Modeling school bus seat belt usage: Nested and mixed logit approaches

School bus seat belt usage has been of great interest to the school transportation community. Understanding factors that influence students’ decisions about wearing seat belts or not is important in determining the most cost-effective ways to improve belt usage rate, and thus the seat belt safety benefits. This paper presents a rigorous empirical analysis on data from Alabama School Bus Pilot Project using discrete choice modeling framework. In order to collect relevant information on individual student-trips, a new data collection protocol is adopted. Three choice alternatives are considered in the study: wearing, not wearing, and improperly wearing seat belts. A student's choice probabilities of these alternatives are modeled as functions of the student's characteristics and trip attributes. The coefficients of the variables in the functions are estimated first using standard multinomial logit model. Moreover, to account for potential correlations among the three choice alternatives and individual-level preference and response heterogeneity among users, nested and mixed logit models are employed in the investigation. Eight significant influence factors are identified by the final models. Their relative impacts are also quantified. The factors include age, gender and the home county of a student, a student's trip length, time of day, seat location, presence and active involvement of bus aide, and two levels of bus driver involvement. The impact of the seat location on students’ seat belt usage is revealed for the first time by this study. Both hypotheses that some of the choice alternatives are correlated and that individual-level heterogeneity exists are tested statistically significant. In view of this, the nested and the mixed logit model are recommended over the standard multinomial logit model to describe and predict students’ seat belt usage behaviors. The final nested logit model uncovers a correlation between improper wearing and not wearing, indicating there are some unknown or unobserved contributing factors that are common to these two choices. In the final random-parameter mixed logit model, individual preference heterogeneity is captured by random coefficients of county variables. Individual response heterogeneity is reflected in the random effect of a driver's remarks on students’ seat belt usage. Both recommended models are helpful in predicting seat belt usage rate quantitatively for given circumstances, and will provide valuable insights in practice of school transportation management.     

Random Effects Model for Attribute Gauge R&R

In some cases of attribute gauge, there is a continuous variable (reference value) behind the attribute‐type decision. In the recent literature, a fixed effect logit model is used for gauge study. In this paper, the random effect concept is applied to the problem. Two different alternatives are studied, the random intercept and the random intercept–random slope model. The random effect concept enables us to characterise the operators in general and to estimate the conditional probabilities of misclassification. Different estimation methods are proposed and compared through simulation. The theoretically less correct, but computationally much simpler estimation method using a fixed effect model proved to be only a slightly less effective than the estimation using a mixed effect model. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of injury severity of large truck crashes in work zones

Work zones are critical parts of the transportation infrastructure renewal process consisting of rehabilitation of roadways, maintenance, and utility work. Given the specific nature of a work zone (complex arrangements of traffic control devices and signs, narrow lanes, duration) a number of crashes occur with varying severities involving different vehicle sizes. In this paper we attempt to investigate the causal factors contributing to injury severity of large truck crashes in work zones. Considering the discrete nature of injury severity categories, a number of comparable econometric models were developed including multinomial logit (MNL), nested logit (NL), ordered logit (ORL), and generalized ordered logit (GORL) models. The MNL and NL models belong to the class of unordered discrete choice models and do not recognize the intrinsic ordinal nature of the injury severity data. The ORL and GORL models, on the other hand, belong to the ordered response framework that was specifically developed for handling ordinal dependent variables. Past literature did not find conclusive evidence in support of either framework. This study compared these alternate modeling frameworks for analyzing injury severity of crashes involving large trucks in work zones. The model estimation was undertaken by compiling a database of crashes that (1) involved large trucks and (2) occurred in work zones in the past 10 years in Minnesota. Empirical findings indicate that the GORL model provided superior data fit as compared to all the other models. Also, elasticity analysis was undertaken to quantify the magnitude of impact of different factors on work zone safety and the results of this analysis suggest the factors that increase the risk propensity of sustaining severe crashes in a work zone include crashes in the daytime, no control of access, higher speed limits, and crashes occurring on rural principal arterials.     

Analysis of crash severities using nested logit model—Accounting for the underreporting of crashes

Recent studies in the area of highway safety have demonstrated the usefulness of logit models for modeling crash injury severities. Use of these models enables one to identify and quantify the effects of factors that contribute to certain levels of severity. Most often, these models are estimated assuming equal probability of the occurrence for each injury severity level in the data. However, traffic crash data are generally characterized by underreporting, especially when crashes result in lower injury severity. Thus, the sample used for an analysis is often outcome-based, which can result in a biased estimation of model parameters. This is more of a problem when a nested logit model specification is used instead of a multinomial logit model and when true shares of the outcomes-injury severity levels in the population are not known (which is almost always the case). This study demonstrates an application of a recently proposed weighted conditional maximum likelihood estimator in tackling the problem of underreporting of crashes when using a nested logit model for crash severity analyses.     

Analysis of driver injury severity in single-vehicle crashes on rural and urban roadways

This study analyzes driver injury severities for single-vehicle crashes occurring in rural and urban areas using data collected in New Mexico from 2010 to 2011. Nested logit models and mixed logit models are developed in order to account for the correlation between severity categories (No injury, Possible injury, Visible injury, Incapacitating injury and fatality) and individual heterogeneity among drivers. Various factors, such as crash and environment characteristics, geometric features, and driver behavior are examined in this study. Nested logit model and mixed logit model reveal similar results in terms of identifying contributing factors for driver injury severities. In the analysis of urban crashes, only the nested logit model is presented since no random parameter is found in the mixed logit model. The results indicate that significant differences exist between factors contributing to driver injury severity in single-vehicle crashes in rural and urban areas. There are 5 variables found only significant in the rural model and six significant variables identified only in the urban crash model. These findings can help transportation agencies develop effective policies or appropriate strategies to reduce injury severity resulting from single-vehicle crashes.     

A dynamic analysis of motorcycle ownership and usage: A panel data modeling approach

This study aims to develop motorcycle ownership and usage models with consideration of the state dependence and heterogeneity effects based on a large-scale questionnaire panel survey on vehicle owners. To account for the independence among alternatives and heterogeneity among individuals, the modeling structure of motorcycle ownership adopts disaggregate choice models considering the multinomial, nested, and mixed logit formulations. Three types of panel data regression models – ordinary, fixed, and random effects – are developed and compared for motorcycle usage. The estimation results show that motorcycle ownership in the previous year does exercise a significantly positive effect on the number of motorcycles owned by households in the current year, suggesting that the state dependence effect does exist in motorcycle ownership decisions. In addition, the fixed effects model is the preferred specification for modeling motorcycle usage, indicating strong evidence for existence of heterogeneity. Among various management strategies evaluated under different scenarios, increasing gas prices and parking fees will lead to larger reductions in total kilometers traveled.     

Markov switching multinomial logit model: An application to accident-injury severities

In this study, two-state Markov switching multinomial logit models are proposed for statistical modeling of accident-injury severities. These models assume Markov switching over time between two unobserved states of roadway safety as a means of accounting for potential unobserved heterogeneity. The states are distinct in the sense that in different states accident-severity outcomes are generated by separate multinomial logit processes. To demonstrate the applicability of the approach, two-state Markov switching multinomial logit models are estimated for severity outcomes of accidents occurring on Indiana roads over a four-year time period. 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) multinomial logit models for a number of roadway classes and accident types. It is found that the more frequent state of roadway safety is correlated with better weather conditions and that the less frequent state is correlated with adverse weather conditions.     

Analysis of driver injury severity in rural single-vehicle crashes

Rural roads carry less than fifty percent of the traffic in the United States. However, more than half of the traffic accident fatalities occurred on rural roads. This research focuses on analyzing injury severities involving single-vehicle crashes on rural roads, utilizing a latent class logit (LCL) model. Similar to multinomial logit (MNL) models, the LCL model has the advantage of not restricting the coefficients of each explanatory variable in different severity functions to be the same, making it possible to identify the impacts of the same explanatory variable on different injury outcomes. In addition, its unique model structure allows the LCL model to better address issues pertinent to the independence from irrelevant alternatives (IIA) property. A MNL model is also included as the benchmark simply because of its popularity in injury severity modeling. The model fitting results of the MNL and LCL models are presented and discussed. Key injury severity impact factors are identified for rural single-vehicle crashes. Also, a comparison of the model fitting, analysis marginal effects, and prediction performance of the MNL and LCL models are conducted, suggesting that the LCL model may be another viable modeling alternative for crash-severity analysis.     

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.     

Estimation of social value of statistical life using willingness-to-pay method in Nanjing,China

Rational decision making regarding the safety related investment programs greatly depends on the economic valuation of traffic crashes. The primary objective of this study was to estimate the social value of statistical life in the city of Nanjing in China. A stated preference survey was conducted to investigate travelers’ willingness to pay for traffic risk reduction. Face-to-face interviews were conducted at stations, shopping centers, schools, and parks in different districts in the urban area of Nanjing. The respondents were categorized into two groups, including motorists and non-motorists. Both the binary logit model and mixed logit model were developed for the two groups of people. The results revealed that the mixed logit model is superior to the fixed coefficient binary logit model. The factors that significantly affect people’s willingness to pay for risk reduction include income, education, gender, age, drive age (for motorists), occupation, whether the charged fees were used to improve private vehicle equipment (for motorists), reduction in fatality rate, and change in travel cost. The Monte Carlo simulation method was used to generate the distribution of value of statistical life (VSL). Based on the mixed logit model, the VSL had a mean value of 3,729,493 RMB ($586,610) with a standard deviation of 2,181,592 RMB ($343,142) for motorists; and a mean of 3,281,283 RMB ($505,318) with a standard deviation of 2,376,975 RMB ($366,054) for non-motorists. Using the tax system to illustrate the contribution of different income groups to social funds, the social value of statistical life was estimated. The average social value of statistical life was found to be 7,184,406 RMB ($1,130,032).     

Predicting accident frequency at their severity levels and its application in site ranking using a two-stage mixed multivariate model

Accident prediction models (APMs) have been extensively used in site ranking with the objective of identifying accident hotspots. Previously this has been achieved by using a univariate count data or a multivariate count data model (e.g. multivariate Poisson-lognormal) for modelling the number of accidents at different severity levels simultaneously. This paper proposes an alternative method to estimate accident frequency at different severity levels, namely the two-stage mixed multivariate model which combines both accident frequency and severity models. The accident, traffic and road characteristics data from the M25 motorway and surrounding major roads in England have been collected to demonstrate the use of the two-stage model. A Bayesian spatial model and a mixed logit model have been employed at each stage for accident frequency and severity analysis respectively, and the results combined to produce estimation of the number of accidents at different severity levels. Based on the results from the two-stage model, the accident hotspots on the M25 and surround have been identified. The ranking result using the two-stage model has also been compared with other ranking methods, such as the naïve ranking method, multivariate Poisson-lognormal and fixed proportion method. Compared to the traditional frequency based analysis, the two-stage model has the advantage in that it utilises more detailed individual accident level data and is able to predict low frequency accidents (such as fatal accidents). Therefore, the two-stage mixed multivariate model is a promising tool in predicting accident frequency according to their severity levels and site ranking.     

Evaluating alternate discrete outcome frameworks for modeling crash injury severity

This paper focuses on the relevance of alternate discrete outcome frameworks for modeling driver injury severity. The study empirically compares the ordered response and unordered response models in the context of driver injury severity in traffic crashes. The alternative modeling approaches considered for the comparison exercise include: for the ordered response framework-ordered logit (OL), generalized ordered logit (GOL), mixed generalized ordered logit (MGOL) and for the unordered response framework-multinomial logit (MNL), nested logit (NL), ordered generalized extreme value logit (OGEV) and mixed multinomial logit (MMNL) model. A host of comparison metrics are computed to evaluate the performance of these alternative models. The study provides a comprehensive comparison exercise of the performance of ordered and unordered response models for examining the impact of exogenous factors on driver injury severity. The research also explores the effect of potential underreporting on alternative frameworks by artificially creating an underreported data sample from the driver injury severity sample. The empirical analysis is based on the 2010 General Estimates System (GES) data base—a nationally representative sample of road crashes collected and compiled from about 60 jurisdictions across the United States. The performance of the alternative frameworks are examined in the context of model estimation and validation (at the aggregate and disaggregate level). Further, the performance of the model frameworks in the presence of underreporting is explored, with and without corrections to the estimates. The results from these extensive analyses point toward the emergence of the GOL framework (MGOL) as a strong competitor to the MMNL model in modeling driver injury severity.     

Heterogeneous impacts of gender-interpreted contributing factors on driver injury severities in single-vehicle rollover crashes

In this study, a mixed logit model is developed to identify the heterogeneous impacts of gender-interpreted contributing factors on driver injury severities in single-vehicle rollover crashes. The random parameter of the variables in the mixed logit model, the heterogeneous mean, is elaborated by driver gender-based linear regression models. The model is estimated using crash data in New Mexico from 2010 to 2012. The percentage changes of factors’ predicted probabilities are calculated in order to better understand the model specifications. Female drivers are found more likely to experience severe or fatal injuries in rollover crashes than male drivers. However, the probability of male drivers being severely injured is higher than female drivers when the road surface is unpaved. Two other factors with fixed parameters are also found to significantly increase driver injury severities, including Wet and Alcohol Influenced. This study provides a better understanding of contributing factors influencing driver injury severities in rollover crashes as well as their heterogeneous impacts in terms of driver gender. Those results are also helpful to develop appropriate countermeasures and policies to reduce driver injury severities in single-vehicle rollover crashes.     

Examining driver injury severity in two vehicle crashes – A copula based approach

A most commonly identified exogenous factor that significantly affects traffic crash injury severity sustained is the collision type variable. Most studies consider collision type only as an explanatory variable in modeling injury. However, it is possible that each collision type has a fundamentally distinct effect on injury severity sustained in the crash. In this paper, we examine the hypothesis that collision type fundamentally alters the injury severity pattern under consideration. Toward this end, we propose a joint modeling framework to study collision type and injury severity sustained as two dimensions of the severity process. We employ a copula based joint framework that ties the collision type (represented as a multinomial logit model) and injury severity (represented as an ordered logit model) through a closed form flexible dependency structure to study the injury severity process. The proposed approach also accommodates the potential heterogeneity (across drivers) in the dependency structure. Further, the study incorporates collision type as a vehicle-level, as opposed to a crash-level variable as hitherto assumed in earlier research, while also examining the impact of a comprehensive set of exogenous factors on driver injury severity. The proposed modeling system is estimated using collision data from the province of Victoria, Australia for the years 2006 through 2010.     

Product line optimisation based on semiparametric choice model

Consumer choice behaviour is important in the product line optimisation problem. The extant literature on product line optimisation is mostly based on traditional consumer choice models, such as the multinomial logit and multinomial probit models. These models either assume that the utility errors are independent from irrelevant alternatives (IIA) or are limited by complex calculation processes or pre-given, specific distributions of measuring errors. The marginal moment model (MMM), which is classified as a semiparametric choice model, does not require specific distributions of errors; thus, it can overcome the IIA shortcoming. This study focuses on the concavity of the profit functions of a product line optimisation model based on MMM. We prove that the profit function based on MMM is concave in market share under a monopoly or oligopoly. Numerical experiments show that the choice probabilities obtained from the MMM, multinomial logit, and multinomial probit models are similar although they are obtained under different assumptions. Experimental results under monopolistic, Cournot, and Bertrand competition based on MMM are compared. Some interesting managerial insights are summarised based on the sensitivity analysis of the various model parameters.     

A two-stage mining framework to explore key risk conditions on one-vehicle crash severity

This paper proposes a two-stage mining framework to explore the key risk conditions that may have contributed to the one-vehicle crash severity in Taiwan's freeways. In the first stage, a genetic mining rule (GMR) model is developed, using a novel stepwise rule-mining algorithm, to identify the potential risk conditions that best elucidate the one-vehicle crash severity. In the second stage, a mixed logit model is estimated, using the antecedent part of the mined-rules as explanatory variables, to test the significance of the risk conditions. A total of 5563 one-vehicle crash cases (226 fatalities, 1593 injuries and 3744 property losses) occurred in Taiwan's freeways over 2003–2007 are analyzed. The GMR model has mined 29 rules for use. By incorporating these 29 mined-rules into a mixed logit model, we further identify one key safe condition and four key risk conditions leading to serious crashes (i.e., fatalities and injuries). Each key risk condition is discussed and compared with its adjacent rules. Based on the findings, some countermeasures to rectify the freeway's serious one-vehicle crashes are proposed.     

Modeling offenses among motorcyclists involved in crashes in Spain

In relative terms, Spanish motorcyclists are more likely to be involved in crashes than other drivers and this tendency is constantly increasing. The objective of this study is to identify the factors that are related to being an offender in motorcycle accidents. A binary logit model is used to differentiate between offender and non-offender motorcyclists. A motorcyclist was considered to be offender when s/he had committed at least one traffic offense at the moment previous to the crash. The analysis is based on the official accident database of the Spanish general directorate of traffic (DGT) for the 2003–2008 time period. A number of explanatory variables including motorcyclist characteristics and environmental factors have been evaluated. The results suggest that inexperienced, older females, not using helmets, absent-minded and non-fatigued riders are more likely to be offenders. Moreover, riding during the night, on weekends, for leisure purposes and along roads in perfect condition, mainly on curves, predict offenses among motorcyclists. The findings of this study are expected to be useful in developing traffic policy decisions in order to improve motorcyclist safety.     

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.     

Product optimization with the improved marginal moment model

The probabilistic choice model is an important theory foundation for investigating consumer choice behavior in product optimization. In most studies, probabilistic choice behavior is simulated by the multinomial logit (MNL) model and a product always obtains some market share even though the utility a consumer obtains from buying the product is negative. However, the MNL model has a very restrictive substitution pattern – the independence of irrelevant alternatives (IIA). This paper investigates a product optimization problem based on the marginal moment model (MMM). Residual utility is involved in the MMM and negative utility is considered as well. The optimization model of product line design, based on the improved MMM, is established to maximize total profit through three types of problems. The established model fits reality better because the MMM does not have the IIA problem and has good statistical performance. Numerical experiments are carried out to evaluate the feasibility of the proposed model. Meanwhile, the relationships are explored between the optimal solutions and several factors, including the competitive products’ prices, utility variance, rate of cost reduction, and utility of competitive products.     

Comprehensive analysis of single- and multi-vehicle large truck at-fault crashes on rural and urban roadways in Alabama

The research described in this paper analyzed injury severities at a disaggregate level for single-vehicle (SV) and multi-vehicle (MV) large truck at-fault accidents for rural and urban locations in Alabama. Given the occurrence of a crash, four separate random parameter logit models of injury severity (with possible outcomes of major, minor, and possible or no injury) were estimated. The models identified different sets of factors that can lead to effective policy decisions aimed at reducing large truck-at-fault accidents for respective locations. The results of the study clearly indicated that there are differences between the influences of a variety of variables on the injury severities resulting from urban vs. rural SV and MV large truck at-fault accidents. The results showed that some variables were significant only in one type of accident model (SV or MV) but not in the other accident model. Again, some variables were found to be significant in one location (rural or urban) but not in other locations. The study also identified important factors that significantly impact the injury severity resulting from SV and MV large truck at-fault accidents in urban and rural locations based on the estimated values of average direct pseudo-elasticity. A careful study of the results of this study will help policy makers and transportation agencies identify location specific recommendations to increase safety awareness related to large truck involved accidents and to improve overall highway safety.