Conditional autoregressive negative binomial model for analysis of crash count using Bayesian methods

In order to improve crash occurrence models to account for the influence of various contributing factors, a conditional autoregressive negative binomial （CAR-NB） model is employed to allow for overdispersion （tackled by the NB component）, unobserved heterogeneity and spatial autocorrelation （captured by the CAR process）, using Markov chain Monte Carlo methods and the Gibbs sampler. Statistical tests suggest that the CAR-NB model is preferred over the CAR-Poisson, NB, zero-inflated Poisson, zero-inflated NB models, due to its lower prediction errors and more robust parameter inference. The study results show that crash frequency and fatalities are positively associated with the number of lanes, curve length, annual average daily traffic （AADT） per lane, as well as rainfall. Speed limit and the distances to the nearest hospitals have negative associations with segment-based crash counts but positive associations with fatality counts, presumably as a result of worsened collision impacts at higher speed and time loss during transporting crash victims.

Poisson and Negative Binomial Modeling Techniques for Better Understanding Pasteuria penetrans Spore Attachment on Root-Knot Nematode Juveniles

Pasteuria penetrans controls root knots nematodes （Meloidogyne spp.） either by preventing invasion or by causing female sterility. The greatest control effect ofP. penetrans occurred when an efficient quantity ofP. penetrans spores attached to nematodes cuticle. The number of spores attaching to J2s within a given time increased with increasing the time of attachment. Based to that, we produced attachment data in vitro recorded encumbered nematodes 1, 3, 6 and 9 h after placing nematodes in a standard P. penetrans spore suspensions. From the count data obtained we modeled P. penetrans attachment using the Poisson and the negative binomial distribution. Attachment count data observed to be over dispersed with respect to high numbers of spores sticks on each J2 after at 6 and 9 h after spores application. We concluded that negative binomial distribution was shown to be the most appropriate model to fit the observed data sets considering that P. penetrans spores are clumped.

A Hurdle Negative Binomial Regression Model for Non-Marital Fertility in Namibia

The rise of non-marital fertility, which seems to defy the Bongaarts model by decoupling marriage from fertility, has become a subject of interest in both the developed and developing world. Consequences of non-marital fertility are mostly negative particularly in developing countries. In Namibia, although premarital childbearing has been reported to be high and increasing, no studies have explicitly analyzed factors influencing non-marital fertility. This paper uses data from the 2006/7 Namibia DHS to establish the determinants of non-marital fertility among women by applying a two-part model, with one part to describe the presence of non-marital birth and the other part to explain its intensity （number of children born）. Using the number of children ever born as an outcome, we explored various count data models. Based on the Voung statistics model comparison, we settled for the Hurdle logit Negative Binomial regression to model the number of non-marital births. Non-marital fertility in Namibia is associated with the age, with young women likely to have lower fertility compared to older women. Women with secondary or higher education had lower fertility compared those with no formal education. Findings also show that rural women higher fertility propensity compared to their urban counterparts even though there was no significant difference in fertility intensity. With regard to socio-economic status, fertility intensity decreased as the women got richer. Intervention efforts should focus on promoting education among girls and women especially in rural areas to improve their socio-economic status, reduce teenage pregnancy and non-marital fertility.

Minimum Density Power Divergence Estimator for Negative Binomial Integer-Valued GARCH Models

In this paper,we study a robust estimation method for the observation-driven integervalued time-series models in which the conditional probability mass of current observations is assumed to follow a negative binomial distribution.Maximum likelihood estimator is highly affected by the outliers.We resort to the minimum density power divergence estimator as a robust estimator and showthat it is strongly consistent and asymptotically normal under some regularity conditions.Simulation results are provided to illustrate the performance of the estimator.An application is performed on data for campylobacteriosis infections.

Application of Poisson Regression Model and Negative Binomial Regression Model in Forest Fire Forecasting

A Poisson regression model and a negative binomial regression model(NB model) are often used in areas such as medicine and economy,but rarely in the domestic forestry sector,especially in the forest fire forecasting.Based on the data of forest fire occurrences in Daxing’anling region in 1980- 2005,this paper profoundly analyzes the application conditions and test methods of the two models.The AIC method was used to check the fitting level of the models and the capability of the models for forecasting forest fires was discussed.This study provided necessary theoretical basis and data support for the application of the two models in the field of forestry in China.

A spatially-explicit count data regression for modeling the density of forest cockchafer(Melolontha hippocastani) larvae in the Hessian Ried(Germany)

Background： In this paper, a regression model for predicting the spatial distribution of forest cockchafer larvae in the Hessian Ried region （Germany） is presented. The forest cockchafer, a native biotic pest, is a major cause of damage in forests in this region particularly during the regeneration phase. The model developed in this study is based on a systematic sample inventory of forest cockchafer larvae by excavation across the Hessian Ried. These forest cockchafer larvae data were characterized by excess zeros and overdispersion. Methods： Using specific generalized additive regression models, different discrete distributions, including the Poisson, negative binomial and zero-inflated Poisson distributions, were compared. The methodology employed allowed the simultaneous estimation of non-linear model effects of causal covariates and, to account for spatial autocorrelation, of a 2-dimensional spatial trend function. In the validation of the models, both the Akaike information criterion （AIC） and more detailed graphical procedures based on randomized quantile residuals were used. Results： The negative binomial distribution was superior to the Poisson and the zero-inflated Poisson distributions, providing a near perfect fit to the data, which was proven in an extensive validation process. The causal predictors found to affect the density of larvae significantly were distance to water table and percentage of pure clay layer in the soil to a depth of I m. Model predictions showed that larva density increased with an increase in distance to the water table up to almost 4 m, after which it remained constant, and with a reduction in the percentage of pure clay layer. However this latter correlation was weak and requires further investigation. The 2-dimensional trend function indicated a strong spatial effect, and thus explained by far the highest proportion of variation in larva density. Conclusions： As such the model can be used to support forest practitioners in their decision making for regeneration and forest protection planning in the Hessian predicting future spatial patterns of the larva density is still comparatively weak. Ried. However, the application of the model for somewhat limited because the causal effects are

The Need for Structural Adjustment: Was It Essential for African Countries over the Decade of the 80’s? An Econometric Analysis Using Count Data Models

Several economists agree to say that the need for adjustment was essential for African countries over the decade of the 80’s. The econometric analysis of a sample of 28 sub-Saharan African countries, from variables regarded as “representatives” for the adjustment objectives, proves that this assertion cannot be completely rejected.

Road Crash Prediction Models: Different Statistical Modeling Approaches

Road crash prediction models are very useful tools in highway safety, given their potential for determining both the crash frequency occurrence and the degree severity of crashes. Crash frequency refers to the prediction of the number of crashes that would occur on a specific road segment or intersection in a time period, while crash severity models generally explore the relationship between crash severity injury and the contributing factors such as driver behavior, vehicle characteristics, roadway geometry, and road-environment conditions. Effective interventions to reduce crash toll include design of safer infrastructure and incorporation of road safety features into land-use and transportation planning;improvement of vehicle safety features;improvement of post-crash care for victims of road crashes;and improvement of driver behavior, such as setting and enforcing laws relating to key risk factors, and raising public awareness. Despite the great efforts that transportation agencies put into preventive measures, the annual number of traffic crashes has not yet significantly decreased. For in-stance, 35,092 traffic fatalities were recorded in the US in 2015, an increase of 7.2% as compared to the previous year. With such a trend, this paper presents an overview of road crash prediction models used by transportation agencies and researchers to gain a better understanding of the techniques used in predicting road accidents and the risk factors that contribute to crash occurrence.

Statistical Modeling of Malaria Incidences in Apac District, Uganda

Malaria is a major cause of morbidity and mortality in Apac district, Northern Uganda. Hence, the study aimed to model malaria incidences with respect to climate variables for the period 2007 to 2016 in Apac district. Data on monthly malaria incidence in Apac district for the period January 2007 to December 2016 was obtained from the Ministry of health, Uganda whereas climate data was obtained from Uganda National Meteorological Authority. Generalized linear models, Poisson and negative binomial regression models were employed to analyze the data. These models were used to fit monthly malaria incidences as a function of monthly rainfall and average temperature. Negative binomial model provided a better fit as compared to the Poisson regression model as indicated by the residual plots and residual deviances. The Pearson correlation test indicated a strong positive association between rainfall and malaria incidences. High malaria incidences were observed in the months of August, September and November. This study showed a significant association between monthly malaria incidence and climate variables that is rainfall and temperature. This study provided useful information for predicting malaria incidence and developing the future warning system. This is an important tool for policy makers to put in place effective control measures for malaria early enough.

Assessing the Effect of Climate Factors on Dengue Incidence via a Generalized Linear Model

Changes in climate factors such as temperature, rainfall, humidity, and wind speed are natural processes that could significantly impact the incidence of infectious diseases. Dengue is a widespread disease that has often been documented when it comes to the impact of climate change. It has become a significant concern, especially for the Malaysian health authorities, due to its rapid spread and serious effects, leading to loss of life. Several statistical models were performed to identify climatic factors associated with infectious diseases. However, because of the complex and nonlinear interactions between climate variables and disease components, modelling their relationships have become the main challenge in climate-health studies. Hence, this study proposed a Generalized Linear Model (GLM) via Poisson and Negative Binomial to examine the effects of the climate factors on dengue incidence by considering the collinearity between variables. This study focuses on the dengue hot spots in Malaysia for the year 2014. Since there exists collinearity between climate factors, the analysis was done separately using three different models. The study revealed that rainfall, temperature, humidity, and wind speed were statistically significant with dengue incidence, and most of them shown a negative effect. Of all variables, wind speed has the most significant impact on dengue incidence. Having this kind of relationships, policymakers should formulate better plans such that precautionary steps can be taken to reduce the spread of dengue diseases.

Spatial Evolution and Locational Determinants of High-tech Industries in Beijing

Using datasets on high-tech industries in Beijing as empirical studies, this paper attempts to interpret spatial shift of high-tech manufacturing firms and to examine the main determinants that have had the greatest effect on this spatial evolution. We aimed at merging these two aspects by using firm level databases in 1996 and 2010. To explain spatial change of the high-tech firms in Beijing, the Kernel density estimation method was used for hotspot analysis and detection by comparing their locations in 1996 and 2010, through which spatial features and their temporal changes could be approximately plotted. Furthermore, to provide quantitative results, Ripley′s K-function was used as an instrument to reveal spatial shift and the dispersion distance of high-tech manufacturing firms in Beijing. By employing a negative binominal regression model, we evaluated the main determinants that have significantly affected the spatial evolution of high-tech manufacturing firms and compared differential influence of these locational factors on overall high-tech firms and each sub-sectors. The empirical analysis shows that high-tech industries in Beijing, in general, have evident agglomeration characteristics, and that the hotspot has shifted from the central city to suburban areas. In combination with the Ripley index, this study concludes that high-tech firms are now more scattered in metropolitan areas of Beijing as compared with 1996. The results of regression model indicate that the firms′ locational decisions are significantly influenced by the spatial planning and regulation policies of the municipal government. In addition, market processes involving transportation accessibility and agglomeration economy have been found to be important in explaining the dynamics of locational variation of high-tech manufacturing firms in Beijing. Research into how markets and the government interact to determine the location of high-tech manufacturing production will be helpful for policymakers to enact effective policies toward a more efficient urban spatial structure.

The Impacts of Mosquito Density and Meteorological Factors on Dengue Fever Epidemics in Guangzhou, China, 2006-2014: a Time-series Analysis

Objective To explore the associations between the monthly number of dengue fever（DF） cases and possible risk factors in Guangzhou, a subtropical city of China. Methods The monthly number of DF cases, Breteau Index （BI）, and meteorological measures during 2006-2014 recorded in Guangzhou, China, were assessed. A negative binomial regression model was used to evaluate the relationships between BI, meteorological factors, and the monthly number of DF cases. Results A total of 39,697 DF cases were detected in Guangzhou during the study period. DF incidence presented an obvious seasonal pattern, with most cases occurring from June to November. The current month＇s BI, average temperature （Tare）, previous month＇s minimum temperature （Train）, and Tare were positively associated with DF incidence. A threshold of 18.25℃ was found in the relationship between the current month＇s Tmin and DF incidence. Conclusion Mosquito density, Tove, and Tmin play a critical role in DF transmission in Guangzhou. These findings could be useful in the development of a DF early warning system and assist in effective control and prevention strategies in the DF epidemic.

Safety Analysis of Riding at Intersection Entrance Using Video Recognition Technology

To study riding safety at intersection entrance,video recognition technology is used to build vehicle-bicycle conflict models based on the Bayesian method.It is analyzed the relationship among the width of nonmotorized lanes at the entrance lane of the intersection,the vehicle-bicycle soft isolation form of the entrance lane of intersection,the traffic volume of right-turning motor vehicles and straight-going non-motor vehicles,the speed of right-turning motor vehicles,and straight-going non-motor vehicles,and the conflict between right-turning motor vehicles and straight-going nonmotor vehicles.Due to the traditional statistical methods,to overcome the discreteness of vehicle-bicycle conflict data and the differences of influencing factors,the Bayesian random effect Poisson-log-normal model and random effect negative binomial regression model are established.The results show that the random effect Poisson-log-normal model is better than the negative binomial distribution of random effects;The width of non-motorized lanes,the form of vehicle-bicycle soft isolation,the traffic volume of right-turning motor vehicles,and the coefficients of straight traffic volume obey a normal distribution.Among them,the type of vehicle-bicycle soft isolation facilities and the vehicle-bicycle traffic volumes are significantly positively correlated with the number of vehicle-bicycle conflicts.The width of non-motorized lanes is significantly negatively correlated with the number of vehicle-bicycle conflicts.Peak periods and flat periods,the average speed of right-turning motor vehicles,and the average speed of straight-going non-motor vehicles have no significant influence on the number of vehicle-bicycle conflicts.

An Alternative Regression-Based Approach to Estimate the Crash Modification Factors of Multiple Treatments Using Before-and-After Data

Before-and-after methods have been effectively used in the road safety studies to estimate Crash Modification Factors (CMFs) of individual treatments as well as the multiple treatments on roadways. Since the common practice is to apply multiple treatments on road segments, it is important to have a method to estimate CMFs of individual treatment so that the effect of each treatment towards improving the road safety can be identified. Even though there are methods introduced by researchers to combine multiple CMFs or to isolate the safety effectiveness of individual treatment from CMFs developed for multiple treatments, those methods have to be tested before using them. This study considered two multiple treatments namely 1) Safety edge with lane widening 2) Adding 2 ft paved shoulders with shoulder rumble strips and/or asphalt resurfacing. The objectives of this research are to propose a regression-based method to estimate individual CMFs estimate CMFs using before-and-after Empirical Bayes method and compare the results. The results showed that having large sample size gives accurate predictions with smaller standard error and p-values of the considered treatments. Also, results obtained from regression method are similar to the EB method even though the values are not exactly the same. Finally, it was seen that the safety edge treatment reduces crashes by 15% - 25% and adding 2 ft shoulders with rumble strips reduces crashes by 25% - 49%.

Predictors of the Aggregate of COVID-19 Cases and Its Case-Fatality: A Global Investigation Involving 120 Countries

Objective: Since the identification of COVID-19 in December 2019 as a pandemic, over 4500 research papers were published with the term “COVID-19” contained in its title. Many of these reports on the COVID-19 pandemic suggested that the coronavirus was associated with more serious chronic diseases and mortality particularly in patients with chronic diseases regardless of country and age. Therefore, there is a need to understand how common comorbidities and other factors are associated with the risk of death due to COVID-19 infection. Our investigation aims at exploring this relationship. Specifically, our analysis aimed to explore the relationship between the total number of COVID-19 cases and mortality associated with COVID-19 infection accounting for other risk factors. Methods: Due to the presence of over dispersion, the Negative Binomial Regression is used to model the aggregate number of COVID-19 cases. Case-fatality associated with this infection is modeled as an outcome variable using machine learning predictive multivariable regression. The data we used are the COVID-19 cases and associated deaths from the start of the pandemic up to December 02-2020, the day Pfizer was granted approval for their new COVID-19 vaccine. Results: Our analysis found significant regional variation in case fatality. Moreover, the aggregate number of cases had several risk factors including chronic kidney disease, population density and the percentage of gross domestic product spent on healthcare. The Conclusions: There are important regional variations in COVID-19 case fatality. We identified three factors to be significantly correlated with case fatality.

Prediction of the Number of Tuberculosis Cases and Estimation of Its Treatment Cost in Saudi Arabia Using Proxy Information

It is well known that the number of people with Tuberculosis (TB) and those who develop multidrug resistance (MDR) are the fundamental components that affect the total cost of treatment of TB. This paper has two-fold objectives. Firstly, we use the Generalized Linear Regression Models (GLM) to predict the future count of persons with TB and MDR. Due to the fact that assessment of TB cost is methodologically difficult, and compounded with the lack of concrete information about the treatment cost in Saudi Arabia, our second objective is to use cost information from the EU countries as proxy to estimate the cost of treating TB. The cost predictions provide essential information that is part of the evidence needed for budgeting and financing the health care facilities of TB services, especially with respect to avoiding under-estimation of the cost of TB-MDR treatment.

Statistical Data Analyses on Aircraft Accidents in Japan: Occurrences, Causes and Countermeasures

We investigate the major characteristics of the occurrences, causes of and counter measures for aircraft accidents in Japan. We apply statistical data analysis and mathematical modeling techniques to determine the relations among economic growth, aviation demand, the frequency of aircraft/helicopter accidents, the major characteristics of the occurrence intervals of accidents, and the number of fatalities due to accidents. The statistical model analysis suggests that the occurrence intervals of accidents and the number of fatalities can be explained by probability distributions such as the exponential distribution and the negative binomial distribution, respectively. We show that countermeasures for preventing accidents have been developed in every aircraft model, and thus they have contributed to a significant decrease in the number of accidents in the last three decades. We find that the major cause of accidents involving large airplanes has been weather, while accidents involving small airplanes and helicopters are mainly due to the pilot error. We also discover that, with respect to accidents mainly due to pilot error, there is a significant decrease in the number of accidents due to the aging of airplanes, whereas the number of accidents due to weather has barely declined. We further determine that accidents involving small and large airplanes mostly occur during takeoff and landing, whereas those involving helicopters are most likely to happen during flight. In order to decrease the number of accidents, i) enhancing safety and security by further developing technologies for aircraft, airports and air control radars, ii) establishing and improving training methods for crew including pilots, mechanics and traffic controllers, iii) tightening public rules, and iv) strengthening efforts made by individual aviation-related companies are absolutely necessary.

Weather Impact on Heat-Related Illness in a Tropical City State, Singapore

In this article we propose a novel hurdle negative binomial (HNB) regression combined with a distributed lag nonlinear model (DLNM) to model weather factors’ impact on heat related illness (HRI) in Singapore. AIC criterion is adopted to help select proper combination of weather variables and check their lagged effect as well as nonlinear effect. The process of model selection and validation is demonstrated. It is observed that the predicted occurrence rate is close to the observed one. The proposed combined model can be used to predict HRI cases for mitigating HRI occurrences and provide inputs for related public health policy considering climate change impact.

Ruin Probability and Joint Distributions of Some Actuarial Random Vectors in the Compound Pascal Model

The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U（T - 1）, ｜U（T）｜ and inf U（n） （i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery） and the distributions of some actuarial random vectors.

The spatial patterns and determinants of internal migration of older adults in China from 1995 to 2015

Although China was one of the countries with the fastest-growing aging population in the world,limited scholarly attention has been paid to migration among older adults in China.The full picture of their migration in the entire country over time remains unknown.This study examines the spatial patterns of older interprovincial migration flows and their drivers in China over the period 1995 to 2015,using four waves of census data and intercensal population sample survey data.Results from eigenvector spatial filtering negative binomial regressions indicate that older adults tend to migrate away from low cost-of-living rural areas to high cost-of-living urban and rural areas,moving away from areas with extreme temperature differences.The location of their grandchildren is among the most important attractions.Our findings suggest that family-oriented migration is more common than amenity-led migration among retired Chinese older adults,and the cost-of-living is an indicator of economic opportunities for adult children and the quality of senior care services.