Exploring the application of the Negative Binomial–Generalized Exponential model for analyzing traffic crash data with excess zeros

Vangala, Prathyusha; Lord, Dominique; Geedipally, Srinivas Reddy

doi:10.1016/j.amar.2015.06.001

Cited by 37 publications

(18 citation statements)

References 20 publications

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“…that make the mixture distributions more closely match the dataset of excess zero observations. The results of studies using this type of approach, with models mainly including the negative binomial Lindley model (NB-L) [49], [50], negative binomial-crack model (NB-CR) [51], negative binomial-generalized index model (NB-GE) [52], Poisson generalized Gaussian [53], Poisson weighted exponential [54], [55], Poisson inverse Gaussian (PIG) [56], and negative binomial with Dirichlet process [57], have verified that the introduction of the new distributions not only explains the logic of crash occurrence but also achieves a better goodness of fit compared to the traditional crash model. For example, Geedipally et al [49] and Lord and Geedipally [50] and verified that the NB-L model has better goodness of fit than the NB model and the ZINB model.…”

Section: Crash Modeling Techniques For Excess Zero Observationsmentioning

confidence: 99%

“…For example, Geedipally et al [49] and Lord and Geedipally [50] and verified that the NB-L model has better goodness of fit than the NB model and the ZINB model. Vangala et al [52] fit the same dataset as Lord and Geedipally [50] using the NB-GE model, demonstrating that the NB-GE model performs comparably to the NB-L model and significantly better than the traditional NB model. Considering the a priori knowledge of the above studies, it is reasonable to develop suitable improved models based on the NB-L model to work with the excess zero-observation characteristics of expressway tunnel crash data.…”

Section: Crash Modeling Techniques For Excess Zero Observationsmentioning

confidence: 99%

See 1 more Smart Citation

Investigation of the Factors Influencing the Crash Frequency in Expressway Tunnels: Considering Excess Zero Observations and Unobserved Heterogeneity

Tang

Cai

et al. 2021

IEEE Access

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The existing crash modeling techniques for expressway tunnels must overcome the following difficulties: 1) The collected risk factors contributing to the tunnel crashes include narrow ranges, especially the pavement conditions and weather conditions of the tunnels are rarely taken into account. 2) Most researchers ignored the estimation deviation caused by the excess zero observations of tunnel crash datasets.3) No existing tunnel crash model can combine the random-parameters approach and spatial-temporal approach to solve the estimation deviation caused by the inter-samples and spatial-temporal heterogeneity.To address these problems, this study presents an investigation of the safety effects of risk factors of tunnel design features, traffic conditions, pavement conditions and weather conditions utilizing a 12-quarter period (3 years) of data as well as five crash frequency models: 1) a fixed parameters negative binomial model (FPNB), 2) a random parameters negative binomial model (RPNB), 3) a random parameters negative binomial Lindley model (RPNBL), 4) a spatial and random parameters negative binomial Lindley model (SP-RPNBL), and 5) a spatial-temporal and random parameters negative binomial Lindley model (ST-RPNBL). The results showed that the ST-RPNBL model solves the deviation that arises from excess zero observations by introducing the Lindley distribution and considers the unobserved heterogeneity by introducing both the random parameters and spatial-temporal parameters that provided better goodness of fit and offered more insights into the factors that contribute to tunnel safety. Furthermore, the ST-RPNBL model detected 16 variables that were significantly correlated with tunnel crash frequency, of which 12 variables were associated with a higher crash frequency and four variables were associated with a lower crash frequency. The random variables of the curvature, the steep downgrade indicator, the proportion of class 5 vehicle and the skidding resistance index (SRI) were identified, and the influence of each significant variable on the crash frequency was analyzed.INDEX TERMS Crash modeling techniques, random parameters approach, spatial-temporal approach, Lindley distribution, tunnel design features, traffic conditions, pavement conditions, weather conditions.

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Section: Crash Modeling Techniques For Excess Zero Observationsmentioning

confidence: 99%

Section: Crash Modeling Techniques For Excess Zero Observationsmentioning

confidence: 99%

Investigation of the Factors Influencing the Crash Frequency in Expressway Tunnels: Considering Excess Zero Observations and Unobserved Heterogeneity

Tang

Cai

et al. 2021

IEEE Access

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“…Modeling efforts to deal with crash data with excess zeros have continued with the introduction of new distributions that are capable of handling observations with small counts and combining them with the parent distributions capturing the crash data generating process (NB distributions). These kinds of models mainly include the negative binomial Lindley (NB-L) model [40], [41], the negative binomial crack (NB-CR) model [42], the negative binomial generalized index (NB-GE) model [43], etc. Moreover, these studies also verify that the improvements of negative binomial distributions are more appropriate for actual crash frequency distributions.…”

Section: B Excess Zero Observations Of Crash Datamentioning

confidence: 99%

“…Furthermore, Geedipally et al [40] modeled crash data with zero observations of 36% in Indiana and zero observations of 70% in Michigan, which verified that the NB-L model has better performance than the NB model and the ZINB model. Vangala et al [43] conducted a further analysis using the same data as that of Lord and Geedipally [41] and found that the performance of the NB-GE model was comparable with the NB-L model and significantly outperformed the traditional NB model. It should be emphasized that the above literatures, which attempt to address the excess zero observations of crash panel data, are all aimed at open roads.…”

Section: B Excess Zero Observations Of Crash Datamentioning

confidence: 99%

Applying a Correlated Random Parameters Negative Binomial Lindley Model to Examine Crash Frequency Along Highway Tunnels in China

Tang

Cai

et al. 2020

IEEE Access

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Highway tunnels have a higher risk of crashing than open roads, which require a systematic approach to tunnel safety. However, previous research had the following problems: (1) Studies have largely focused on open roads, with very little research on tunnels. (2) The collected crash contributing factors involve narrow ranges, with very little tunnel crash data including both tunnel design features, traffic conditions and pavement conditions. (3) None of the studies considered both excess zero observations and unobserved heterogeneity with its interactions. To address these issues, this paper first established an appropriate tunnel dataset containing 3 to 5 years of crash data from several highways in China and the influence factors of tunnel design features, traffic conditions and pavement conditions. A correlated random parameters negative binomial Lindley (CRPNB-L) model that considers both excess zero observations and unobserved heterogeneity with its interaction effects was then proposed. Compared to the uncorrelated random parameters negative binomial Lindley (URPNB-L) model, fixed parameters negative binomial Lindley (FPNB-L) model and fixed parameters negative binomial (FPNB) model, the CRPNB-L model solves the deviation that arises from excess zero observations by introducing the Lindley distribution and considers the unobserved heterogeneity with its interactions by introducing correlated random parameters. In the comparisons, the CRPNB-L model achieves the best effects in the goodness-of-fit. Furthermore, the estimated results of the CRPNB-L model showed that segment length, traffic volume, proportion of class 5 vehicle (heavy trucks and trailers), tunnel entrance and exit segments, and steep uphill and downhill segments were associated with higher crash frequency, while curvature, tunnel length, pavement damage condition index (PCI) and skid resistance index (SRI) were associated with lower crash frequency. In addition, the random variables of the curvature, the steep downgrade indicator, the proportion of class 5 vehicle and SRI were identified and their intercorrelations were analyzed. INDEX TERMS Tunnel safety, correlated random parameters, negative binomial Lindley model, tunnel design features, traffic conditions, pavement conditions.

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“…The limitation of the logistic regression model is that there is no dependency assumption among the influencing risk factors. The critical values of the severity of risks for expressways are unclear [37][38][39]. The TTC distribution is uncertain in practice.…”

Section: Introductionmentioning

confidence: 99%

Crash Risk Assessment of Off-Ramps, Based on the Gaussian Mixture Model Using Video Trajectories

Hao

Cui

et al. 2020

Sustainability

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The focus of this paper is the crash risk assessment of off-ramps in Xi’an. The time-to-collision (TTC) is used for the measurement and cross-comparison of the crash risk of each location. Five sites from the urban expressway in Xi’an were selected to explore the TTC distribution. An unmanned aerial vehicle and a camera were used to collect traffic flow data for 20 min at each site. The parameters, including speed, deceleration rate, truck percentage, traffic volume, and vehicle trajectories, were extracted from video images. The TTCs were calculated for each vehicle. The Gaussian mixture model (GMM) was proposed to predict the TTC probability density functions (PDFs) and cumulative density functions (CDFs) for five sites. The Kolmogorov–Smirnov (K-S) test indicated that the samples followed the estimated GMM distribution. The relationship between the crash risk level and influencing factors was studied by an ordinal logistic regression model and a naive Bayesian model. The results showed that the naive Bayesian model had an accuracy of 86.71%, while the ordinal logistic regression model had an accuracy of 84.81%. The naive Bayesian model outperformed the ordinal logistic regression model, and it could be applied to the real-time collision warning system.

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Exploring the application of the Negative Binomial–Generalized Exponential model for analyzing traffic crash data with excess zeros

Cited by 37 publications

References 20 publications

Investigation of the Factors Influencing the Crash Frequency in Expressway Tunnels: Considering Excess Zero Observations and Unobserved Heterogeneity

Investigation of the Factors Influencing the Crash Frequency in Expressway Tunnels: Considering Excess Zero Observations and Unobserved Heterogeneity

Applying a Correlated Random Parameters Negative Binomial Lindley Model to Examine Crash Frequency Along Highway Tunnels in China

Crash Risk Assessment of Off-Ramps, Based on the Gaussian Mixture Model Using Video Trajectories

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