Evaluating alternate discrete choice frameworks for modeling ordinal discrete variables

There is considerable debate on the appropriate discrete choice framework for examining injury severity. Researchers in the safety field have employed ordered and unordered frameworks for examining the various factors influencing injury severity. The objective of the current study is to investigate the performance of the ordered and unordered response frameworks at a fundamental level. Towards this end, we undertake a comparison of the alternative frameworks by estimating ordered and unordered response models using data generated through ordered, unordered data and a combination of ordered and unordered data generation processes. We also examine the influence of aggregate sample shares on the appropriateness of the modeling framework. Rather than be limited by the aggregate sample shares in an empirical dataset, simulation allows us to explore the influence of a broad spectrum of sample shares on the performance of ordered and unordered frameworks. We also extend the data generation process based analysis to under reported data and compare the performance of the ordered and unordered response frameworks. Finally, based on these simulation exercises, we provide a discussion of the merits of the different approaches. The results clearly highlight the emergence of the generalized ordered logit model as a true equivalent ordered response model to the multinomial logit model for ordinal discrete variables.     

Analysis of driver and passenger crash injury severity using partial proportional odds models

The question of whether crash injury severity should be modeled using an ordinal response model or a non-ordered (multinomial) response model is persistent in traffic safety engineering. This paper proposes the use of the partial proportional odds (PPO) model as a statistical modeling technique that both bridges the gap between ordered and non-ordered response modeling, and avoids violating the key assumptions in the behavior of crash severity inherent in these two alternatives. The partial proportional odds model is a type of logistic regression that allows certain individual predictor variables to ignore the proportional odds assumption which normally forces predictor variables to affect each level of the response variable with the same magnitude, while other predictor variables retain this proportional odds assumption. This research looks at the effectiveness of this PPO technique in predicting vehicular crash severities on Connecticut state roads using data from 1995 to 2009. The PPO model is compared to ordinal and multinomial response models on the basis of adequacy of model fit, significance of covariates, and out-of-sample prediction accuracy. The results of this study show that the PPO model has adequate fit and performs best overall in terms of covariate significance and holdout prediction accuracy. Combined with the ability to accurately represent the theoretical process of crash injury severity prediction, this makes the PPO technique a favorable approach for crash injury severity modeling by adequately modeling and predicting the ordinal nature of the crash severity process and addressing the non-proportional contributions of some covariates.     

Partial proportional odds model—An alternate choice for analyzing pedestrian crash injury severities

The conventional methods for crash injury severity analyses include either treating the severity data as ordered (e.g. ordered logit/probit models) or non-ordered (e.g. multinomial models). The ordered models require the data to meet proportional odds assumption, according to which the predictors can only have the same effect on different levels of the dependent variable, which is often not the case with crash injury severities. On the other hand, non-ordered analyses completely ignore the inherent hierarchical nature of crash injury severities. Therefore, treating the crash severity data as either ordered or non-ordered results in violating some of the key principles. To address these concerns, this paper explores the application of a partial proportional odds (PPO) model to bridge the gap between ordered and non-ordered severity modeling frameworks. The PPO model allows the covariates that meet the proportional odds assumption to affect different crash severity levels with the same magnitude; whereas the covariates that do not meet the proportional odds assumption can have different effects on different severity levels. This study is based on a five-year (2008–2012) national pedestrian safety dataset for Switzerland. A comparison between the application of PPO models, ordered logit models, and multinomial logit models for pedestrian injury severity evaluation is also included here. The study shows that PPO models outperform the other models considered based on different evaluation criteria. Hence, it is a viable method for analyzing pedestrian crash injury severities.     

A kinetic energy model of two-vehicle crash injury severity

An important part of any model of vehicle crashes is the development of a procedure to estimate crash injury severity. After reviewing existing models of crash severity, this paper outlines the development of a modelling approach aimed at measuring the injury severity of people in two-vehicle road crashes. This model can be incorporated into a discrete event traffic simulation model, using simulation model outputs as its input. The model can then serve as an integral part of a simulation model estimating the crash potential of components of the traffic system. The model is developed using Newtonian Mechanics and Generalised Linear Regression. The factors contributing to the speed change (ΔV_s) of a subject vehicle are identified using the law of conservation of momentum. A Log-Gamma regression model is fitted to measure speed change (ΔV_s) of the subject vehicle based on the identified crash characteristics. The kinetic energy applied to the subject vehicle is calculated by the model, which in turn uses a Log-Gamma Regression Model to estimate the Injury Severity Score of the crash from the calculated kinetic energy, crash impact type, presence of airbag and/or seat belt and occupant age.     

Using support vector machine models for crash injury severity analysis

The study presented in this paper investigated the possibility of using support vector machine (SVM) models for crash injury severity analysis. Based on crash data collected at 326 freeway diverge areas, a SVM model was developed for predicting the injury severity associated with individual crashes. An ordered probit (OP) model was also developed using the same dataset. The research team compared the performance of the SVM model and the OP model. It was found that the SVM model produced better prediction performance for crash injury severity than did the OP model. The percent of correct prediction for the SVM model was found to be 48.8%, which was higher than that produced by the OP model (44.0%). Even though the SVM model may suffer from the multi-class classification problem, it still provides better prediction results for small proportion injury severities than the OP model does.     

Discrete distributions when modeling the disability severity score of motor victims

Many European countries apply score systems to evaluate the disability severity of non-fatal motor victims under the law of third-party liability. The score is a non-negative integer with an upper bound at 100 that increases with severity. It may be automatically converted into financial terms and thus also reflects the compensation cost for disability. In this paper, standard and zero-altered discrete regression models are applied to model the disability severity score of victims. An application using data from Spain is provided in which the hurdle-Negative Binomial regression was the preferred method. The effects of victims’ characteristics, type of road user and recovery duration are examined. The results suggest that the expected permanent disability severity is higher for older women with long recovery periods. The results provide traffic decision makers with a model to quantify the compensation cost savings due to disability severity reductions.     

Evaluating the road safety effects of a fuel cost increase measure by means of zonal crash prediction modeling

Travel demand management (TDM) consists of a variety of policy measures that affect the transportation system's effectiveness by changing travel behavior. The primary objective to implement such TDM strategies is not to improve traffic safety, although their impact on traffic safety should not be neglected. The main purpose of this study is to evaluate the traffic safety impact of conducting a fuel-cost increase scenario (i.e. increasing the fuel price by 20%) in Flanders, Belgium. Since TDM strategies are usually conducted at an aggregate level, crash prediction models (CPMs) should also be developed at a geographically aggregated level. Therefore zonal crash prediction models (ZCPMs) are considered to present the association between observed crashes in each zone and a set of predictor variables. To this end, an activity-based transportation model framework is applied to produce exposure metrics which will be used in prediction models. This allows us to conduct a more detailed and reliable assessment while TDM strategies are inherently modeled in the activity-based models unlike traditional models in which the impact of TDM strategies are assumed. The crash data used in this study consist of fatal and injury crashes observed between 2004 and 2007. The network and socio-demographic variables are also collected from other sources. In this study, different ZCPMs are developed to predict the number of injury crashes (NOCs) (disaggregated by different severity levels and crash types) for both the null and the fuel-cost increase scenario. The results show a considerable traffic safety benefit of conducting the fuel-cost increase scenario apart from its impact on the reduction of the total vehicle kilometers traveled (VKT). A 20% increase in fuel price is predicted to reduce the annual VKT by 5.02 billion (11.57% of the total annual VKT in Flanders), which causes the total NOCs to decline by 2.83%.     

A stable and optimized neural network model for crash injury severity prediction

The study proposes a convex combination (CC) algorithm to fast and stably train a neural network (NN) model for crash injury severity prediction, and a modified NN pruning for function approximation (N2PFA) algorithm to optimize the network structure. To demonstrate the proposed approaches and to compare them with the NN trained by traditional back-propagation (BP) algorithm and an ordered logit (OL) model, a two-vehicle crash dataset in 2006 provided by the Florida Department of Highway Safety and Motor Vehicles (DHSMV) was employed. According to the results, the CC algorithm outperforms the BP algorithm both in convergence ability and training speed. Compared with a fully connected NN, the optimized NN contains much less network nodes and achieves comparable classification accuracy. Both of them have better fitting and predicting performance than the OL model, which again demonstrates the NN’s superiority over statistical models for predicting crash injury severity. The pruned input nodes also justify the ability of the structure optimization method for identifying the factors irrelevant to crash-injury outcomes. A sensitivity analysis of the optimized NN is further conducted to determine the explanatory variables’ impact on each injury severity outcome. While most of the results conform to the coefficient estimation in the OL model and previous studies, some variables are found to have non-linear relationships with injury severity, which further verifies the strength of the proposed method.     

Relating crash frequency and severity: Evaluating the effectiveness of shoulder rumble strips on reducing fatal and major injury crashes

To approach the goal of “Toward Zero Deaths,” there is a need to develop an analysis paradigm to better understand the effects of a countermeasure on reducing the number of severe crashes. One of the goals in traffic safety research is to search for an effective treatment to reduce fatal and major injury crashes, referred to as severe crashes. To achieve this goal, the selection of promising countermeasures is of utmost importance, and relies on the effectiveness of candidate countermeasures in reducing severe crashes. Although it is important to precisely evaluate the effectiveness of candidate countermeasures in reducing the number of severe crashes at a site, the current state-of-the-practice often leads to biased estimates. While there have been a few advanced statistical models developed to mitigate the problem in practice, these models are computationally difficult to estimate because severe crashes are dispersed spatially and temporally, and cannot be integrated into the Highway Safety Manual framework, which develops a series of safety performance functions and crash modification factors to predict the number of crashes. Crash severity outcomes are generally integrated into the Highway Safety Manual using deterministic distributions rather than statistical models. Accounting for the variability in crash severity as a function geometric design, traffic flow, and other roadway and roadside features is afforded by estimating statistical models. Therefore, there is a need to develop a new analysis paradigm to resolve the limitations in the current Highway Safety Manual methods. We propose an approach which decomposes the severe crash frequency into a function of the change in the total number of crashes and the probability of a crash becoming a severe crash before and after a countermeasure is implemented. We tested this approach by evaluating the effectiveness of shoulder rumble strips on reducing the number of severe crashes. A total of 310 segments that have had shoulder rumble strips installed during 2002–2009 are included in the analysis. It was found that shoulder rumble strips reduce the total number of crashes, but have no statistically significant effect on reducing the probability of a severe crash outcome.     

一阶超对策模型中结局偏好认知信息集结的模式识别法

针对一类一阶n人超对策模型．提出了一种结局偏好认知信息的集鲒方法．首先通过对单一局中人中不同专家给出的对其他局中人结局偏好信息的不同认知进行关联分析，确定出专家的权重评价值．进而运用模糊模式识别原理，通过建立一个非线性规划模型，给出了一种新的超对策结局偏好认知信息的集结方法．最后。用一个数值例子对文中所提方法进行了说明．     

The discrete method of separation of variables for composite material problems

In this paper, we propose the discrete method of separation of variables for the numerical solutions of the composite material problems on a polygon. After a suitable transformation of coordinates, the original boundary value problem is reduced to a discontinuous coefficients problem on a semi-infinite strip. Then we get the semi-discrete approximation of the discontinuous coefficients problem which is equivalent to a boundary value problem of a system of ordinary differential equations (O.D.E's) with constant coefficients. After solving the boundary value problem of the system by a direct method, then the semi-discrete approximation of the original problem is obtained. Especially we can see that the semi-discrete approximation in form of separable variables naturally possesses the singularity of the original problem. Finally, the numerical examples show that our method is feasible and very effective for solving composite material problems numerically.     

A latent class modeling approach for identifying vehicle driver injury severity factors at highway-railway crossings

In this paper, we aim to identify the different factors that influence injury severity of highway vehicle occupants, in particular drivers, involved in a vehicle-train collision at highway-railway grade crossings. The commonly used approach to modeling vehicle occupant injury severity is the traditional ordered response model that assumes the effect of various exogenous factors on injury severity to be constant across all accidents. The current research effort attempts to address this issue by applying an innovative latent segmentation based ordered logit model to evaluate the effects of various factors on the injury severity of vehicle drivers. In this model, the highway-railway crossings are assigned probabilistically to different segments based on their attributes with a separate injury severity component for each segment. The validity and strength of the formulated collision consequence model is tested using the US Federal Railroad Administration database which includes inventory data of all the railroad crossings in the US and collision data at these highway railway crossings from 1997 to 2006. The model estimation results clearly highlight the existence of risk segmentation within the affected grade crossing population by the presence of active warning devices, presence of permanent structure near the crossing and roadway type. The key factors influencing injury severity include driver age, time of the accident, presence of snow and/or rain, vehicle role in the crash and motorist action prior to the crash.     

基于离散元法的双组份复合涂料搅拌螺杆参数优化

为了提高双组份复合涂料的混合均匀度,对搅拌螺杆的参数进行优化。以混合销钉式搅拌螺杆为对象,建立其三维模型后导入EDEM软件,然后基于离散元法对双组份复合涂料在该搅拌螺杆中的搅拌过程进行仿真分析,研究了螺杆的转速、螺距和长径比对混合均匀度的影响。最后通过单轴压缩实验对螺杆参数优化后的搅拌效果进行了对比验证。结果表明：螺杆转速、螺距和长径比分别通过改变颗粒抛撒程度、螺旋叶片间隙和螺杆长度来影响复合涂料的混合均匀度;稳定出料后,螺杆转速为200 r/min、螺距为80 mm、长径比为5.57∶1时的搅拌效果最佳;实验验证了利用优化后搅拌螺杆搅拌时复合涂料的力学性能优于手工搅拌时的。研究结果可为自动化搅拌螺杆的结构设计和参数优化提供理论依据。     

Refined triangular discrete Kirchhoff plate element for thin plate bending,vibration and buckling analysis

A refined triangular discrete Kirchhoff thin plate bending element RDKT which can be used to improve the original triangular discrete Kirchhoff thin plate bending element DKT is presented. In order to improve the accuracy of the analysis a simple explicit expression of a refined constant strain matrix with an adjustable constant can be introduced into its formulation. The new element displacement function can be used to formulate a mass matrix called combined mass matrix for calculation of the natural frequency and in the same way a combined geometric stiffness matrix can be obtained for buckling analysis. Numerical examples are presented to show that the present methods indeed, can improve the accuracy of thin plate bending, vibration and buckling analysis. © 1998 John Wiley & Sons, Ltd.