A Horvitz-type estimation on incomplete traffic accident data analyzed via a zero-inflated Poisson model

The paper aims to provide insights of choosing suitable time series models and analysing road traffic accidents and injuries taking road traffic accident (RTA) and injuries (RTI) data in Oman as a case study as the country faces one of the highest numbers of road accidents per year. Data from January 2000 to June 2019 from several secondary sources were gathered. Time series decomposition, stationarity and seasonality checking were performed to identify the appropriate models for RTA and RTI. SARIMA (3, 1, 1)(2, 0, 0)(12) and SARIMA (0, 1, 1)(1, 0, 2)(12) models were found to be the best for the road traffic accident and injury data, respectively, comparing many different models. AIC, BIC and other error values were used to choose the best model. Model diagnostics were also performed to confirm the statistical assumptions, and 2-year forecasting was performed. The analyses in this paper would help many government departments, academic researchers and decision-makers to generate policies to reduce accidents and injuries.

In many experimental situations the sample may present excess zero observations and generally are used probabilistic models for zero inflated to represent them. However no one knows precisely the amount of zero observations that these models support. Depending on the sample size and null observations number the Poisson model can be used. Based on this question, the objective of this paper is to evaluate the properties of Type I error and power of the score test (proposed by Van Den Broek (1995) to discriminate the Poisson and Zero-inflated Poisson models) and ascertain the most appropriate model to represent a sample with excess zeros without compromising the statistical inference. Through Monte Carlo simulation we concluded that when considering a sample of size at least n = 40 with 30% of the null observations, the score test had a high discriminatory power between the ZIP and Poisson model indicating that in fact is relevant the use of the ZIP model.

Road traffic accident databases provide the basis for road traffic accident analysis, the data inside which usually has a radial, multidimensional, and multilayered structure. Traditional data mining algorithms such as association rules, when applied alone, often yield uncertain and unreliable results. An improved association rule algorithm based on Particle Swarm Optimization (PSO) put forward by this paper can be used to analyze the correlation between accident attributes and causes. The new algorithm focuses on characteristics of the hyperstereo structure of road traffic accident data, and the association rules of accident causes can be calculated more accurately and in higher rates. A new concept of Association Entropy is also defined to help compare the importance between different accident attributes. T-test model and Delphi method were deployed to test and verify the accuracy of the improved algorithm, the result of which was a ten times faster speed for random traffic accident data sampling analyses on average. In the paper, the algorithms were tested on a sample database of more than twenty thousand items, each with 56 accident attributes. And the final result proves that the improved algorithm was accurate and stable.

This study applied GIS-based statistical analytic techniques to investigate the influence of accident Severity Index (SI) on temporal-spatial patterns of accident hotspots related to the specific time intervals of day and seasons. Road Traffic Accident (RTA) data in 3 years (2015 − 2017) in Hanoi, Vietnam were used to analyze and test this approach. Firstly, the RTA data were divided into four seasons in accordance with Hanoi’s weather conditions and the time intervals such as the daytime, nighttime, or peak hours. Then, the Kernel Density Estimation (KDE) method was applied to analyze hotspots according to the time intervals and seasons. Finally, the results were presented by using the comap technique. This study considered both analyses with and without SI. The accident SI measures the seriousness of an accident. The approach method is to give higher weights to the more serious accidents, but not with the extremely high values calculated on a direct rate to the accident expenditures. The results showed that both analyses determined the relatively similar hotspots, but the rankings of some hotspots were quite different due to the integration of SI. It is better to take into account SI in determining RTA hotspots because the gained results are more precise and the rankings of hotspots are more accurate. From there, the traffic authorities can easily understand the causes behind each accident and provide reasonable solutions to solve the most dangerous hotspots in case of limited budget and resources appropriately. This is also the first study about this issue in Vietnam, so the contribution of the article will help the traffic authorities easily solve this problem not only in Hanoi but also in other cities.

Underreporting in traffic accident data, bias in parameters and the structure of injury severity models

Road traffic safety: An analysis of the cross-effects of economic, road and population factors

Microorganisms play critical roles in human health and disease. They live in diverse communities in which they interact synergistically or antagonistically. Thus for estimating microbial associations with clinical covariates, such as treatment effects, joint (multivariate) statistical models are preferred. Multivariate models allow one to estimate and exploit complex interdependencies among multiple taxa, yielding more powerful tests of exposure or treatment effects than application of taxon-specific univariate analyses. Analysis of microbial count data also requires special attention because data commonly exhibit zero inflation, i.e., more zeros than expected from a standard count distribution. To meet these needs, we developed a Bayesian variable selection model for multivariate count data with excess zeros that incorporates information on the covariance structure of the outcomes (counts for multiple taxa), while estimating associations with the mean levels of these outcomes. Though there has been much work on zero-inflated models for longitudinal data, little attention has been given to high-dimensional multivariate zero-inflated data modeled via a general correlation structure. Through simulation, we compared performance of the proposed method to that of existing univariate approaches, for both the binary ("excess zero") and count parts of the model. When outcomes were correlated the proposed variable selection method maintained type I error while boosting the ability to identify true associations in the binary component of the model. For the count part of the model, in some scenarios the univariate method had higher power than the multivariate approach. This higher power was at a cost of a highly inflated false discovery rate not observed with the proposed multivariate method. We applied the approach to oral microbiome data from the Pediatric HIV/AIDS Cohort Oral Health Study and identified five (of 44) species associated with HIV infection.

ObjectiveTo propose a more realistic model for disease cluster detection, through a modification of the spatial scan statistic to account simultaneously for inflated zeros and overdispersion.IntroductionSpatial Scan Statistics [1] usually assume Poisson or Binomial distributed data, which is not adequate in many disease surveillance scenarios. For example, small areas distant from hospitals may exhibit a smaller number of cases than expected in those simple models. Also, underreporting may occur in underdeveloped regions, due to inefficient data collection or the difficulty to access remote sites. Those factors generate excess zero case counts or overdispersion, inducing a violation of the statistical model and also increasing the type I error (false alarms). Overdispersion occurs when data variance is greater than the predicted by the used model. To accommodate it, an extra parameter must be included; in the Poisson model, one makes the variance equal to the mean.MethodsTools like the Generalized Poisson (GP) and the Double Poisson [2] may be a better option for this kind of problem, modeling separately the mean and variance, which could be easily adjusted by covariates. When excess zeros occur, the Zero Inflated Poisson (ZIP) model is used, although ZIP’s estimated parameters may be severely biased if nonzero counts are too dispersed, compared to the Poisson distribution. In this case the Inflated Zero models for the Generalized Poisson (ZIGP), Double Poisson (ZIDP) and Negative Binomial (ZINB) could be good alternatives to the joint modeling of excess zeros and overdispersion. By one hand, Zero Inflated Poisson (ZIP) models were proposed using the spatial scan statistic to deal with the excess zeros [3]. By the other hand, another spatial scan statistic was based on a Poisson-Gamma mixture model for overdispersion [4]. In this work we present a model which includes inflated zeros and overdispersion simultaneously, based on the ZIDP model. Let the parameter p indicate the zero inflation. As the the remaining parameters of the observed cases map and the parameter p are not independent, the likelihood maximization process is not straightforward; it becomes even more complicated when we include covariates in the analysis. To solve this problem we introduce a vector of latent variables in order to factorize the likelihood, and obtain a facilitator for the maximization process using the E-M (Expectation-Maximization) algorithm. We derive the formulas to maximize iteratively the likelihood, and implement a computer program using the E-M algorithm to estimate the parameters under null and alternative hypothesis. The p-value is obtained via the Fast Double Bootstrap Test [5].ResultsNumerical simulations are conducted to assess the effectiveness of the method. We present results for Hanseniasis surveillance in the Brazilian Amazon in 2010 using this technique. We obtain the most likely spatial clusters for the Poisson, ZIP, Poisson-Gamma mixture and ZIDP models and compare the results.ConclusionsThe Zero Inflated Double Poisson Spatial Scan Statistic for disease cluster detection incorporates the flexibility of previous models, accounting for inflated zeros and overdispersion simultaneously.The Hanseniasis study case map, due to excess of zero cases counts in many municipalities of the Brazilian Amazon and the presence of overdispersion, was a good benchmark to test the ZIDP model. The results obtained are easier to understand compared to each of the previous spatial scan statistic models, the Zero Inflated Poisson (ZIP) model and the Poisson-Gamma mixture model for overdispersion, taken separetely. The E-M algorithm and the Fast Double Bootstrap test are computationally efficient for this type of problem.

In Nigeria, literature on the integration of traffic of pavement condition and traffic characteristics in predicting road traffic accident frequency on 2-lane highways are scanty, hence this article to fill the gap. A comparison of road traffic accident frequency prediction models on IIesha-Akure-Owo road based on the data observed between 2012 and 2014 is presented. Negative Binomial (NB), Ordered Logistic (OL) and Zero Inflated Negative Binomial (ZINB) models were used to model the frequency of road traffic accident occurrence using road traffic accident data from the Federal Road Safety Commission (FRSC) and pavement conditions parameters from pavement evaluation unit of the Federal Ministry of Works, Kaduna. The explanatory variables were: annual average daily traffic (aadt), shoulder factor (sf), rut depth (rd), pavement condition index (pci), and international roughness index (iri). The explanatory variables that were statistically significant for the three models are aadt, sf and iri with the estimated coefficients having the expected signs. The number of road traffic accident on the road increases with the traffic volume and the international roughness index while it decreases with shoulder factor. The systematic variation explained by the models amounts to 87.7, 78.1 and 74.4% for NB, ZINB and OL respectively. The research findings suggest the accident prediction models that should be integrated into pavement rehabilitation.
 
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Evaluating the speed camera sites selection criteria in the UK

Road traffic safety is a social issue of widespread concern. It is important for traffic managers to understand the distribution patterns of road traffic accidents. To this end, this study examines the spatial and temporal patterns of road traffic accidents from both accident frequency and accident severity perspectives. Road traffic accident data from 2016 to 2018 in Harbin, China, were used for the analysis. First, the spatial localization of accidents was completed using geocoding, and the localized accident data were classified by season. Then, density analysis was performed both with and without considering road network density. The results of the density analysis showed that when road network density was considered, accidents were mainly distributed in urban centers, while accidents were more dispersed when road network density was not considered. Third, a cluster analysis considering accident severity found that low-severity accident clusters occurred mostly in urban centers. High-severity accident clusters were mostly present in suburban areas. Finally, the results of these two methods are shown by using the comap technique. Areas of the city with a high frequency and severity of crashes in each season were identified. This study will help traffic management to have a more visual and intuitive understanding of the urban traffic safety situation and to take targeted measures to improve it accordingly.

Traffic data is a fundamental component for applications and researches in transportation systems. However, real traffic data collected from loop detectors or other channels often include missing data which affects the relative applications and researches. This paper proposes an approach based on deep learning to impute the missing traffic data. The proposed approach treats the traffic data including observed data and missing data as a whole data item and restores the complete data with the deep structural network. The deep learning approach can discover the correlations contained in the data structure by a layer-wise pre-training and improve the imputation accuracy by conducting a fine-tuning afterwards. The authors analyze the imputation patterns that can be realized with the proposed approach and conduct a series of experiments. The results show that the proposed approach can keep a stable error under different traffic data missing rate. Deep learning is promising in the field of traffic data imputation.

Most of the existing methodologies for evaluating heterogeneity in zero-inflated Poisson (ZIP) models are often assuming that the Poisson mean is a function of nuisance parameters. However, these nuisance parameters can be misspecified when performing these methodologies, the validity and the power of the test may be affected. In this article, we primarily focus on investigating the impact of misspecification on the performance of score test for homogeneity in ZIP models. Through an intensive simulation study, we find that: 1) under misspecification, the limiting distribution of the score test statistic under the null no longer follows a distribution. A parametric bootstrap methodology is suggested to use to find the true null limiting distribution of the score test statistic; 2) the power of the test decreases as the number of covariates in the Poisson mean increases. The test with a constant Poisson mean has the highest power, even compared to the test with a well-specified mean. At last, simulation results are applied to the Wuhan Inpatient Care Insurance data which contain excess zeros.

Objective To establish an autoregression moving average (ARMA) model for predicting general traffic accidents and analyzing distributional difference on time series and frequency of common traffic accident so as to provide certain basis for a prediction model with better stability and accuracy. Methods The data of road traffic accidents in one newly developed zone of Chongqing in 2000-2005 were collected. The monthly distribution regularity of road traffic accidents was analyzed with descriptive epidemiologic method. ARMA model was set up for retrospective and prospective prediction. The predicted data were compared. Results Based on the characteristics of monthly distribution, the frequency of general traffic accidents in this area showed a cyclic fashion. The frequency of general traffic accidents predicted by ARMA model had over 80% of coincidence with the actual value. Conclusion The ARMA model can be used to predict the frequency of general traffic accidents, with better accuracy of short-term prediction than the long-term prediction. Key words: Accidents, traffic; ARMA; Time series; Prediction model

Along with the development of the economy and society and the speedy increasing number of personal vehicles, especially motorcycles, many cities in developing countries like Hanoi (Vietnam) are facing many transportation problems, notably traffic accidents involving motorcyclists. Motorcycle accidents are caused by main human-error factors, and could be considered as the typical grey system with the features of complexity and imperfect information. In this study, a grey relational analysis (GRA) model of the human-error factors is presented to quickly explore the main human-error factors contributing to traffic accidents caused by motorcycles. In this model, the grey relational degree and the grey relational order of each human-error factor also are determined to rank the main contributing human-error factors. Taking the data of road traffic accidents caused by motorcycles in Hanoi, the capital of Vietnam between 2015 and 2017 as experimental data, the grey relational degrees of human-error factors have been analyzed quantitatively through the GRA model. The experimental results show the first three human-error factors include wrong lane shifting, poor road observation, and speeding, respectively. The results also help to conduct effective countermeasures for controlling human errors and reducing road traffic accidents.