristics on bicycle safety: A multivariate Poisson-lognormal model

• Multivariate Poisson-lognormal model is applied to model the bicycle crash of different types. • Multivariate correlation between counts of bicycle-bicycle and bicycle-vehicle crashes is accounted. • Population socio-economics, land use, road density, railway station, and intersection density affect the risk of bicycle-related crashes. • Network accessibility is positively associated with bicycle-vehicle and bicycle-bicycle crashes. • Network connectivity is positively associated with bicycle-bicycle crash only. Although cycling has benefits to environment and physical health, bicyclists are vulnerable road users. Prior studies have identified the environment, traffic and road user factors that affect the risk of bicycle-related crashes. However, it is rare that difference in their effects on the risk amongst different bicycle crash types is investigated. For instance, there is possible correlation between counts of different crash types. In this study, multivariate Poisson-lognormal regression method is applied to examine the relationship between bicycle crash frequencies and possible explanatory factors, with which the correlation between bicycle-vehicle and bicycle-bicycle crashes is considered, using the crash data from London in 2018 and 2019. In addition, effects of road network characteristics on bicycle crash frequencies are also considered. Results indicate that proposed multivariate Poisson-lognormal model outperforms conventional univariate Poisson-lognormal models, in term of the metrics like deviance information criterion (DIC). In addition, factors including population socio-economics, land use, and road network characteristics that affect bicycle crash risk are identified. For instance, effects of traffic flow, residential area, network connectivity, and intersection density on the crash counts are different between bicycle-vehicle and bicycle-bicycle crashes. Findings are useful for the implementation of remedial measures that can improve overall bicycle safety in the long run.

Calibrating safety-based design charts for horizontal curves using system reliability analysis and multivariate models

The majority of previous studies on reliability-based highway design focussed on assessing the risk associated with only one mode of non-compliance (i.e. insufficient sight distance on horizontal curves using 2 D sight distance calculations). Only a handful number of studies established a link between risk levels and collisions. This paper calibrates safety-based design charts for horizontal curves considering a system reliability analysis (i.e., multi-mode) where the non-compliance could result from limited sight distance and vehicle skidding. The paper first utilised LiDAR data to collect curve attributes and assess the Available Sight Distance in a 3 D environment on 244 horizontal curves in Alberta, Canada. Monte Carlo Simulation was then used to calculate the associated risk levels, and full-Bayes multivariate Poisson lognormal regression was utilised to develop statistically significant safety performance functions that relate risk levels to collisions. Safety-based design charts were calibrated to relate curve attributes to risk levels and collisions. The calibrated charts showed the importance of using multi-mode reliability analysis. An example of using the calibrated charts in estimating the expected safety benefits of geometric improvements was introduced. The developed charts can offer designers a tool to estimate the safety consequences of design alternatives and aid the decision-making process of rehabilitation projects.

Bayesian analysis of multivariate crash counts using copulas

There has been growing interest in jointly modeling correlated multivariate crash counts in road safety research over the past decade. To assess the effects of roadway characteristics or environmental factors on crash counts by severity level or by collision type, various models including multivariate Poisson regression models, multivariate negative binomial regression models, and multivariate Poisson-Lognormal regression models have been suggested. We introduce more general copula-based multivariate count regression models with correlated random effects within a Bayesian framework. Our models incorporate the dependence among the multivariate crash counts by modeling multivariate random effects using copulas. Copulas provide a flexible way to construct valid multivariate distributions by decomposing any joint distribution into a copula and the marginal distributions. Overdispersion as well as general correlation structures including both positive and negative correlations in multivariate crash counts can easily be accounted for by this approach. Our copular-based models can also encompass previously suggested multivariate count regression models including multivariate Poisson-Gamma mixture models and multivariate Poisson-Lognormal regression models. The proposed method is illustrated with crash count data of five different severity levels collected from 451 three-leg unsignalized intersections in California.

Impacts of speed variations on freeway crashes by severity and vehicle type

Speed variations are identified as potentially important predictors of freeway crash rates; however, their impacts on crashes are not entirely known. Existing findings tend to be inconsistent possibly because of the different definitions for speed variations, different crash type consideration or different modelling and data aggregation approaches. This study explores the relationships of speed variations with crashes on a freeway section in the UK. Crashes split by vehicle type (heavy and light vehicles) and by severity mode (killed/serious injury and slight injury crashes) are aggregated based on the similarities of the conditions just before their occurrence (condition-based approach) and modelled using Multivariate Poisson lognormal regression. The models control for speed variations along with other traffic and weather variables as well as their interactions. Speed variations are expressed as two separate variables namely the standard deviations of speed within the same lane and between-lanes over a five-minute interval. The results, similar for all crash types (by coefficient significance and sign), suggest that crash rates increase as the within lane speed variations raise, especially at higher traffic volumes. Higher speeds coupled with greater volume and high between-lanes speed variation also increase crash likelihood. Overall, the results suggest that specific combinations of traffic characteristics increase the likelihood of crash occurrences rather than their individual effects. Identification of these specific crash prone conditions could improve our understanding of crash risk and would support the development of more efficient safety countermeasures.

Risk analysis of animal–vehicle crashes: a hierarchical Bayesian approach to spatial modelling

ABSTRACTDriving along any rural road within Western Australia involves some level of uncertainty about encountering an animal whether it is wildlife, farm stock or domestic. This level of uncertainty can vary depending on factors such as the surrounding land use, water source, geometry of the road, speed limits and signage. This paper aims to model the risk of animal–vehicle crashes (AVCs) on a segmented highway. A hierarchical Bayesian model involving multivariate Poisson lognormal regression is used in establishing the relationship between AVCs and the contributing factors. Findings of this study show that farming on both sides of a road, a mixture of farming and forest roadside vegetation and roadside vegetation have significant positive effect on AVCs, while speed limits and horizontal curves indicate a negative effect. AVCs consist of both spatial- and segment-specific contributions, even though the spatial random error does not dominate model variability. Segment 15 is identified as the highest risk segment and its nearby segments also exhibit high risk.

Predicting the safety impact of a speed limit increase using condition-based multivariate Poisson lognormal regression

ABSTRACTSpeed limit changes are considered to lead to proportional changes in the number and severity of crashes. To predict the impact of a speed limit alteration, it is necessary to define a relationship between crashes and speed on a road network. This paper examines the relationship of crashes with speed, as well as with other traffic and geometric variables, on the UK motorways in order to estimate the impact of a potential speed limit increase from 70 to 80 mph on traffic safety. Full Bayesian multivariate Poisson lognormal regression models are applied to a data set aggregated using the condition-based approach for crashes by vehicle (i.e. single vehicle and multiple vehicle) and severity (i.e. fatal or serious and slight). The results show that single-vehicle crashes of all severities and fatal or serious injury crashes involving multiple vehicles increase at higher speed conditions and particularly when these are combined with lower volumes. Slight injury multiple-vehicle crashes are found not to be related to high speeds, but instead with congested traffic. Using the speed elasticity values derived from the models, the predicted annual increase in crashes after a speed limit increase on the UK motorway is found to be 6.2–12.1% for fatal or serious injury crashes and 1.3–2.7% for slight injury, or else up to 167 more crashes.

Re-visiting crash–speed relationships: A new perspective in crash modelling

Although speed is considered to be one of the main crash contributory factors, research findings are inconsistent. Independent of the robustness of their statistical approaches, crash frequency models typically employ crash data that are aggregated using spatial criteria (e.g., crash counts by link termed as a link-based approach). In this approach, the variability in crashes between links is explained by highly aggregated average measures that may be inappropriate, especially for time-varying variables such as speed and volume. This paper re-examines crash–speed relationships by creating a new crash data aggregation approach that enables improved representation of the road conditions just before crash occurrences. Crashes are aggregated according to the similarity of their pre-crash traffic and geometric conditions, forming an alternative crash count dataset termed as a condition-based approach. Crash–speed relationships are separately developed and compared for both approaches by employing the annual crashes that occurred on the Strategic Road Network of England in 2012. The datasets are modelled by injury severity using multivariate Poisson lognormal regression, with multivariate spatial effects for the link-based model, using a full Bayesian inference approach. The results of the condition-based approach show that high speeds trigger crash frequency. The outcome of the link-based model is the opposite; suggesting that the speed–crash relationship is negative regardless of crash severity. The differences between the results imply that data aggregation is a crucial, yet so far overlooked, methodological element of crash data analyses that may have direct impact on the modelling outcomes.

Multivariate Full Bayesian Hot Spot Identification and Ranking

The present study introduces a new technique for multivariate identification and ranking of hot spots based on the Mahalanobis distance. This approach aims to extend the univariate potential for safety improvement to cases in which multiple response variables are modeled jointly. Because the literature shows that ranking techniques based on Bayesian methods are superior to those that rely simply on the observed collision count, the proposed method was developed in a full Bayesian (FB) context. The new technique involves the following steps: (a) applying multivariate Poisson–lognormal regression models to the data by means of the FB method, (b) using the estimates of the Poisson posterior means for each site to compute the multivariate (Mahalanobis) distance from what is the normal Poisson mean for similar sites, and (c) preparing an ordered list of potentially hazardous sites. This method was applied to a sample of 173 signalized intersections in the city of Vancouver, British Columbia, Canada, for the years 2008 to 2012. The study also examines the consistency of the technique itself by analyzing the mathematical intersection of ranked sites identified in subsequent time periods. Finally, the consistency of the multivariate FB ranking was assessed against the independent (separate) univariate one that is still dominant in road safety evaluations.

Multivariate Poisson-Lognormal Regression for Crash Prediction of Different Types on Freeways Diverge Areas

The primary objective of this study was to develop a multivariate Poisson-lognormal regression model (MVPLN) to evaluate the effects of contributing factors to crash frequency and to identify the correlations among different types. Crash data were collected at 282 exit-ramps on freeways in Florida, US.The Markov chain Monte Carlo (MCMC) method was used to get the solutions of the MVPLN model.The effects of crash-related factors of different types were explored in the MVPLN model considering the correlation structure.It was found thatmainline lane number was the contributing factor for both single-lane and two-lane exit ramp.

A multivariate Poisson-lognormal regression model for prediction of crash counts by severity, using Bayesian methods

Numerous efforts have been devoted to investigating crash occurrence as related to roadway design features, environmental factors and traffic conditions. However, most of the research has relied on univariate count models; that is, traffic crash counts at different levels of severity are estimated separately, which may neglect shared information in unobserved error terms, reduce efficiency in parameter estimates, and lead to potential biases in sample databases. This paper offers a multivariate Poisson-lognormal (MVPLN) specification that simultaneously models crash counts by injury severity. The MVPLN specification allows for a more general correlation structure as well as overdispersion. This approach addresses several questions that are difficult to answer when estimating crash counts separately. Thanks to recent advances in crash modeling and Bayesian statistics, parameter estimation is done within the Bayesian paradigm, using a Gibbs Sampler and the Metropolis–Hastings (M–H) algorithms for crashes on Washington State rural two-lane highways. Estimation results from the MVPLN approach show statistically significant correlations between crash counts at different levels of injury severity. The non-zero diagonal elements suggest overdispersion in crash counts at all levels of severity. The results lend themselves to several recommendations for highway safety treatments and design policies. For example, wide lanes and shoulders are key for reducing crash frequencies, as are longer vertical curves.

Multivariate Poisson-Lognormal Models for Jointly Modeling Crash Frequency by Severity

A new multivariate approach is introduced for jointly modeling data on crash counts by severity on the basis of multivariate Poisson-lognormal models. Although the data on crash frequency by severity are multivariate in nature, they have often been analyzed by modeling each severity level separately, without taking into account correlations that exist among different severity levels. The new multivariate Poisson-lognormal regression approach can cope with both overdispersion and a fully general correlation structure in the data, as opposed to the recently suggested multivariate Poisson regression approach, which allows for neither overdispersion nor a general correlation structure in the data. The new method is applied to the multivariate crash counts obtained from intersections in California for 10 years. The results show promise toward the goal of obtaining more accurate estimates by accounting for correlations in the multivariate crash counts and overdispersion.