Markov switching negative binomial models: An application to vehicle accident frequencies

In this paper, two-state Markov switching models are proposed to study accident frequencies. These models assume that there are two unobserved states of roadway safety, and that roadway entities (roadway segments) can switch between these states over time. The states are distinct, in the sense that in the different states accident frequencies are generated by separate counting processes (by separate Poisson or negative binomial processes). To demonstrate the applicability of the approach presented herein, two-state Markov switching negative binomial models are estimated using five-year accident frequencies on Indiana interstate highway segments. Bayesian inference methods and Markov Chain Monte Carlo (MCMC) simulations are used for model estimation. The estimated Markov switching models result in a superior statistical fit relative to the standard (single-state) negative binomial model. It is found that the more frequent state is safer and it is correlated with better weather conditions. The less frequent state is found to be less safe and to be correlated with adverse weather conditions.     

A multinomial logit analysis of risk factors influencing road traffic injury severities in the Erzurum and Kars Provinces of Turkey

A retrospective cross-sectional study is conducted analysing 11,771 traffic accidents reported by the police between January 2008 and December 2013 which are classified into three injury severity categories: fatal, injury, and no injury. Based on this classification, a multinomial logit analysis is performed to determine the risk factors affecting the severity of traffic injuries. The estimation results reveal that the following factors increase the probability of fatal injuries: drivers over the age of 65; primary-educated drivers; single-vehicle accidents; accidents occurring on state routes, highways or provincial roads; and the presence of pedestrian crosswalks. The results also indicate that accidents involving cars or private vehicles or those occurring during the evening peak, under clear weather conditions, on local city streets or in the presence of traffic lights decrease the probability of fatal injuries. This study comprises the most comprehensive database ever created for a Turkish sample. This study is also the first attempt to use an unordered response model to determine risk factors influencing the severity of traffic injuries in Turkey.     

Zero-state Markov switching count-data models: An empirical assessment

In this study, a two-state Markov switching count-data model is proposed as an alternative to zero-inflated models to account for the preponderance of zeros sometimes observed in transportation count data, such as the number of accidents occurring on a roadway segment over some period of time. For this accident-frequency case, zero-inflated models assume the existence of two states: one of the states is a zero-accident count state, which has accident probabilities that are so low that they cannot be statistically distinguished from zero, and the other state is a normal-count state, in which counts can be non-negative integers that are generated by some counting process, for example, a Poisson or negative binomial. While zero-inflated models have come under some criticism with regard to accident-frequency applications - one fact is undeniable - in many applications they provide a statistically superior fit to the data. The Markov switching approach we propose seeks to overcome some of the criticism associated with the zero-accident state of the zero-inflated model by allowing individual roadway segments to switch between zero and normal-count states over time. An important advantage of this Markov switching approach is that it allows for the direct statistical estimation of the specific roadway-segment state (i.e., zero-accident or normal-count state) whereas traditional zero-inflated models do not. To demonstrate the applicability of this approach, a two-state Markov switching negative binomial model (estimated with Bayesian inference) and standard zero-inflated negative binomial models are estimated using five-year accident frequencies on Indiana interstate highway segments. It is shown that the Markov switching model is a viable alternative and results in a superior statistical fit relative to the zero-inflated models.     

Highway accident severities and the mixed logit model: an exploratory empirical analysis

Many transportation agencies use accident frequencies, and statistical models of accidents frequencies, as a basis for prioritizing highway safety improvements. However, the use of accident severities in safety programming has been often been limited to the locational assessment of accident fatalities, with little or no emphasis being placed on the full severity distribution of accidents (property damage only, possible injury, injury)-which is needed to fully assess the benefits of competing safety-improvement projects. In this paper we demonstrate a modeling approach that can be used to better understand the injury-severity distributions of accidents on highway segments, and the effect that traffic, highway and weather characteristics have on these distributions. The approach we use allows for the possibility that estimated model parameters can vary randomly across roadway segments to account for unobserved effects potentially relating to roadway characteristics, environmental factors, and driver behavior. Using highway-injury data from Washington State, a mixed (random parameters) logit model is estimated. Estimation findings indicate that volume-related variables such as average daily traffic per lane, average daily truck traffic, truck percentage, interchanges per mile and weather effects such as snowfall are best modeled as random-parameters-while roadway characteristics such as the number of horizontal curves, number of grade breaks per mile and pavement friction are best modeled as fixed parameters. Our results show that the mixed logit model has considerable promise as a methodological tool in highway safety programming.     

A multinomial logit model-Bayesian network hybrid approach for driver injury severity analyses in rear-end crashes

Rear-end crash is one of the most common types of traffic crashes in the U.S. A good understanding of its characteristics and contributing factors is of practical importance. Previously, both multinomial Logit models and Bayesian network methods have been used in crash modeling and analysis, respectively, although each of them has its own application restrictions and limitations. In this study, a hybrid approach is developed to combine multinomial logit models and Bayesian network methods for comprehensively analyzing driver injury severities in rear-end crashes based on state-wide crash data collected in New Mexico from 2010 to 2011. A multinomial logit model is developed to investigate and identify significant contributing factors for rear-end crash driver injury severities classified into three categories: no injury, injury, and fatality. Then, the identified significant factors are utilized to establish a Bayesian network to explicitly formulate statistical associations between injury severity outcomes and explanatory attributes, including driver behavior, demographic features, vehicle factors, geometric and environmental characteristics, etc. The test results demonstrate that the proposed hybrid approach performs reasonably well. The Bayesian network reference analyses indicate that the factors including truck-involvement, inferior lighting conditions, windy weather conditions, the number of vehicles involved, etc. could significantly increase driver injury severities in rear-end crashes. The developed methodology and estimation results provide insights for developing effective countermeasures to reduce rear-end crash injury severities and improve traffic system safety performance.     

An empirical analysis of farm vehicle crash injury severities on Iowa's public road system

Farm vehicle crashes are a major safety concern for farmers as well as all other users of the public road system in agricultural states. Using data on farm vehicle crashes that occurred on Iowa's public roads between 2004 and 2006, we estimate a multinomial logit model to identify crash-, farm vehicle-, and driver-specific factors that determine farm vehicle crash injury severity outcomes. Estimation findings indicate that there are crash patterns (rear-end manner of collision; single-vehicle crash; farm vehicle crossed the centerline or median) and conditions (obstructed vision and crash in rural area; dry road, dark lighting, speed limit 55 mph or higher, and harvesting season), as well as farm vehicle and driver-contributing characteristics (old farm vehicle, young farm vehicle driver), where targeted intervention can help reduce the severity of crash outcomes. Determining these contributing factors and their effect is the first step to identifying countermeasures and safety strategies in a bid to improve transportation safety for all users on the public road system in Iowa as well as other agricultural states.     

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 mixed logit analysis of two-vehicle crash severities involving a motorcycle

Using motorcycle crash data for Iowa from 2001 to 2008, this paper estimates a mixed logit model to investigate the factors that affect crash severity outcomes in a collision between a motorcycle and another vehicle. These include crash-specific factors (such as manner of collision, motorcycle rider and non-motorcycle driver and vehicle actions), roadway and environmental conditions, location and time, motorcycle rider and non-motorcycle driver and vehicle attributes. The methodological approach allows the parameters to vary across observations as opposed to a single parameter representing all observations. Our results showed non-uniform effects of rear-end collisions on minor injury crashes, as well as of the roadway speed limit greater or equal to 55 mph, the type of area (urban), the riding season (summer) and motorcyclist's gender on low severity crashes. We also found significant effects of the roadway surface condition, clear vision (not obscured by moving vehicles, trees, buildings, or other), light conditions, speed limit, and helmet use on severe injury outcomes.     

Differences in rural and urban driver-injury severities in accidents involving large-trucks: an exploratory analysis

This study explores the differences between urban and rural driver injuries (both passenger-vehicle and large-truck driver injuries) in accidents that involve large trucks (in excess of 10,000 pounds). Using 4 years of California accident data, and considering four driver-injury severity categories (no injury, complaint of pain, visible injury, and severe/fatal injury), a multinomial logit analysis of the data was conducted. Significant differences with respect to various risk factors including driver, vehicle, environmental, road geometry and traffic characteristics were found to exist between urban and rural models. For example, in rural accidents involving tractor-trailer combinations, the probability of drivers' injuries being severe/fatal increased about 26% relative to accidents involving single-unit trucks. In urban areas, this same probability increased nearly 700%. In accidents where alcohol or drug use was identified as being the primary cause of the accident, the probability of severe/fatal injury increased roughly 250% percent in rural areas and nearly 800% in urban areas. While many of the same variables were found to be significant in both rural and urban models (although often with quite different impact), there were 13 variables that significantly influenced driver-injury severity in rural but not urban areas, and 17 variables that significantly influenced driver-injury severity in urban but not rural areas. We speculate that the significant differences between rural and urban injury severities may be at least partially attributable to the different perceptual, cognitive and response demands placed on drivers in rural versus urban areas.     

Differences in male and female injury severities in sport-utility vehicle, minivan, pickup and passenger car accidents

This research explores differences in injury severity between male and female drivers in single and two-vehicle accidents involving passenger cars, pickups, sport-utility vehicles (SUVs), and minivans. Separate multivariate multinomial logit models of injury severity are estimated for male and female drivers. The models predict the probability of four injury severity outcomes: no injury (property damage only), possible injury, evident injury, and fatal/disabling injury. The models are conditioned on driver gender and the number and type of vehicles involved in the accident. The conditional structure avoids bias caused by men and women's different reporting rates, choices of vehicle type, and their different rates of participation as drivers, which would affect a joint model of all crashes. We found variables that have opposite effects for the genders, such as striking a barrier or a guardrail, and crashing while starting a vehicle. The results suggest there are important behavioral and physiological differences between male and female drivers that must be explored further and addressed in vehicle and roadway design.     

A flexible brand choice model based on neural net methodology A comparison to the linear utility multinomial logit model and its latent class extension

Brand choice models as a rule have a linear (deterministic) utility function, i.e. they conceive utility as linear combination of predictors like price, sales promotion variables, brand name and other product attributes. To discover nonlinear effects on brands' utilities in a flexible way we specify deterministic utility by means of a certain type of neural net. This feedforward multilayer perceptron is able to approximate any continuous multivariate function and its derivatives with the desired level of precision. In an empirical study the neural net based choice model leads to better out-of-sample results than homogeneous and heterogeneous versions of linear utility MNL models. On the other hand the latent class variant of the linear utility MNL model attains better fit values for estimation data than the neural net model. The neural net approach implies different choice elasticities for most predictors and identifies nonlinear effects (like interaction effects, thresholds, saturation effects). Received: November 3, 2000 / Accepted: March 7, 2002     

Examining driver injury severity outcomes in rural non-interstate roadway crashes using a hierarchical ordered logit model

Rural non-interstate crashes induce a significant amount of severe injuries and fatalities. Examination of such injury patterns and the associated contributing factors is of practical importance. Taking into account the ordinal nature of injury severity levels and the hierarchical feature of crash data, this study employs a hierarchical ordered logit model to examine the significant factors in predicting driver injury severities in rural non-interstate crashes based on two-year New Mexico crash records. Bayesian inference is utilized in model estimation procedure and 95% Bayesian Credible Interval (BCI) is applied to testing variable significance. An ordinary ordered logit model omitting the between-crash variance effect is evaluated as well for model performance comparison. Results indicate that the model employed in this study outperforms ordinary ordered logit model in model fit and parameter estimation. Variables regarding crash features, environment conditions, and driver and vehicle characteristics are found to have significant influence on the predictions of driver injury severities in rural non-interstate crashes. Factors such as road segments far from intersection, wet road surface condition, collision with animals, heavy vehicle drivers, male drivers and driver seatbelt used tend to induce less severe driver injury outcomes than the factors such as multiple-vehicle crashes, severe vehicle damage in a crash, motorcyclists, females, senior drivers, driver with alcohol or drug impairment, and other major collision types. Research limitations regarding crash data and model assumptions are also discussed. Overall, this research provides reasonable results and insight in developing effective road safety measures for crash injury severity reduction and prevention.     

Estimation with the nested logit model: specifications and software particularities

The paper discusses the nested logit model for choices between a set of mutually exclusive alternatives (e.g. brand choice, strategy decisions, modes of transportation, etc.). Due to the ability of the nested logit model to allow and account for similarities between pairs of alternatives, the model has become very popular for the empirical analysis of choice decisions. However the fact that there are two different specifications of the nested logit model (with different outcomes) has not received adequate attention. The utility maximization nested logit (UMNL) model and the non-normalized nested logit (NNNL) model have different properties, influencing the estimation results in a different manner. This paper introduces distinct specifications of the nested logit model and indicates particularities arising from model estimation. The effects of using various software packages on the estimation results of a nested logit model are shown using simulated data sets for an artificial decision situation. Financial support by the German Research Foundation (DFG) through the research project #BO1952/1 and the SFB 649 “Economic Risk” is gratefully acknowledged. The authors would like to thank two anonymous reviewers for their helpful and constructive comments.     

Effects of excessive speeding and falling asleep while driving on crash injury severity in Ethiopia: A generalized ordered logit model analysis

The severity of injury from vehicle crash is a result of a complex interaction of factors related to drivers’ behavior, vehicle characteristics, road geometric and environmental conditions. Knowing to what extent each factor contributes to the severity of an injury is very important. The objective of the study was to assess factors that contribute to crash injury severity in Ethiopia. Data was collected from June 2012 to July 2013 on one of the main and busiest highway of Ethiopia, which extends from the capital Addis Ababa to Hawassa. During the study period a total of 819 road crashes was recorded and investigated by trained crash detectors. A generalized ordered logit/partial proportional odds model was used to examine factors that might influence the severity of crash injury. Model estimation result suggested that, alcohol use (Coef. = 0.5565; p-value = 0.017), falling asleep while driving (Coef. = 1.3102; p-value = 0.000), driving at night time in the absence of street light (Coef. = 0.3920; p-value = 0.033), rainfall (Coef. = 0.9164; p-value = 0.000) and being a minibus or vans (Coef. = 0.5065; p-value = 0.013) were found to be increased crash injury severity. On the other hand, speeding was identified to have varying coefficients for different injury levels, its highest effects on sever and fatal crashes. In this study risky driving behaviors (speeding, alcohol use and sleep/fatigue) were a powerful predictor of crash injury severity. Therefore, better driver licensing and road safety awareness campaign complimented with strict police enforcement can play a pivotal role to improve road safety. Further effort needed as well to monitor speed control strategies like; using the radar control and physical speed restraint measures (i.e., rumble strips).     

A joint-probability approach to crash prediction models

Many road safety researchers have used crash prediction models, such as Poisson and negative binomial regression models, to investigate the associations between crash occurrence and explanatory factors. Typically, they have attempted to separately model the crash frequencies of different severity levels. However, this method may suffer from serious correlations between the model estimates among different levels of crash severity. Despite efforts to improve the statistical fit of crash prediction models by modifying the data structure and model estimation method, little work has addressed the appropriate interpretation of the effects of explanatory factors on crash occurrence among different levels of crash severity. In this paper, a joint probability model is developed to integrate the predictions of both crash occurrence and crash severity into a single framework. For instance, the Markov chain Monte Carlo (MCMC) approach full Bayesian method is applied to estimate the effects of explanatory factors. As an illustration of the appropriateness of the proposed joint probability model, a case study is conducted on crash risk at signalized intersections in Hong Kong. The results of the case study indicate that the proposed model demonstrates a good statistical fit and provides an appropriate analysis of the influences of explanatory factors.     

结构物理参数识别的贝叶斯估计马尔可夫蒙特卡罗方法

从结构动力特征方程出发,以结构主模态参数为观测量,推得结构物理参数线性回归模型。对该模型应用贝叶斯估计理论得到物理参数后验联合分布,再结合马尔可夫蒙特卡罗抽样方法给出各个物理参数的边缘概率分布和最优估计值,而提出了基于结构主模态参数的结构物理参数识别贝叶斯估计马尔可夫蒙特卡罗方法。对五层剪切型结构的数值研究表明,此方法能够利用少数主模态参数给出结构质量和刚度参数的概率分布和最优识别值,而且在主模态参数较准确时识别误差很小。     

A general formulation for transition probabilities of Markov model and the application to fracture of composite materials

A generalized method for formulating unit-jump Markov chain model is presented. This method uses geometric series to determine the transition probabilities instead of using a moment generation function. Recursive equation for the transition probabilities has been derived in terms of the mean values. Present method is also compared by other method for robustness. Application of the unit-jump Markov chain model for characterizing fracture process of composites is described. By introducing a proper scaling factor, the entire probability history of the crack propagation at any loading states can be evaluated by the present model.     

Mechanism of conductance switching: An optical investigation

Electronic conductance switching in devices based on thin films of an organic molecule has been studied. Switching between two conducting states has been induced by voltage pulse, while the states have been probed by optical and electrical measurements simultaneously. In situ optical measurements showed that electroreduction of molecules led to conductance switching and appearance of high-conducting state in the device. We could “write” or “erase” a state by applying electrical pulse and “read” it by measuring electronic absorbance and conductivity. The “write” and “read” processes have been carried out for many cycles to exhibit a correspondence between conductance switching and electrochromism.     

Modeling occupant-level injury severity: An application to large-truck crashes

Most of the injury-severity analyses to date have focused primarily on modeling the most-severe injury of any crash, although a substantial fraction of crashes involve multiple vehicles and multiple persons. In this study, we present an extensive exploratory analysis that highlights that the highest injury severity is not necessarily the comprehensive indicator of the overall severity of any crash. Subsequently, we present a panel, hetroskedastic ordered-probit model to simultaneously analyze the injury severities of all persons involved in a crash. The models are estimated in the context of large-truck crashes. The results indicate strong effects of person-, driver-, vehicle-, and crash-characteristics on the injury severities of persons involved in large-truck crashes. For example, several driver behavior characteristics (such as use of illegal drugs, DUI, and inattention) were found to be statistically significant predictors of injury severity. The availability of airbags and the use of seat-belts are also found to be associated with less-severe injuries to car-drivers and car-passengers in the event of crashes with large trucks. Car drivers’ familiarity with the vehicle and the roadway are also important for both the car drivers and passengers. Finally, the models also indicate the strong presence of intra-vehicle correlations (effect of common vehicle-specific unobserved factors) among the injury propensities of all persons within a vehicle.     

A new belief Markov chain model and its application in inventory prediction

The Markov chain model is widely applied in many fields, especially the field of prediction. The discrete-time Markov chain (DTMC) is a common method for prediction. However, the classical DTMC model has some limitations when the system is complex with uncertain information or state space is not discrete. To address it, a new belief Markov chain (BMC) model combining Dempster-Shafer evidence theory and the DTMC is proposed. In our model, the uncertain data are allowed to be handled in the form of interval number, and the basic probability assignment is generated by an optimisation method based on the distance between interval numbers. The shortcoming of classical DTMC is overcome in the BMC model. Also, it has an efficient ability of dealing with uncertain information, including both the uncertainty of collected data and discerning states. Our model is applied to do the prediction of inventory demand and the result is close to the practical. Also, sensitivity analysis and some comparisons are accomplished to show the effectiveness and rationality of our proposed model.