Yajie Zou

Application of finite mixture of negative binomial regression models with varying weight parameters for vehicle crash data analysis

Recently, a finite mixture of negative binomial (NB) regression models has been proposed to address the unobserved heterogeneity problem in vehicle crash data. This approach can provide useful information about features of the population under study. For a standard finite mixture of regression models, previous studies have used a fixed weight parameter that is applied to the entire dataset. However, various studies suggest modeling the weight parameter as a function of the explanatory variables in the data. The objective of this study is to investigate the differences on the modeling and fitting results between the two-component finite mixture of NB regression models with fixed weight parameters (FMNB-2) and the two-component finite mixture of NB regression models with varying weight parameters (GFMNB-2), and compare the group classification from both models. To accomplish the objective of this study, the FMNB-2 and GFMNB-2 models are applied to two crash datasets. The important findings can be summarized as follows: first, the GFMNB-2 models can provide more reasonable classification results, as well as better statistical fitting performance than the FMNB-2 models; second, the GFMNB-2 models can be used to better reveal the source of dispersion observed in the crash data than the FMNB-2 models. Therefore, it is concluded that in many cases the GFMNB-2 models may be a better alternative to the FMNB-2 models for explaining the heterogeneity and the nature of the dispersion in the crash data.

Lane-changes prediction based on adaptive fuzzy neural network

Abstract Lane changing maneuver is one of the most important driving behaviors. Unreasonable lane changes can cause serious collisions and consequent traffic delays. High precision prediction of lane changing intent is helpful for improving driving safety. In this study, by fusing information from vehicle sensors, a lane changing predictor based on Adaptive Fuzzy Neural Network (AFFN) is proposed to predict steering angles. The prediction model includes two parts: fuzzy neural network based on Takagi–Sugeno fuzzy inference, in which an improved Least Squares Estimator (LSE) is adopt to optimize parameters; adaptive learning algorithm to update membership functions and rule base. Experiments are conducted in the driving simulator under scenarios with different speed levels of lead vehicle: 60u202fkm/h, 80u202fkm/h and 100u202fkm/h. Prediction results show that the proposed method is able to accurately follow steering angle patterns. Furthermore, comparison of prediction performance with several machine learning methods further verifies the learning ability of the AFNN. Finally, a sensibility analysis indicates heading angles and acceleration of vehicle are also important factors for predicting lane changing behavior.

Use of Skew-Normal and Skew-t Distributions for Mixture Modeling of Freeway Speed Data

Normal, lognormal, and other forms of distribution have been used to characterize speed data. Recently, several researchers have used the normal mixture model to fit the distribution of speed. To investigate the applicability of mixture models with other types of component density, a study was done that fits 24-h speed data collected on I-35 in Texas by using skew-normal and skew-t mixture models with an algorithm of expectation maximization type. The results show that a finite mixture of skew distributions can significantly improve the goodness of fit of speed data. Compared with normal distribution, skew-normal and skew-t distributions can accommodate skewness and excess kurtosis themselves; thus the skew mixture models require fewer components than normal mixture models to capture the asymmetry and bimodality present in speed data. The results of the study indicate that a two-component skew-t mixture model is the optimal model, and this model can better account for heterogeneity in the data. The study verifies that traffic flow condition is the main cause for heterogeneity in the 24-h speed data. The research methodology can be used to analyze freeway speed data characteristics. The findings can also be used in development and validation of microscopic simulation of freeway traffic.

Assessing the Agreement among Pavement Condition Indexes

Pavement condition indexes are numerical indicators of the structural and material integrity of a pavement. Because these indexes appear to be similar (essentially a 0–100 scale, with 100 indicating ideal condition), it can be tempting to use different indexes for comparing the performance of pavement networks in different states or jurisdictions within a state. To ascertain the level of agreement among these condition indexes, six pavement condition indexes from five DOTs in the United States are discussed and compared using distress and ride quality data obtained from the Pavement Management Information System of the Texas Department of Transportation. The computed scores were compared visually (using scatter plots) and statistically (using paired t -test). The results provide empirical evidence that there are significant differences among seemingly similar pavement condition indexes.

Constructing a bivariate distribution for freeway speed and headway data

Accurate description of speed and headway distributions is critical for developing microscopic traffic simulation models. A number of microscopic simulation models generate vehicle speeds and vehicle arrival times as independent inputs to the simulation process. However, this traditional approach ignores the possible correlation between speed and headway. This article proposes a Farlie–Gumbel–Morgenstern (FGM) approach to construct a bivariate distribution to simultaneously describe the characteristics of speed and headway. For the FGM approach, the distributions of speed and headway need to be specified separately before the construction of the bivariate distribution. While using conventional distributions for headway, this study uses normal, skew-normal and skew-t mixture distributions for speed. To examine the applicability of the FGM, the proposed approach is applied to a 24-hour speed and headway dataset collected on IH-35 in Austin, Texas. The results show the FGM approach has successfully constructed the bivariate distribution for speed and headway. Moreover, data analyses indicate that there is a weak correlation coefficient between speed and headway. The methodology in this research can be used in analysing the characteristics of speed and headway data. The findings can also be used in the development and validation of microscopic simulation models for freeway traffic.

Comparison of Sichel and Negative Binomial Models in Estimating Empirical Bayes Estimates

Traditionally, transportation safety analysts have used the empirical Bayes (EB) method to improve the estimate of the long-term mean of individual sites and to identify hotspot locations. The EB method combines two sources of information: (a) the expected number of crashes estimated by crash prediction models and (b) the observed number of crashes at individual sites. Because of the overdispersion commonly found in crash data, a negative binomial (NB) modeling framework has been used extensively in crash prediction estimation models. Recent studies have shown that the Sichel (SI) distribution provides a promising avenue for developing crash prediction models. The objective of this study was to examine the application of the SI model in calculating EB estimates. The study used crash data collected at four-lane undivided rural highways in Texas to develop SI models with fixed and varying dispersion terms. The results led to the following main conclusions: (a) the selection of the crash prediction model (i.e., the SI or the NB model) affected the value of the weight factor used for estimating the EB output and (b) the identification of hazardous sites, based on the EB method, could be different when the SI model was used. Finally, a simulation study that is designed to examine which crash prediction model can identify hotspots better is recommended for future research.

The Poisson inverse Gaussian (PIG) generalized linear regression model for analyzing motor vehicle crash data

ABSTRACT This article documents the application of the Poisson inverse Gaussian (PIG) regression model for modeling motor vehicle crash data. The PIG distribution, which mixes the Poisson distribution and inverse Gaussian distribution, has the potential for modeling highly dispersed count data due to the flexibility of inverse Gaussian distribution. The objectives of this article were to evaluate the application of PIG regression model for analyzing motor vehicle crash data and compare the results with negative binomial (NB) model, especially when varying dispersion parameter is introduced. To accomplish these objectives, NB and PIG models were developed with fixed and varying dispersion parameters and compared using two data sets. The results of this study show that PIG models perform better than the NB models in terms of goodness-of-fit statistics. Moreover, the PIG model can perform as well as the NB model in capturing the variance of crash data. Lastly, PIG models demonstrate almost the same prediction performance compared to NB models. Considering the simple form of PIG model and its easiness of applications, PIG model could be used as a potential alternative to the NB model for analyzing crash data.

Travel Time Estimation Using Freeway Point Detector Data Based on Evolving Fuzzy Neural Inference System

Travel time is an important measurement used to evaluate the extent of congestion within road networks. This paper presents a new method to estimate the travel time based on an evolving fuzzy neural inference system. The input variables in the system are traffic flow data (volume, occupancy, and speed) collected from loop detectors located at points both upstream and downstream of a given link, and the output variable is the link travel time. A first order Takagi-Sugeno fuzzy rule set is used to complete the inference. For training the evolving fuzzy neural network (EFNN), two learning processes are proposed: (1) a K-means method is employed to partition input samples into different clusters, and a Gaussian fuzzy membership function is designed for each cluster to measure the membership degree of samples to the cluster centers. As the number of input samples increases, the cluster centers are modified and membership functions are also updated; (2) a weighted recursive least squares estimator is used to optimize the parameters of the linear functions in the Takagi-Sugeno type fuzzy rules. Testing datasets consisting of actual and simulated data are used to test the proposed method. Three common criteria including mean absolute error (MAE), root mean square error (RMSE), and mean absolute relative error (MARE) are utilized to evaluate the estimation performance. Estimation results demonstrate the accuracy and effectiveness of the EFNN method through comparison with existing methods including: multiple linear regression (MLR), instantaneous model (IM), linear model (LM), neural network (NN), and cumulative plots (CP).

Comparison of Sichel and Negative Binomial Models in Hot Spot Identification

Identification of crash hot spots is the critical component of the highway safety management process. Errors in hot spot identification (HSID) may result in the inefficient use of resources for safety improvements. One HSID method that is based on the empirical Bayesian (EB) method has been widely used as an effective approach for identifying crash-prone sites. For the EB method, the negative binomial (NB) model is usually needed to obtain the EB estimates. Recently, some studies have shown that the Sichel (SI) model can be easily used in the EB modeling framework and potentially yield better EB estimates. The objective of this study was to compare the performance of the two crash prediction (SI and NB) models in identifying hot spots with the EB method. To accomplish the objective of this study, empirical crash data collected at highway segments in Texas were used to generate simulated crash counts. Three commonly used HSID methods (simple ranking, confidence interval, and EB) were applied with the use of simulated data. False positives, false negatives, and false identifications were calculated and compared across the methods. The simulation results in this study suggested that the SI-based EB method could consistently provide a better HSID result than the NB-based EB method. Moreover, EB methods yielded the lowest error percentage of the three HSID methods. This study confirmed that the EB technique was an effective method for identifying hazardous sites. On the basis of the findings in this study, it is recommended that transportation safety researchers consider the SI model as an alternative crash prediction model when the EB approach is used.

Mixture modeling of freeway speed and headway data using multivariate skew-t distributions

ABSTRACT The knowledge of vehicle speed and headway distributions is very useful for developing microscopic traffic simulation models. Traditionally, speed and headway distributions are often not studied jointly and some microscopic traffic simulation models consider vehicle speeds and arrival times as independent inputs to the traffic simulation process. However, the traditional approaches ignore the possible correlation between freeway vehicle speed and headway. Recently, a Farlie–Gumbel–Morgenstern (FGM) approach was used to construct bivariate distributions to describe the characteristics of speed and headway. The FGM approach only allows a weak statistical dependency and lacks the ability to consider the dynamic correlation structure for speed and headway data collected under different traffic conditions. The objective of this study is to explore the applicability of the finite mixtures of multivariate skew-t distributions to capture the heterogeneity in speed and headway data. The proposed bivariate mixture modeling approach is applied to the 24-hour traffic data collected on IH-35 in Austin, Texas. The results of this study show that the bivariate skew-t mixture model can provide an excellent fit to the multimodal speed and headway distribution. Moreover, the mixture modeling approach can naturally accommodate the varying correlation coefficient by assigning different covariance matrixes for each component in the finite mixture model. The findings in this study can also improve car-following models for simulation purposes.