Crash prediction based on random effect negative binomial model considering data heterogeneity

Statistical modelling for falls count data

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.

The foliage in a fully-leafed deciduous forest canopy is clumped. Consequently, theory indicates that the probability of beam penetration will be estimated more accurately with a model based on the negative binomial distribution than with a model based on the Poisson distribution, incorporating an assumption of a spherical leaf inclination angle distribution. Flux densities of photosynthetically active radiation (PAR) were measured in and above a deciduous forest canopy and were computed with the canopy radiative transfer models based on the negative binomial and Poisson distributions. These radiation values were used to compute canopy photosynthesis and stomatal conductance. Canopy photosynthesis and stomatal conductance, based on the negative binomial model, overestimated values computed from measured PAR profiles by 8 and 9%. respectively. The canopy photosynthesis and stomatal conductance values computed with the spherical Poisson model under-estimated measured values by 17 and 10%, respectively. Thus, the negative binomial radiative transfer model improves estimates of canopy photosynthesis and, to a lesser extent, stomatal conductance, inside a deciduous forest.

More than 60% of accidents in Iran occur within 30 kilometers of cities entrance roads. Therefore the number of accidents per kilometer in these regions, in contrast to the other parts of roads is very considerable. The city of Tehran, as the capital of Iran, is the cross point of major arterials of passenger and freight transportation. Thus the evaluation of road safety, entering and exiting the city in the 30 kilometers buffer, can be considered to improve countrywide road safety. To investigate the effects of roadway characteristics and traffic conditions, including number of traffic violations, on accident frequency within 30 km of Tehran entrance roads, Poisson and Negative Binomial regression model were calibrated in this study. Although the goodness of fit index in Poisson model is much greater than the Negative Binomial model, the accident data dispersion in this study implies that Negative Binomial model is more appropriate to show the influences of effective variables. According to results of modeling, the variables including average daily volume, share of heavy vehicles, average daily speed violations and number of direct accesses and interchanges have effective influence on accident frequencies. Controlling access to roads and using effective actions to reduce the speed and number of speed violation can be accounted as effective policies to reduce accident frequencies within 30 km of Tehran entrance roads.

The scaling relation between the size of a galaxy’s globular cluster (GC) population (N GC) and the galaxy’s stellar mass (M *) is usually described with a continuous, linear model, but in reality it is a count relationship that should be modeled as such. For massive galaxies, a negative binomial (NB) model has been shown to describe the data well, but it is unclear how the scaling relation behaves at low galaxy masses where a substantial portion of galaxies have N GC = 0. In this work, we test the utility of Poisson and NB models for describing the low-mass end of the N GC−M * scaling relation. We introduce the use of zero-inflated versions of these models, which allow for larger zero populations (e.g., galaxies without GCs) than would otherwise be predicted. We evaluate our models with a variety of predictive model comparison methods, including predictive intervals, the leave-one-out cross-validation criterion, and posterior predictive comparisons. We find that the NB model is consistent with our data, but the naive Poisson is not. Moreover, we find that zero inflation of the models is not necessary to describe the population of low-mass galaxies that lack GCs, suggesting that a single formation and evolutionary process acts over all galaxy masses. Under the NB model, there does not appear to be anything unique about the lack of GCs in many low-mass galaxies; they are simply the low-mass extension of the larger N GC−M * scaling relation.

A semiparametric negative binomial generalized linear model for modeling over-dispersed count data with a heavy tail: Characteristics and applications to crash data

Application of the Conway–Maxwell–Poisson generalized linear model for analyzing motor vehicle crashes

Modeling over-dispersed crash data with a long tail: Examining the accuracy of the dispersion parameter in Negative Binomial models

Analyzing angle crashes at unsignalized intersections using machine learning techniques

S ome P oints of D iscussion • Why hasn't the PIG model been widely used before this? • What types of data are best modeled using a PIG regression? • How do we model data with a very high initial peak and long right skew? • How do we know whether a PIG is a better-fitted model than negative binomial or Poisson models? P oisson I nverse G aussian M odel A ssumptions The Poisson inverse Gaussian (PIG) model is similar to the negative binomial model in that both are mixture models. The negative binomial model is a mixture of Poisson and gamma distributions , whereas the inverse Gaussian model is a mixture of Poisson and inverse Gaussian distributions . Those of you who are familiar with generalized linear models will notice that there are three GLM continuous distributions: normal, gamma, and inverse Gaussian. The normal distribution is typically parameterized to a lognormal distribution when associated with count models, presumably because the log link forces the distribution to have only nonnegative values. The Poisson and negative binomial (both NB2 and NB1) models have log links. Recall that the negative binomial is a mixture of the Poisson and gamma distributions, with variances of μ and μ 2 / v , respectively. We inverted v so that there is a direct relationship between the mean, dispersion, and variance function. Likewise, the inverse Gaussian is a mixture of Poisson and inverse Gaussian distributions, with an inverse Gaussian variance of μ 3 Φ.

Crashes present different collision types at freeway diverge areas. The research reported in this paper applies the multivariate modeling technique to evaluate the crash risks by collision type. Three years crash data are obtained from 282 freeway exit ramps. Three types of crashes are considered [i.e., (1) rear-end, (2) sideswipe, and (3) angle collisions]. A multivariate Poisson-lognormal (MVPLN) model is estimated to jointly evaluate the impacts of explanatory variables on different collision risks. For comparison purpose, univariate negative binomial (NB) models are also estimated based on the same dataset. The results show that the MVPLN model successfully captures the correlation of latent effects among the crash counts of different collision types. Thus, the MNPLN model estimates the impacts of variables more accurately than the NB model. The MVPLN model is found outperform the NB models in predicting the crash count of each collision type. Findings of this paper can help better understand ...

Effect of increasing the freeway posted speed limit on entry ramp speed-change lane crash frequency

Methodologic Challenges in the Analysis of Count Data in Radiology Health Services Research

The main objective of this study was to investigate the impact of factors linked to the geometric, roadway and traffic flow characteristics on traffic accident occurrence at Hazardous Road Locations (HRL) in the region of Sousse, Tunisia using longitudinal data of 52 HRLs for an 11-year monitoring period from January 1, 2004 to December 31, 2014. The results of estimation of Negative Binomial model and the Random Effects Negative Binomial model reported that the different variables representing the presence of rural segment, the curved alignment, the visibility, the average daily traffic volume, the presence of public lighting, the number of lane, the presence of vertical/horizontal sign, the presence of drainage system, the presence of paved shoulder, the roadway surface condition, and the presence of major road were the main significant variables influencing accident occurrences. Therefore, the results could be useful for deciders in the transport sector in order to implement effective measures to improve road safety by adopting proper sound use practices, establishing efficient transportation systems and formulating appropriate traffic policies and legislation.

The analysis of RNA-Seq data has been focused on three main categories, including gene expression, relative exon usage and transcript expression. Methods have been proposed independently for each category using a negative binomial (NB) model. However, counts following a NB distribution on one feature (e.g., exon) do not guarantee a NB distribution for the other two features (e.g., gene/transcript). In this paper we propose a family of Negative Binomial models, which integrates the gene, exon and transcript analysis under a coherent NB model. The proposed model easily incorporates the uncertainty of assigning reads to transcripts and simplifies substantially the estimation for the relative usage. We developed simple Gibbs sampling algorithms for the posterior inference by exploiting fully tractable closed-forms of computation via suitable conjugate priors. The proposed models were investigated under extensive simulations. Finally, we applied our model to a real data set.