Random Parameter Negative Binomial Model Research Articles

Development of Accident Frequency Models with Random Parameters on Interstate Roadway Segments with and without Lighting Systems

This study explored factors affecting traffic accidents in roadway segments with and without lighting systems using a random parameter negative binomial model. This study sought to make up for a shortcoming of the fixed parameter model that constrained the estimated parameters to be fixed across observations, by applying random parameters that can take into account unobserved heterogeneity. Three variables had a random parameter among nine significant variables in segments with lighting systems, while seven of the eleven significant variables in a segment without a lighting system had random parameters. The different influence of interstate highway geometrics on vehicle crashes with and without lighting systems found through this study considering unobserved heterogeneity may hopefully help reduce accident frequencies and consider installation of lighting systems on interstate highways in the future.

The effect of zonal factors in estimating crash risks by transportation modes: Motor vehicle, bicycle and pedestrian

ObjectivesThis paper aimed to (i) differentiate the effects of contributory factors on crash risks related to different transportation modes, i.e., motor vehicle, bicycle and pedestrian; (ii) explore the potential contribution of zone-level factors which are traditionally excluded or omitted, so as to track the source of heterogeneous effects of certain risk factors in crash-frequency models by different modes. MethodsTwo analytical methods, i.e. negative binomial models (NB) and random parameters negative binomial models (RPNB), were employed to relate crash frequencies of different transportation modes to a variety of risk factors at intersections. Five years of crash data, traffic volume, geometric design as well as macroscopic variables at traffic analysis zone (TAZ) level for 279 intersections were used for analysis as a case study. ResultsAmong the findings are: (1) the sets of significant variables in crash-frequency analysis differed for different transportation modes; (2) omission of macroscopic variables would result in biased parameters estimation and incorrect inferences; (3) the zonal factors (macroscopic factors) considered played a more important role in elevating the model performance for non-motorized than motor-vehicle crashes; (4) a relatively smaller buffer width to extract macroscopic factors surrounding the intersection yielded better estimations.

Analyzing the effectiveness of implemented highway safety laws for traffic safety across U.S. states

ABSTRACTSince highway safety laws vary greatly from state to state in the U.S., there is a need to analyze the effectiveness and performances of the implemented highway safety laws. The random-parameter zero-truncated negative binomial (RZTNB) models are proposed to analyze the effects of highway safety laws on fatal crashes at state levels. The results show that the proposed models are useful in describing the relationships between the fatal crashes and the explanatory variables with better goodness of fit. By accounting for the heterogeneities, the RZTNB model outperforms the negative binomial model and reveals new insights. The findings indicate that (1) compared to the secondary ban, the primary handheld cellphone ban is more effective; (2) establishing reasonable and acceptable speed limits can enhance the traffic safety; and (3) the implemented speed camera system and ignition interlock device have weaknesses and alternative methods should be considered when upgrading laws and regulations.

A comparative empirical analysis of statistical models for evaluating highway segment crash frequency

Abstract The present study conducted an empirical highway segment crash frequency analysis on the basis of fixed-parameters negative binomial and random-parameters negative binomial models. Using a 4-year data from a total of 158 highway segments, with a total of 11,168 crashes, the results from both models were presented, discussed, and compared. About 58% of the selected variables produced normally distributed parameters across highway segments, while the remaining produced fixed parameters. The presence of a noise barrier along a highway segment would increase mean annual crash frequency by 0.492 for 88.21% of the highway segments, and would decrease crash frequency for 11.79% of the remaining highway segments. Besides, the number of vertical curves per mile along a segment would increase mean annual crash frequency by 0.006 for 84.13% of the highway segments, and would decrease crash frequency for 15.87% of the remaining highway segments. Thus, constraining the parameters to be fixed across all highway segments would lead to an inaccurate conclusion. Although, the estimated parameters from both models showed consistency in direction, the magnitudes were significantly different. Out of the two models, the random-parameters negative binomial model was found to be statistically superior in evaluating highway segment crashes compared with the fixed-parameters negative binomial model. On average, the marginal effects from the fixed-parameters negative binomial model were observed to be significantly overestimated compared with those from the random-parameters negative binomial model.

A method to account for and estimate underreporting in crash frequency research

Underreporting is a well-known issue in crash frequency research. However, statistical methods that can account for underreporting have received little attention in the published literature. This paper compares results from underreporting models to models that account for unobserved heterogeneity. The difference in the elasticities between the negative binomial underreporting model and random parameters negative binomial models, which accounts for unobserved heterogeneity in crash frequency models, are used as the basis for comparison. The paper also includes a comparison of the predicted number of unreported PDO crashes based on the negative binomial underreporting model with crashes that were reported to police but were not considered reportable to PennDOT to assess the ability of the underreporting models to predict non-reportable crashes.The data used in this study included 21,340 segments of two-lane rural highways that are owned and maintained by PennDOT. Reported accident frequencies over an eight year period (2005⿿2012) were included in the sample, producing a total of 170,468 segment-years of data. The results indicate that if a variable impacts both the true accident frequency and the probability of accidents being reported, statistical modeling methods that ignore underreporting produce biased regression coefficients. The magnitude of the bias in the present study (based on elasticities) ranged from 0.00⿿16.79%. If the variable affects the true accident frequency, but not the probability of accidents being reported, the results from the negative binomial underreporting models are consistent with analysis methods that do not account for underreporting.

Spatiotemporal and random parameter panel data models of traffic crash fatalities in Vietnam

This paper investigates factors associated with traffic crash fatalities in 63 provinces of Vietnam during the period from 2012 to 2014. Random effect negative binomial (RENB) and random parameter negative binomial (RPNB) panel data models are adopted to consider spatial heterogeneity across provinces. In addition, a spatiotemporal model with conditional autoregressive priors (ST-CAR) is utilised to account for spatiotemporal autocorrelation in the data. The statistical comparison indicates the ST-CAR model outperforms the RENB and RPNB models. Estimation results provide several significant findings. For example, traffic crash fatalities tend to be higher in provinces with greater numbers of level crossings. Passenger distance travelled and road lengths are also positively associated with fatalities. However, hospital densities are negatively associated with fatalities. The safety impact of the national highway 1A, the main transport corridor of the country, is also highlighted.

Macroscopic modeling of pedestrian and bicycle crashes: A cross-comparison of estimation methods

The paper presents a cross-comparison of different estimation methods to model pedestrian and bicycle crashes. The study contributes to macro level safety studies by providing further methodological and empirical evidence on the various factors that influence the frequency of pedestrian and bicycle crashes at the planning level. Random parameter negative binomial (RPNB) models are estimated to explore the effects of various planning factors associated with total, serious injury and minor injury crashes while accounting for unobserved heterogeneity. Results of the RPNB models were compared with the results of a non-spatial negative binomial (NB) model and a Poisson-Gamma-CAR model. Key findings are, (1) the RPNB model performed best with the lowest mean absolute deviation, mean squared predicted error and Akaiki information criterion measures and (2) signs of estimated parameters are consistent if these variables are significant in models with the same response variables. We found that vehicle kilometers traveled (VKT), population, percentage of commuters cycling or walking to work, and percentage of households without motor vehicles have a significant and positive correlation with the number of pedestrian and bicycle crashes. Mixed land use is also found to have a positive association with the number of pedestrian and bicycle crashes. Results have planning and policy implications aimed at encouraging the use of sustainable modes of transportation while ensuring the safety of pedestrians and cyclist.

A study of factors affecting intersection crash frequencies using random-parameter multivariate zero-inflated models

Recent research demonstrates the appropriateness of multivariate regression models in crash count modelling when one specific type of crash counts needs to be analysed, since they can better handle the correlated issues in multiple crash counts. In this paper, a random-parameter multivariate zero-inflated Poisson (RMZIP) regression model is proposed as an alternative multivariate methodology for jointly modelling crash counts simultaneously. Using this RMZIP model, we are able to account for the heterogeneity due to the unobserved roadway geometric design features and traffic characteristics. Our formulation also has the merit of handling excess zeros in correlated crash counts, a phenomenon that is commonly found in practice. The Bayesian method is employed to estimate the model parameters. We use the proposed modelling framework to predict crash frequencies at urban signalized intersections in Tennessee. To investigate the model performances, three models – a fixed-parameter MZIP model, a random-parameter multivariate negative binomial (RMNB) model, and a random-parameter multivariate zero-inflated negative binomial (RMZINB) model – have been employed as the comparison methods. The comparison results show that the proposed RMZIP models provide a satisfied statistical fit with more variables producing statistically significant parameters. In other word, the RMZIP models have the potential to provide a fuller understanding of how the factors affect crash frequencies on specific roadway intersections. A variety of variables are found to significantly influence the crash frequencies by varying magnitudes. These variables result in random parameters and thereby their effects on crash frequencies are found to vary significantly across the sampled intersections.

Random Parameter Negative Binomial Model of Signalized Intersections

Factors affecting accident frequencies at 72 signalized intersections in the Gyeonggi-Do (province) over a four-year period (2007~2010) were explored using the random parameters negative binomial model. The empirical results from the comparison with fixed parameters binomial model show that the random parameters model outperforms its fixed parameters counterpart and provides a fuller understanding of the factors which determine accident frequencies at signalized intersections. In addition, elasticity and marginal effect were estimated to gain more insight into the effects of one-percent and one-unit changes in the dependent variable from changes in the independent variables.

Preference Heterogeneity in Contingent Behaviour Travel Cost Models with On‐site Samples: A Random Parameter vs. a Latent Class Approach

AbstractIn this paper, we examine heterogeneity in the trip preferences of recreationists. We apply a random parameters negative binomial model and a latent class negative binomial model to a panel dataset of beach users at a site on the west coast of Ireland, where access across farmland has been restricted. This approach allows us to account for heterogeneity with respect to the impact of the chosen explanatory variables in a contingent behaviour travel cost model of demand where the researcher must also account for the fact that the sample data has been collected on‐site. The analysis also develops individual consumer surplus estimates and finds that estimates are systematically affected by both the random parameter and latent class specifications. There is also evidence that accounting for individual heterogeneity improves the statistical fit of the models and provides a more informative description of the drivers of recreationalist trip behaviour.

Integration of geometric consistency contributory factors in three-leg junctions collision prediction models of Portuguese two-lane national highways

This paper aims at developing a collision prediction model for three-leg junctions located in national roads (NR) in Northern Portugal. The focus is to identify factors that contribute for collision type crashes in those locations, mainly factors related to road geometric consistency, since literature is scarce on those, and to research the impact of three modeling methods: generalized estimating equations, random-effects negative binomial models and random-parameters negative binomial models, on the factors of those models. The database used included data published between 2008 and 2010 of 177 three-leg junctions. It was split in three groups of contributing factors which were tested sequentially for each of the adopted models: at first only traffic, then, traffic and the geometric characteristics of the junctions within their area of influence; and, lastly, factors which show the difference between the geometric characteristics of the segments boarding the junctions’ area of influence and the segment included in that area were added. The choice of the best modeling technique was supported by the result of a cross validation made to ascertain the best model for the three sets of researched contributing factors. The models fitted with random-parameters negative binomial models had the best performance in the process. In the best models obtained for every modeling technique, the characteristics of the road environment, including proxy measures for the geometric consistency, along with traffic volume, contribute significantly to the number of collisions. Both the variables concerning junctions and the various national highway segments in their area of influence, as well as variations from those characteristics concerning roadway segments which border the already mentioned area of influence have proven their relevance and, therefore, there is a rightful need to incorporate the effect of geometric consistency in the three-leg junctions safety studies.

Investigation of pedestrian crashes on two-way two-lane rural roads in Ethiopia

Understanding pedestrian crash causes and contributing factors in developing countries is critically important as they account for about 55% of all traffic crashes. Not surprisingly, considerable attention in the literature has been paid to road traffic crash prediction models and methodologies in developing countries of late. Despite this interest, there are significant challenges confronting safety managers in developing countries. For example, in spite of the prominence of pedestrian crashes occurring on two-way two-lane rural roads, it has proven difficult to develop pedestrian crash prediction models due to a lack of both traffic and pedestrian exposure data. This general lack of available data has further hampered identification of pedestrian crash causes and subsequent estimation of pedestrian safety performance functions. The challenges are similar across developing nations, where little is known about the relationship between pedestrian crashes, traffic flow, and road environment variables on rural two-way roads, and where unique predictor variables may be needed to capture the unique crash risk circumstances. This paper describes pedestrian crash safety performance functions for two-way two-lane rural roads in Ethiopia as a function of traffic flow, pedestrian flows, and road geometry characteristics. In particular, random parameter negative binomial model was used to investigate pedestrian crashes. The models and their interpretations make important contributions to road crash analysis and prevention in developing countries. They also assist in the identification of the contributing factors to pedestrian crashes, with the intent to identify potential design and operational improvements.

Comparison and analysis of road tunnel traffic accident frequencies and rates using random-parameter models

ABSTRACTThe article provides an analysis of severe crashes (fatal and injury accidents only) that occurred in 260 Italian road tunnels on the basis of random-parameters regression models. In particular, factors influencing “crash frequency” over a 4-year monitoring period are investigated by means of a random-parameters negative binomial model (RPNB). This approach reveals that some regression model parameters should be considered as random variables, thus contributing to gaining new insights into the way the corresponding covariates influence accident frequency. The presence of a year effect on the number of accidents was also investigated. To this aim, random-parameters models with random-effects were considered to account for temporal correlation in the data collected from the same road tunnel over successive time periods. In particular, a negative binomial model in which the intercept and regression parameters are allowed to vary randomly was developed. It was found that in the present case study the unobserved heterogeneity is small, so it is sufficient just using the random-intercept model. This study also explores the use of crash rate instead of crash frequency as dependent variable of the regression model, to understand more especially the effect of this choice on the significance of the covariates. A random-parameters tobit regression model showed that the significance of some independent variables is in contrast with the results found upon the RPNB model based on crash frequency.

Longitudinal Analysis of Rural Interstate Fatalities in Relation to Speed Limit Policies

Existing research literature has shown that traffic fatalities increase at higher speed limits. A related issue is the establishment of maximum speed limits for trucks and buses. As of 2014, eight states have a differential speed limit in place that establishes a higher limit for passenger vehicles than for trucks and buses. This study aimed to inform the continuing debate regarding the safety impacts of speed limits by comparing states with various speed limit policies. The study included a longitudinal comparison of state-level rural Interstate fatalities in the United States from 1999 through 2011. In addition to an examination of differences in traffic fatalities as a function of maximum speed limits, comparisons were also made between states with differential limits for truck and buses. Random parameter negative binomial models were estimated for annual total and truck-involved fatalities. A random parameter framework allowed for consideration of temporal correlation in annual fatality counts within states as well as for unobserved heterogeneity across states. The results of this study provided further evidence that both overall and truck-involved fatalities increased with maximum speed limits. States with differential speed limits were found to have marginal differences in total fatalities as compared with states with uniform speed limits. However, truck-involved fatalities were significantly lower in states where differential limits were in place. The effects of speed limit policies as well as other covariates were found to vary significantly across states. The random parameter models demonstrated significantly improved goodness of fit as compared with standard Poisson and negative binomial models.

Impacts of Signal-Related Characteristics on Crash Frequency at Urban Signalized Intersections

The effect of signals at urban intersections is critical in reducing death, injuries, and property loss. Unfortunately, the signal-related factors that can effectively reduce crash frequencies have not been adequately explored. This study investigates the impacts of signal-related, traffic, and highway geometric characteristics on crash frequency at urban signalized intersections. Seven-year crash data from 381 intersections in Illinois, United States of America, was used to estimate a random-parameters negative binomial model. The estimation results showed that a unit increase in the number of signal phases would increase crash frequency by 0.4. Additionally, the ratio of traffic volume on the major road to the traffic volume on the minor road was shown to unambiguously increase crash frequency. On the other hand, the number of approach lanes and the maximum green time of different approaches in a signal revealed an ambiguous effect, whereas increasing crash frequency on 76.33%, and 93.32% and decreasing it on the remaining 23.67%, and 6.68% of the signalized intersections, respectively. Although, this study is exploratory in nature, the results showed that ignoring these factors at urban signalized intersections would lead to the design of ineffective safety-related countermeasures, and the impacts could be underestimated by 5% to 25%.

Modeling crash spatial heterogeneity: Random parameter versus geographically weighting

The widely adopted techniques for regional crash modeling include the negative binomial model (NB) and Bayesian negative binomial model with conditional autoregressive prior (CAR). The outputs from both models consist of a set of fixed global parameter estimates. However, the impacts of predicting variables on crash counts might not be stationary over space. This study intended to quantitatively investigate this spatial heterogeneity in regional safety modeling using two advanced approaches, i.e., random parameter negative binomial model (RPNB) and semi-parametric geographically weighted Poisson regression model (S-GWPR).Based on a 3-year data set from the county of Hillsborough, Florida, results revealed that (1) both RPNB and S-GWPR successfully capture the spatially varying relationship, but the two methods yield notably different sets of results; (2) the S-GWPR performs best with the highest value of Rd2 as well as the lowest mean absolute deviance and Akaike information criterion measures. Whereas the RPNB is comparable to the CAR, in some cases, it provides less accurate predictions; (3) a moderately significant spatial correlation is found in the residuals of RPNB and NB, implying the inadequacy in accounting for the spatial correlation existed across adjacent zones.As crash data are typically collected with reference to location dimension, it is desirable to firstly make use of the geographical component to explore explicitly spatial aspects of the crash data (i.e., the spatial heterogeneity, or the spatially structured varying relationships), then is the unobserved heterogeneity by non-spatial or fuzzy techniques. The S-GWPR is proven to be more appropriate for regional crash modeling as the method outperforms the global models in capturing the spatial heterogeneity occurring in the relationship that is model, and compared with the non-spatial model, it is capable of accounting for the spatial correlation in crash data.

RPNB 모형을 이용한 고속도로 인터체인지 구간에서의 교통사고모형 - 인터체인지 형태별/지역별로

PURPOSES : The objective was to develop the advanced method which could not explain each observation's specific characteristic in the present negative binomial method that results in under-estimation of the standard error(t-value inflation) and affects the confidence of whole derived results. METHODS : This study dealt with traffic accidents occurring within interchange segment on highway main line with RPNB(Random Parameter Negative Binomial) method that enables to take account of heterogeneity. RESULTS : As a result, AADT and lighting installation type on the road were revealed to have random parameter and in terms of other geometric variables, all were derived as fixed parameter(same effect on every segment). Also, marginal effects were adapted to analyze the relative effects on traffic accidents. CONCLUSIONS : This study proves that RPNB method which considers each observation's specific characteristics is better fitted to the accident data with geometrics. Thus, it is recommended that RPNB model or other methods which could consider the heterogeneity needs to be adapted in accident analysis.

A heterogeneity-in-means count model for evaluating the effects of interchange type on heterogeneous influences of interstate geometrics on crash frequencies

This paper presents a heterogeneity-in-means, random-parameter negative binomial (HMRPNB) model of interchange type effects on interchange and non-interchange segment crash frequencies. For non-interchange segments, upstream and downstream type combinations were evaluated. Eight interchange types, namely, directional, semidirectional, clover, partclover, diamond, part diamond, single-point-urban-interchange (SPUI), and other were studied on the Washington State interstate system. A total of 575 interchange and 578 non-interchange segments were analyzed for the period 1999–2007. In interchange segments, semidirectional, partclover and other (excluding directional, diamond, SPUI, or fullclover) types significantly contributed to heterogeneity in the random parameter effects of average daily traffic, median continuous lighting proportion, minimum and maximum vertical gradients. Full and partial diamond types contributed to heterogeneity in the random parameter effects of median continuous lighting proportion, maximum horizontal degree of curvature, minimum and maximum vertical gradients. In non-interchange segments, the upstream type set including directional, semidirectional, and clover/collector-distributor type, and downstream set of directional, semidirectional, diamond, partclover, partdiamond and other type significantly contributed to heterogeneity in the random parameter means of total length of adjacent interchanges, two foot left shoulder width and two foot right shoulder width proportions. Statistically significant fixed parametric effects included urban/rural location, right continuous lighting proportion, proportion by length of three lane cross section, four lane cross section, three-to-four foot left shoulder, five-to-nine foot left shoulder, ten foot left shoulder, three-to-four foot right shoulder, five-to-nine foot right shoulder, and ten foot right shoulder, as well as number of horizontal curves in segment, and shortest horizontal curve length.

Modeling safety of highway work zones with random parameters and random effects models

This paper presents an investigation of traffic safety in highway work zones using detailed data obtained from the results of a survey of project engineers and existing datasets. The observations were organized in monthly clusters that correspond to individual work zones; and a two-level random parameters negative binomial model that reflected the structure of the observations was estimated. The safety effects of various work zone design and traffic management features were identified, including lane shift, lane split, and detour, whose safety effects have not been evaluated in past research. This new insight into highway work zone safety was accomplished thanks to the better data acquired and the improved statistical model. A fixed parameters negative binomial model with random effects then was estimated to check its viability as an alternative to the random parameters model when the sample's large size makes estimation of the latter challenging. From a practical standpoint, the marginal effects on crash frequency computed from the model with random effects were quite similar to those computed from the random parameters model. This result indicates that, at least in some cases, convenient fixed parameters models may be a practical alternative to random parameters models. Utilization of an entire sample to estimate these conventional models may further compensate a less advanced model specification. The obtained negative binomial model with random effects has become useful for programming police enforcement in highway work zones in Indiana.

Random parameter models of interstate crash frequencies by severity, number of vehicles involved, collision and location type

A nine-year (1999–2007) continuous panel of crash histories on interstates in Washington State, USA, was used to estimate random parameter negative binomial (RPNB) models for various aggregations of crashes.A total of 21 different models were assessed in terms of four ways to aggregate crashes, by: (a) severity, (b) number of vehicles involved, (c) crash type, and by (d) location characteristics. The models within these aggregations include specifications for all severities (property damage only, possible injury, evident injury, disabling injury, and fatality), number of vehicles involved (one-vehicle to five-or-more-vehicle), crash type (sideswipe, same direction, overturn, head-on, fixed object, rear-end, and other), and location types (urban interchange, rural interchange, urban non-interchange, rural non-interchange). A total of 1153 directional road segments comprising of the seven Washington State interstates were analyzed, yielding statistical models of crash frequency based on 10,377 observations. These results suggest that in general there was a significant improvement in log-likelihood when using RPNB compared to a fixed parameter negative binomial baseline model. Heterogeneity effects are most noticeable for lighting type, road curvature, and traffic volume (ADT). Median lighting or right-side lighting are linked to increased crash frequencies in many models for more than half of the road segments compared to both-sides lighting. Both-sides lighting thereby appears to generally lead to a safety improvement. Traffic volume has a random parameter but the effect is always toward increasing crash frequencies as expected. However that the effect is random shows that the effect of traffic volume on crash frequency is complex and varies by road segment. The number of lanes has a random parameter effect only in the interchange type models. The results show that road segment-specific insights into crash frequency occurrence can lead to improved design policy and project prioritization.