Bivariate Negative Binomial Regression Research Articles

Copula-based bivariate count data regression models for simultaneous estimation of crash counts based on severity and number of vehicles

Statistical models of crash frequency typically apply univariate regression models to estimate total crash frequency or crash counts by various categories. However, a possible correlation between the dependent variables or unobserved variables associated with the dependent variables is not considered when univariate models are used to estimate categorized crash counts—such as different severity levels or numbers of vehicles involved. This may lead to inefficient parameter estimates compared to multivariate models that directly consider these correlations. This paper compares the results obtained from univariate negative binomial regression models of property-damage only (PDO) and fatal plus injury (FI) crash frequencies to models using traditional bivariate and copula-based bivariate negative binomial regression models. A similar comparison was made using models for the expected crash frequency of single- (SV) and multi-vehicle (MV) crashes. The models were estimated using two-lane, two-way rural highway segment-level data from an engineering district in Pennsylvania. The results show that all bivariate negative binomial models (with or without copulas) outperformed the corresponding univariate negative binomial models for PDO and FI, as well as SV and MV, crashes. Second, the statistical association of various traffic and roadway/roadside features with PDO and FI, as well as SV and MV crashes, were not the same relative to their corresponding relationships in the univariate models. The bivariate negative binomial model with normal copula outperformed all other models based on the goodness-of-fit statistics. The results suggest that copula-based bivariate negative binomial regression models may be a valuable alternative for univariate models when simultaneously modeling two disaggregate levels of crash counts.

Bivariate Negative Binomial Regression for Modelling Covid-19 Confirmed Cases and Death Cases in Kalimantan

Coronavirus disease (Covid-19) caused a pandemic severely affecting various sectors and paralyzed health services in Indonesia. As of June 2020, the percentage of Covid-19 confirmed cases in Kalimantan, the second largest island in Indonesia, contributed about 7% of the total national cases. In the same period, the percentage of Covid-19 deaths reached 12% of the national figure. This study used regression models to respond to bi-response count data consisting of Covid-19 confirmed cases and Covid-19 deaths in regencies/cities in Central Kalimantan and South Kalimantan provinces. This study compared the results of bivariate Poisson regression and bivariate negative binomial regression. There were thirteen predictors representing the determinants of health, social, economic, and demography indicators. The results showed that the prevalence of pneumonia had positive effect on Covid-19 confirmed cases and Covid-19 deaths. The percentage of elderly had negative effect on confirmed cases, while it had no significant effect on Covid-19 deaths. Bivariate negative binomial regression showed more satisfying performance on modeling Covid-19 cases and Covid-19 deaths jointly because it produced lower AIC and deviance than that of Poisson one. The negative bivariate model was also better than the Poisson one because it was able to overcome over-dispersion.

Geographically weighted negative bivariate binomial regression for modelling the number of dengue diseases and their mortality in East Nusa Tenggara, Indonesia

Dengue disease usually occurs in tropical countries. In 2020, East Nusa Tenggara (NTT), Indonesia was the highest number in the mortality of dengue. For that reason, analysis of spread dengue is indispensable. One of the statistical modelling methods to spread dengue and its factors based on spatial analysis is Geographically Weighted Regression (GWR). GWR was developed to Geographically Weighted Poisson Regression (GWPR) and Geographically Weighted Negative Binomial Regression (GWNB) as handling overdispersion. GWNB has improvement analysis into Geographically Weighted Bivariate Negative Binomial regression (GWBNB) model. This paper applied the GWBNB model for the number of dengue cases and their mortality (as dependent variables) based on population density, percentage of poverty, the number of doctors, the number of health facilities, and the percentage of the area that has good sanitation (as independent variables). It resulted from the BNB model, the factors that impacted the dengue’s number and their mortality were poverty, health facilities, and the percentage of areas with good sanitation. In BNB model resulted in 364.4725 of AIC. However, the spatial testing has shown spatial contiguity of dengue’s number and their mortality. As a result of the GWBNB model, shown most of the variables were significant and it established the cluster based on its estimation. Besides, with the GWBNB model, the heterogeneity of spatial can be solved. The accuracy of GWBNB estimation was 73% for predict the number of dengue and their mortality in East Nusa Tenggara, Indonesia. The GWBNB model resulted better than the BNB model based on AIC’s value.

Exploring the Need to Model Two- and Multiple-Vehicle Crashes Separately

Single-vehicle crashes have been shown to differ from two-plus vehicle crashes. Several studies have discussed the issues with modeling single-vehicle and two-plus vehicle crashes together. However, none of the empirical studies have attempted to study two-vehicle (2V) and multiple-vehicle (MV), that is, three-plus crash groups, to understand their correlation and influencing factors. This study first investigated whether there is a need to develop separate safety performance functions for 2V and MV crashes, in addition to single-vehicle crashes. Then, the correlation and influencing factors of 2V and MV were evaluated. Three regression models—a correlated bivariate negative binomial regression (BNR) model, an uncorrelated bivariate negative binomial regression (NR) model, and a univariate negative binomial regression (UNR) model, were developed and compared. The analysis was based on the 2011–2015 crashes that occurred on I-4 in Florida. Findings indicated that the BNR model significantly outperformed the NR and the UNR models. The model results suggest that disaggregating 2V and MV crashes while allowing correlation between the groups for the latent effects in the model best describes the data. Traffic volume, posted speed limit, and median type were found significant in contributing to the occurrence of both 2V and MV crashes. Additional contributing factors for 2V crashes included the presence of interchange influence area, and for MV crashes, the presence of a vertical curve and the presence of a horizontal curve. Study findings could assist transportation officials in implementing specific safety countermeasures for road segments identified as hotspots for 2V and MV crashes.

Homocysteine and long-term recurrent infarction following an acute coronary syndrome.

There are no well-established predictors of recurrent ischemic coronary events after an acute coronary syndrome (ACS). Higher levels of homocysteine have been reported to be associated with an increased atherosclerotic burden. The primary endpoint was to assess the relationship between homocysteine at discharge and very long-term recurrent myocardial infarction (MI). 1306 consecutive patients with ACS were evaluated (862 with non-ST-segment elevation ACS [NSTEACS] and 444 with ST-segment elevation myocardial infarction [STEMI]) discharged from October 2000 to June 2003 in a single teaching-center. The relationship between homocysteine at discharge and recurrent MI was evaluated through bivariate negative binomial regression accounting for mortality as a competitive event. The mean age was 66.8 ± 12.4 years, 69.1% were men, and 32.2% showed prior diabetes mellitus. Most of the patients were admitted for an NSTEACS (66.0%). The median (interquartile range) GRACE risk score, Charlson comorbidity index, and homocysteine were 144 (122-175) points, 1 (1-2) points, and 11.9 (9.3-15.6) μmol/L, respectively. In-hospital revascularization was performed in 26.3% of patients. At a median follow-up of 9.7 (4.5-15.1) years, 709 (54.3%) deaths were registered and 779 recurrent MI in 478 (36.6%) patients. The rates of recurrent MI were higher in patients in the upper homocysteine quartiles (p < 0.001). After a multivariate adjustment, homocysteine along its continuum remained almost linearly associated with a higher risk of recurrent MI (p = 0.001) and all-cause mortality (p < 0.001). In patients with ACS, higher homocysteine levels identified those at a higher risk of recurrent MI at very long-term follow-up.

Geographically weighted negative bivariate binomial regression for modelling the number of dengue diseases and their mortality in East Nusa Tenggara, Indonesia

Dengue disease usually occurs in tropical countries. In 2020, East Nusa Tenggara (NTT), Indonesia was the highest number in the mortality of dengue. For that reason, analysis of spread dengue is indispensable. One of the statistical modelling methods to spread dengue and its factors based on spatial analysis is Geographically Weighted Regression (GWR). GWR was developed to Geographically Weighted Poisson Regression (GWPR) and Geographically Weighted Negative Binomial Regression (GWNB) as handling overdispersion. GWNB has improvement analysis into Geographically Weighted Bivariate Negative Binomial regression (GWBNB) model. This paper applied the GWBNB model for the number of dengue cases and their mortality (as dependent variables) based on population density, percentage of poverty, the number of doctors, the number of health facilities, and the percentage of the area that has good sanitation (as independent variables). It resulted from the BNB model, the factors that impacted the dengue’s number and their mortality were poverty, health facilities, and the percentage of areas with good sanitation. In BNB model resulted in 364.4725 of AIC. However, the spatial testing has shown spatial contiguity of dengue’s number and their mortality. As a result of the GWBNB model, shown most of the variables were significant and it established the cluster based on its estimation. Besides, with the GWBNB model, the heterogeneity of spatial can be solved. The accuracy of GWBNB estimation was 73% for predict the number of dengue and their mortality in East Nusa Tenggara, Indonesia. The GWBNB model resulted better than the BNB model based on AIC’s value.

Estimation of Location and Extent of Labral Tear Based on Preoperative Range of Motion in Patients Undergoing Arthroscopic Stabilization for Anterior Shoulder Instability

PurposeTo determine whether range of motion (ROM) varies with the location and extent of labral tear seen in patients undergoing arthroscopic anterior shoulder stabilization.MethodsConsecutive patients undergoing arthroscopic anterior shoulder stabilization who were enrolled in the Multicenter Orthopaedic Outcomes Network Shoulder Instability database underwent a preoperative physical examination and intraoperative examination under anesthesia in which ROM was recorded. Intraoperatively, the location and extent of the labral tear was recorded using conventional clock-face coordinates. Patients were grouped by combinations of quadrants involved in the labral tear (G1-G7): G1 = anterior only, G2 = anterior + inferior, G3 = anterior + inferior + posterior, G4 = all quadrants, G5 = superior + anterior, G6 = superior + anterior + inferior, and G7 = posterior + superior + anterior. Statistical analyses were performed with the Kruskal–Wallis rank-sum test. When P < .05, a post-hoc Dunn’s test was performed. For categorical variables, the χ2 test was performed. We performed a series of bivariate negative binomial regression models testing pairwise combinations of ROM parameters predicting the count of labral tear locations (possible: 0-5) within each quadrant.ResultsA total of 467 patients were included, with 13 (2.8%) in G1, 221 (47.3%) in G2, 40 (8.6%) in G3, 51 (10.9%) in G4, 18 (3.9%) in G5, 121 (25.9%) in G6, and 3 (0.6%) in G7. Multiple statistically significant differences were noted in ROM, specifically active internal rotation at side (IRS) (P = .005), active abduction (P = .02), passive IRS (P = .02), and passive external rotation in abduction (P = .0007). Regression modeling revealed a positive correlation between passive abduction and predicted count of labral tear locations in the superior quadrant and between passive IRS and predicted count of labral tear location in the inferior quadrant.ConclusionsIn patients undergoing arthroscopic shoulder stabilization for anterior instability, ROM varies with location and extent of labral tear. However, the clinical relevance of such small ROM differences remains undetermined.Level of evidenceII, prospective comparative study.

An Economic Analysis of Tropical Forest Resource Conservation in a Protected Area

In this paper, we develop a reduced form model for factors influencing the conservation of forest resources. We then estimate it using a bivariate negative binomial regression model with cases of illegal farming and illegal cattle grazing in the W Reserve in West Africa. Our results show that population size and farm area in the periphery of the W Reserve are associated with an increase of 2.4% and 7.1% of the illegal farming, respectively. On the other hand, income level, the existence of a checkpoint, and the distance between the villages and the reserve decrease the illegal grazing activities by 7.3%, 63.2%, and 2.3%, respectively.

Modelling of Diarrheal Sufferers Percentage and Certified Drink Water Providers in East Java Using Bivariate Binomial Negative Regression Method

Diarrheal is a disease with the condition of faeces becoming soft or fluid. In general, diarrheal results from food and drinks exposed to viruses, bacteria or parasites. Diarrheal is one of the health problems of people in poor and developing countries. Diarrheal often occurs due to the lack of clean water that pass health requirements. The method used in this research is bivariate negative binomial regression which is a regression method to model a pair of response variables, each of which has a negative binomial distribution and correlates. This study uses 38 secondary data from the East Java Provincial Health Office in 2016 about the number of diarrheal sufferers and the number of certified drink water providers which pass health requirements. The results of this research, there are 4 factors that significantly influence the model of diarrheal sufferers and drink water providers who pass health requirements, that are the percentage of residents with access to proper sanitation, public places that pass health requirements, population literacy rates and food management places tested.

Modeling of HIV and AIDS in Indonesia Using Bivariate Negative Binomial Regression

The problem of HIV and AIDS in Indonesia is a frightening health problem with a number of cases that tend to increase each year. The aim of this research is to model the number of HIV and AIDS cases in Indonesia using bivariate negative binomial regression approach. Bivariate negative binomial regression is a regression method for modeling a pair of response variables in the form of count data with negative binomial distribution and correlating to each other. This research uses secondary data from the ministry of health in 2017 about the number of HIV and AIDS cases in Indonesia. From the results of this research, we obtained the deviance value of 38.9197 which was used to describe the goodness of fit test.

The Mediating Role of Sleep Quality and Quantity in the Link Between Food Insecurity and Obesity Across Race and Ethnicity.

The objective of the study was to examine the mediating role of sleep quality and quantity in the relationship between food insecurity and obesity across races/ethnicities. Bivariate negative binomial regression and multinomial logistic regression were used to examine direct associations between food insecurity and sleep quality and quantity among non-Hispanic Native Hawaiian and other Pacific Islanders (NHPI) relative to non-Hispanic White, Black, Asian, and Hispanic individuals with obesity. The potential outcomes approach and adjusted Wald test were used to explore the mediating role of sleep quality and quantity and the moderating role of race/ethnicity, respectively. Among adults with obesity, the study found a positive and direct relationship between food insecurity and trouble falling asleep in each racial/ethnic group. Trouble staying asleep was associated with food insecurity in each racial/ethnic group, except in the Asian group. Positive and direct associations were observed between food insecurity and short/very short sleep. A positive and direct relationship was found between food insecurity and having obesity in each racial/ethnic group, except in the Black group. Sleep quality and sleep quantity partially mediated the relationship between food insecurity and obesity in non-Hispanic NHPI, White, Asian, and Hispanic individuals. Race/ethnicity moderated the indirect effects of food insecurity on sleep quality and quantity. Food security and sleep hygiene should be an integral part of the fight against obesity.

Application of bivariate negative binomial regression model in analysing insurance count data

AbstractIn this paper we analyse insurance claim frequency data using the bivariate negative binomial regression (BNBR) model. We use general insurance data on claims from simple third-party liability insurance and comprehensive insurance. We find that bivariate regression, with its capacity for modelling correlation between the two observed claim counts, provides both a superior fit and out-of-sample prediction compared with the more common practice of fitting univariate negative binomial regression models separately to each claim type. Noting the complexity of BNBR models and their potential for a large number of parameters, we explore the use of model shrinkage methodology, namely the least absolute shrinkage and selection operator (Lasso) and ridge regression. We find that models estimated using shrinkage methods outperform the ordinary likelihood-based models when being used to make predictions out-of-sample. We find that the Lasso performs better than ridge regression as a method of shrinkage.

Malaria incidence during early childhood in rural Burkina Faso: Analysis of a birth cohort protected with insecticide-treated mosquito nets

BackgroundEven in the high transmission areas of sub-Saharan Africa (SSA), the incidence of falciparum malaria varies greatly depending on factors such as age, rainfall pattern, distance to breeding places, quality of houses, and existing vector control measures. Insecticide-treated mosquito nets (ITN) have now become the vector control standard in nearly all of SSA. This study aims to describe and analyse the incidence of malaria in a cohort of young children protected with ITN in rural West Africa. MethodsData of a subsample from a large community trial in rural north-western Burkina Faso consisting of 420 children were analysed. The main aim of the trial was to evaluate the long-term effects of ITNs in two groups of new-borns; Group A was protected with ITN from birth onwards while Group B was protected only from month six onwards. The primary objective of this study was to describe malaria incidence in detail with an analysis of the impact of potentially relevant determinants of malaria incidence, in particular age, sex, ITN protection, village, month and season as secondary objective. Bivariate negative binomial regression analysis was used to calculate incidence rate ratios of malaria incidence. Moreover, relevant variables were included in a multivariate negative binomial regression model to examine possible risk factors for malaria. ResultsOut of the 420 study children 387 (92.1%) developed a total of 1822 falciparum malaria episodes; the malaria incidence rate was 7.6 per 1000 child days. Group A children had lower malaria incidence rates compared to group B, but only in early infancy. Malaria incidence varied significantly between villages and increased with age, but no sex-specific differences were observed; these findings were confirmed in the multi-variate analysis. Malaria incidence peaked sharply towards the end of the rainy season in September but there were no differences in the seasonal pattern by study group. ConclusionsThe study, carried out in a high-transmission West African area, shows that malaria incidence remains high in spite of maximum ITN coverage.

Socioeconomic disparities in household secondhand smoke exposure among non-smoking adolescents in the Republic of Korea

ABSTRACTThis nationally representative study examined (a) gender and age differences in household secondhand smoke exposure (HSHSE) and (b) associations between socioeconomic status (SES) and HSHSE among non-smoking Korean adolescents. Two subsamples were analysed: males (n = 25,648) and females (n = 30,240). The HSHSE measures were incidence of HSHSE (yes/no) and number of days of HSHSE (1–7 days); the SES measures were parental education, perceived economic status, and family wealth. For the first aim, chi-square test, t-test, and bivariate negative binomial regression analysis were performed; For the second aim, multivariate logistic regression and negative binomial regression analyses were performed. The incidence and number of days of HSHSE were significantly higher among females (32.35% and 3.48 days) than males (26.83% and 3.08 days). The HSHSE incidence was significantly higher among younger adolescents (23.32% to 31.08% of males and 26.58% to 37.03% of females). Lower SES was associated with (a) greater odds of HSHSE (odds ratio: 1.12–1.58 among males and 1.19–1.85 among females) and (b) greater incidence rates of HSHSE (incidence rate ratio: 1.05–1.17 among males and 1.10–1.14 among females). Efforts should be made to decrease HSHSE among adolescents, particularly low-SES youth.

A crash-prediction model for road tunnels

Considerable research has been carried out into open roads to establish relationships between crashes and traffic flow, geometry of infrastructure and environmental factors, whereas crash-prediction models for road tunnels, have rarely been investigated. In addition different results have been sometimes obtained regarding the effects of traffic and geometry on crashes in road tunnels. However, most research has focused on tunnels where traffic and geometric conditions, as well as driving behaviour, differ from those in Italy. Thus, in this paper crash prediction-models that had not yet been proposed for Italian road tunnels have been developed. For the purpose, a 4-year monitoring period extending from 2006 to 2009 was considered. The tunnels investigated are single-tube ones with unidirectional traffic. The Bivariate Negative Binomial regression model, jointly applied to non-severe crashes (accidents involving material-damage only) and severe crashes (fatal and injury accidents only), was used to model the frequency of accident occurrence. The year effect on severe crashes was also analyzed by the Random Effects Binomial regression model and the Negative Multinomial regression model. Regression parameters were estimated by the Maximum Likelihood Method. The Cumulative Residual Method was used to test the adequacy of the regression model through the range of annual average daily traffic per lane. The candidate set of variables was: tunnel length (L), annual average daily traffic per lane (AADTL), percentage of trucks (%Tr), number of lanes (NL), and the presence of a sidewalk. Both for non-severe crashes and severe crashes, prediction-models showed that significant variables are: L, AADTL, %Tr, and NL. A significant year effect consisting in a systematic reduction of severe crashes over time was also detected. The analysis developed in this paper appears to be useful for many applications such as the estimation of accident reductions due to improvement in existing tunnels and/or to modifications of traffic control systems, as well as for the prediction of accidents when different tunnel design options are compared.

Comparisons of some bivariate regression models

The bivariate negative binomial regression (BNBR) and the bivariate Poisson log-normal regression (BPLR) models have been used to describe count data that are over-dispersed. In this paper, a new bivariate generalized Poisson regression (BGPR) model is defined. An advantage of the new regression model over the BNBR and BPLR models is that the BGPR can be used to model bivariate count data with either over-dispersion or under-dispersion. In this paper, we carry out a simulation study to compare the three regression models when the true data-generating process exhibits over-dispersion. In the simulation experiment, we observe that the bivariate generalized Poisson regression model performs better than the bivariate negative binomial regression model and the BPLR model.

On the bivariate negative binomial regression model

In this paper, a new bivariate negative binomial regression (BNBR) model allowing any type of correlation is defined and studied. The marginal means of the bivariate model are functions of the explanatory variables. The parameters of the bivariate regression model are estimated by using the maximum likelihood method. Some test statistics including goodness-of-fit are discussed. Two numerical data sets are used to illustrate the techniques. The BNBR model tends to perform better than the bivariate Poisson regression model, but compares well with the bivariate Poisson log-normal regression model.

Tests for independence in a bivariate negative binomial model

The score test and LR test statistic for testing independence are proposed in a bivariate negative binomial regression model. We also propose an adjusted score test in order to enhance the efficiency of the score test. This study is an extension of the work in a univariate model by Dean and Lawless [Dean, C., Lawless, F. (1989). Tests for detecting overdispersion in Poisson regression models. Journal of the American Statistical Association, 84, 467–472]. The adjusted score test proposed in this study is more efficient than the complicated LR test.

Score tests for overdispersion in the bivariate negative binomial models

In this paper, we derive the score test statistic for testing overdispersion and covariance parameter in the bivariate negative binomial (BNB) models. The testing procedures are extended to the BNB regression models. Two empirical examples with and without covariates are provided to illustrate the results.

Generalized bivariate count data regression models

This paper proposes a flexible bivariate count data regression model that nests the bivariate negative binomial regression. An application to the demand for health services is given.