Geographically Weighted Negative Binomial Regression Research Articles

Geographically Weighted Zero-Inflated Negative Binomial Regression: A general case for count data

Poisson and Negative Binomial Regression Models are often used to describe the relationship between a count dependent variable and a set of independent variables. However, these models fail to analyze data with an excess of zeros, being Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) models the most appropriate to fit this kind of data. To Incorporate the spatial dimension into the count data models, Geographically Weighted Poisson Regression (GWPR), Geographically Weighted Negative Binomial Regression (GWNBR) and Geographically Weighted Zero-Inflated Poisson Regression (GWZIPR) have been developed, but the zero-inflation part of the negative binomial distribution is undeveloped in order to incorporate the overdispersion and the excess of zeros, as was at the beginning of the COVID-19 pandemic, whereas some places were having an outbreak of cases and in others places, there were no cases yet. Therefore, we propose a Geographically Weighted Zero-Inflated Negative Binomial Regression (GWZINBR) model which can be considered a general case for count data, since locally it can become a GWZIPR, GWNBR or a GWPR model. We applied this model to simulated data and to the cases of COVID-19 in South Korea at the beginning of the pandemic in 2020 and the results showed a better understanding of the phenomenon compared to the GWNBR model.

Local modeling as a solution to the lack of stop-level ridership data

Transit ridership modeling at the bus stop level is an important tool for bus network planning and transit-oriented development. However, many cities, especially in developing countries, face a lack of boarding and alighting data due to the high costs of collection. Solutions based on smartcards often rely on assumptions that negatively affect the data accuracy. Noting that previous studies suggest the existence of spatial heterogeneity and dependence in factors affecting stop-level ridership, the present paper proposes the application of Geographically Weighted Negative Binomial Regression (GWNBR) to modeling the transit ridership along bus lines in São Paulo – SP (Brazil) under missing data conditions. Four important topics are analyzed: 1) whether the spatial variation of predictors' effects is statistically significant; 2) the consistency of parameter estimates; 3) the prediction power sensitivity to missing data scenarios; and 4) the use of network distances replacing the traditional Euclidean ones. Of the five predictors that explained the transit ridership better, overlapping and frequency proved to have coefficients with statistically significant spatial variation. Goodness-of-fit measures indicated that GWNBR is an effective tool to the transit ridership estimation in uncounted bus stops, even when the availability of data is low. GWNBR in missing data scenarios could, in fact, reproduce the spatial pattern of effects shown in the complete database model, for some explanatory variables. Network distances may better represent the spatial relationship between transit ridership and some of its predictors. In addition, GWNBR models were able to address the spatial dependence found in the Negative Binomial Regression.

Stay or travel? Spatial heterogeneity impact of air pollution on travel intention

ABSTRACT Air pollution help shape people's travel preferences and behaviour, and when facing air pollution, individuals may consider travelling out for a short or long time as a coping strategy. We apply a Geographically Weighted Negative Binomial Regression (GWNBR) to analyze the effects of air pollution on people's travel intentions from origins. Our research covers 332 prefecture-level cities across China and collects daily air quality index (AQI), the Baidu indexes of ‘tourism’, and weather data from 2015 and 2018. The results show that AQI is positively associated with people's willingness to travel, and the long-term threat of air deterioration will strengthen people's willingness to flee. We estimate a series of GWNBR models with different air pollutants and cities with varying levels of air quality. The distribution of GWNBR regression results shows a more obvious strip characteristic, with coefficients of AQI in most cities are positive. Residents in cities with better air quality are more sensitive to air deterioration, compared with the residents in heavily polluted cities, who demonstrate a higher tolerance to air pollution. Finally, we provide the theoretical and practical implications of these effects on tourism.

Investigating the effects of POI-based land use on traffic accidents in Suzhou Industrial Park, China

The development of city transportation often promotes prosperity in urban economies, but it can also cause safety issues that adversely affect local residents. It is widely acknowledged that the built environment has a significant impact on traffic accidents. Many studies have shown a link between different land use characteristics and accidents, although these investigations have used different land use characteristic variables, and but few have attempted to allow for spatial heterogeneity. To better understand how urban land use affects the frequency of traffic accidents, this study undertakes a quantitative analysis of the spatial relationship by analyzing the case study of Suzhou Industrial Park, China. We introduce a term frequency-inverse document frequency (TF-IDF) algorithm to identify land use characteristics based on point of interest (POI) data and adopt Geographically Weighted Negative Binomial Regression (GWNBR) model to accomplish this task. This study confirms that local models outperform global models in terms of their explanatory power. The modeling results demonstrate different effects of POI-based land use on traffic accidents and verify the assumption that inherent non-stationarity exists in the estimation of parameters across space.

Localizing safety performance functions for two-way STOP-controlled (TWST) three-leg intersections on rural two-lane two-way (TLTW) roadways in Alabama: A geospatial modeling approach with clustering analysis

Safety Performance Functions (SPFs) can be used to predict the number of crashes for highway facilities by site characteristics, including traffic exposures and other specific site factors. The traditional approach to developing SPFs relies on factors that are observed in the data and has an unstated assumption that the relationships between safety performance and observed factors are stationary. However, there might be factors that are not captured by the data but also have significant impacts on roadway safety performance. These factors can lead to significant unobserved heterogeneity in safety performance at different sites. Failure to capture such unobserved heterogeneity in developing SPFs may result in biases and decrease the predictive accuracy. Given the interactions between highway traffic and roadway environments, the unobserved heterogeneity is likely related to the geographic space of the highway network. This study employs a spatial modeling approach, namely Geographically Weighted Negative Binomial Regression (GWNBR), to incorporate spatial heterogeneity into SPF model estimation. The GWNBR model can generate a local SPF for every site instead of a global SPF for one entire jurisdiction (e.g., a state) from the traditional approach. Local SPFs (or l-SPFs) are high-resolution and may be difficult for practitioners to use. To support the implementation of l-SPFs, this study proposes a method to aggregate l-SPFs to various geographic levels. This study first uses the 2014–2018 geo-referenced crash data from Alabama to develop l-SPFs for two-way STOP-controlled (TWST) three-leg intersections on rural two-lane two-way (TLTW) roadways in the state. The results show that l-SPFs vary substantially across Alabama. For example, the coefficients of traffic volume (AADT) on major roads range from 0.126 to 1.203 across different areas of the state. Then, an aggregation method based on K-means clustering is demonstrated to aggregate l-SPFs to various geographic levels of interest. The l-SPFs and their aggregation provide geographic flexibility in developing countermeasures and allocating funds to improve traffic safety considering local conditions.

Determinants of Multidrug-Resistant Pulmonary Tuberculosis in Indonesia: A Spatial Analysis Perspective

Tuberculosis is caused by Mycobacterium Tuberculosis (MT). MT usually attacks the lungs and causes pulmonary-tuberculosis. Tuberculosis cases in Indonesia keep increasing over the years. The presence of Multidrug-Resistant Tuberculosis (MDR-TB) has been one of the main obstacles in eradicating tuberculosis because it couldn’t be cured using standard drugs. In fact, the success rate of MDR-TB treatment in 2019 at the global level was only 57 percent. Research on MDR-TB can be related to the spatial aspect because this disease can be transmitted quickly. This study aims to obtain an overview and model the number of Indonesia’s pulmonary MDR-TB cases in 2019 using the Geographically Weighted Negative Binomial Regression (GWNBR) method. The independent variables used in the model are population density, percentage of poor population, health center ratio per 100 thousand population, the ratio of health workers per 10 thousand population, percentage of smokers, percentage of the region with PHBS policies, and percentage of BCG immunization coverage. The finding reveals that the model forms 12 regional groups based on significant variables where GWNBR gives better results compared to NBR. The significant spatial correlation implies that the collaboration among regional governments plays an important role in reducing the number of pulmonary MDR-TB.

Segment-Level Spatial Heterogeneity of Arterial Crash Frequency Using Locally Weighted Generalized Linear Models

Decades of literature in traffic crash modeling show the popularity of generalized linear models (GLMs). However, because of the failure to accommodate spatial heterogeneity, parameters estimated with these models are inconsistent and inefficient. In light of that, this study aims to investigate the spatial heterogeneity of crashes aggregated at roadway segment levels using geographically weighted Poisson regression (GWPR) and two variants of the geographically weighted negative binomial regression (GWNBR) model. The results indicate: (i) the GWNBR model with global dispersion parameter outperforms conventional Poisson, GWPR, and negative binomial (NB) models; (ii) the performance of the GWNBR model further enhances as the dispersion parameter becomes spatially non-stationary; (iii) tests of spatial heterogeneity and autocorrelation reveal the existence of non-stationarity and less than 1% likelihood of randomness; and (iv) median of parameter estimates reveal a positive association between crashes and posted speed limit, number of lanes, number of three-leg intersections, number of access points, and vehicle miles traveled (VMT). The study concludes that, when spatial heterogeneity is evident, conventional GLMs should be avoided to circumvent the futile estimation of parameters on the arterial segments. The findings are expected to contribute to the small pool of literature on spatial non-stationarity of parameters in segment-based aggregation, identification and selection of segments with similar influence factors in corridor-level studies, and spatial analysis of arterial crashes.

Modeling Geographically Weighted Negative Binomial Regression (GWNBR) on Stunting Incidence in Malang Regency

Discrete data on the response variable can be analyzed using poisson regression. The assumption of equidispersion in poisson regression must be fulfilled, but in practice there are many problems of overdispersion. The negative binomial regression model is used to overcome the problem of overdispersion, but this model is global while in some cases each location has different characteristics. Therefore, a method that considers the effects of spatial heterogeneity is needed. If the response variable is discrete data that is overdispersed and includes spatial effects, a model called Geographically Weighted Negative Binomial Regression (GWNBR) is developed. The GWNBR method can be applied in the health sector, such as in stunting. The prevalence of stunting in Malang Regency is still quite high, there is 25.7%. By conducting the GWNBR test, 385 models were obtained, one of them is Tulungrejo Village with factors influencing the incidence of stunting, namely access to permanent healthy latrines, access to posyandu, exclusive breastfeeding, population density and community empowerment. From three weights used, namely the Adaptive Gaussian Kernel, Adaptive Bisquare Kernel and Adaptive Tricube Kernel, the best model was obtained from the Adaptive Bisquare Kernel weighting with the smallest AIC is -211.3763.

Geographically Weighted Negative Binomial Regression Modeling using Adaptive Kernel on the Number of Maternal Deaths during Childbirth

The standard model that is used for count data is Poisson Regression. In fact, most of the count data is overdispersed, which means that the response variable has greater variance than the mean. So the Poisson Regression cannot be used because overdispersion can cause inaccurate parameter estimators. One of the most widely used methods to overcome overdispersion is Negative Binomial Regression. If there are spatial effects such as spatial heterogeneity that are taken into Negative Binomial model, the appropriate method to analyze is Geographically Weighted Negative Binomial Regression (GWNBR). A spatial weighting matrix is required in the GWNBR model. In this study, three weighting functions were used, that is Adaptive Gaussian Kernel, Adaptive Bisquare Kernel, and Adaptive Tricube Kernel. From the three weighting functions, a model will be formed and the best model will be selected based on the smallest AIC. Count data used in this study is maternal deaths during childbirth in West Java Province, which is the highest case in Indonesia. The results of the analysis show that based on the smallest AIC, the best modeling in maternal deaths during childbirth in West Java is the GWNBR model using the Adaptive Gaussian Kernel weight. The results of the best model were obtained from three groups based on the predictor variables that had a significant effect.

Spatial analysis of collision risk of child pedestrians – A case of urban elementary school districts in Busan, Korea

A comprehensive understanding of the relationship between pedestrian collision risks for children and the environment is crucial for planning safety policies. Although pedestrian-vehicle collisions are an extensively studied subject in many cities, only a handful of studies focus on children. Previous studies that examined the relationship between pedestrian collision risk for children and environmental factors primarily relied on statistical models, which were limited from accounting for the relationship's spatial heterogeneity. This study takes both statistical and spatial modeling techniques to understand the geography of pedestrian collision risk for children in Busan, Korea. Namely, negative binomial regression and geographically-weighted negative binomial regression were used in modeling the relationship between child pedestrians' collision risk and various environmental factors. Utilizing the collision data from 2014 to 2019, a total of 788 collisions in 297 elementary school districts were analyzed with a set of socioeconomic, transportation, and land-use characteristics. The study found that the geographically-weighted negative binomial regression outperform the negative binomial regression, while both models provided informative results toward characterizing the collision risk of child pedestrians by identifying a set of collision-inducing factors from both global and local perspectives. This study shows that geographically-weighted negative binomial regression is a promising tool for designing safety policies accounting for different regional contexts in various cities. This study found that collision risk varies by school district and local characteristics, thus, a collaborative network between city planners, schools, and local communities is needed to create a safer walking environment for children.

Assessing the safety effect of red-light camera deactivation: a geographically weighted negative binomial regression approach

Municipalities across the country have debated the safety effect of automatic red-light cameras (RLC) and their political and financial implications. Most empirical studies have used the Empirical Bayesian (EB) approach to assess the safe effects to facilitate policy debates. While popular, the EB method has several limitations in data requirement, reference site selection, and control of confounding factors. Moreover, empirical studies of the RLC deactivation effects are limited. This study fills these gaps using the Moran’s I statistic and the Geographically Weighted Negative Binomial Regression (GWNBR) approach for data in the City of Arlington, Texas. The results indicate that the total, injury, and angle crashes in Arlington are on the rise over the study period and that crashes are higher at RLC deactivation intersections than those at other intersections. The direct safety effect of removing RLCs is statistically significant. The spillover effect is observed but statistically insignificant. Speed limit plays an important role in road safety. The findings have significant implications for safety research and practices.

Spatial Analysis of Crime in East Java Province in 2019

Crime is one of the consequences of fluctuations in the economic condition of a country. Crime incidents harm many parties. The number of criminal acts increased in 2019, especially in Sumatra and Java Island. Most provinces experienced an increasing number of criminal acts, one of them was East Java. East Java contributed more than a quarter of the number of crimes throughout Java Island. The number of criminal acts is count data with overdispersion because its variance is higher than its average. This study aims to analyze the number of criminal acts by applying Geographically Weighted Negative Binomial Regression (GWNBR). The result shows that GWNBR formed two regional groups based on significant variables. The four independent variables namely the unemployment rate, the number of poor people, the Gini ratio, and the police population ratio have a significant effect on all districts/cities. However, the mean year of schooling shows a significant effect only in certain districts/cities. The GWNBR is the best model in modelling the number of criminal acts in East Java.

Spatial Modeling of leprosy disease in east java province with spatially varying regression coefficients models.

Indonesia ranks third with the most leprosy cases globally. East Java is the province that has the highest leprosy cases. The Provincial Government socialized the East Java Leprosy Eradication Program, which targets a maximum of one leprosy case per 10,000 residents. We propose spatially varying regression coefficients models to evaluate the effects of risk factors on of leprosy cases in East Java, use Geographically Weighted Generalized Poisson Regression and Geographically Weighted Negative Binomial Regression (GWNBR) models. The best models GWNBR categorize municipalities into six groups based on variables that have a significant impact on leprosy cases. The percentage of households with access to adequate sanitation is a significant factor in determining leprosy cases in all municipalities in East Java. We can conclude that clean and healthy living behavior, health facilities, and health workers significantly affect the number of leprosy cases in East Java.

GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION UNTUK MENANGANI OVERDISPERSI PADA JUMLAH PENDUDUK MISKIN

Poverty is a condition that is often associated with needs, difficulties an deficiencies in various life circumstances. The number of poor people in Indonesia increase in 2020. This research focus on modelling the number of poor people in Indonesia using Geographically Weighted Negative Binomial Regression (GWNBR) method. The number of poor people is count data, so analysis used to model the count data is poisson regression. If there is overdispersion, it can be overcome using negative binomial regression. Meanwhile to see the spatial effect, we can use the Geographically Weighted Negative Binomial Regression method. GWNBR uses a adaptive bisquare kernel for weighting function. GWNBR is better at modelling the number of poor people because it has the smallest AIC value than poisson regression and negative binomial regression. While the GWNBR method obtained 13 groups of province based on significant variables.

Geographically Weighted Negative Binomial Regression (GWNBR) Modeling to Analyze Factors Affecting the Number of New HIV/AIDS Cases on The Island of Java in 2019

One of the problems in the health sector is the HIV/AIDS epidemic. The country of Indonesia itself is in the 5th most at risk of HIV/AIDS in the Asian continent (Ministry of Health of the Republic of Indonesia, 2013). The island of Java as the area with the highest number of cases with a population of about 56 percent of the total population of Indonesia. The purposes of this study are to find out the general description of the distribution of HIV/AIDS in Java and to identify the influencing factors by considering the effect of regional proximity. The results of the analysis show that the distribution of the number of HIV/AIDS cases is relatively clustered between regions that have high and low number of cases, this indicates a spatial effect between regions. Then the GWNBR shows that there are differences in the significance of the variables in each region and forms 9 groups of regency/municipality based on the significant variables.

PEMODELAN DENGAN GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION (Studi kasus: Banyaknya Penderita Kusta di Jawa Barat)

The number of leper in West Java is an example of the count data case. The analyzes commonly used in count data is Poisson regression. This research will determine the variables that influence the number of leper in West Java. The data used is the number of leper in West Java in 2019. This data has an overdispersion condition and spatial heterogenity. To handle overdispersion, the negative binomial regression model can be employed. While spatial heterogenity is overcome by adding adaptive bisquare kernel weight. This research resulted Geographically Weighted Negative Binomial Regression (GWNBR) with a weighting adaptive bisquare kernel classifies regency/city in West Java into ten groups based on the variables that sigfinicantly influence the number of leper. In general, the variable in the percentage of households with Clean and Healthy Behavior (PHBS) has a significant effect in all regency/city in West Java. Especially for Bogor Regency, Depok City, Bogor City, and Pangandaran Regency, the variable of the percentage of people poverty does not have a significant effect on the number leper.

Spatial Modelling of Covid-19 Confirmed Cases in Kalimantan, Indonesia: How Neighborhood Matters?

The Covid-19 outbreak has hit all countries across the globe, including Indonesia, in which the impact is detrimental and costly. We investigated 14 determinants that could spatially influence Covid-19 cases in Central Kalimantan and South Kalimantan provinces in mid-2020 by using the Geographically Weighted Negative Binomial Regression (GWNBR) and Mixed Geographically Weighted Negative Binomial Regression (MGWNBR). This study conducted iterative Limited-memory Broyden-Fletcher-Goldfarb-Shanno with boundaries (L-BFGS-B) to utilize the numerical parameter estimation of MGWNBR. MGWNBR identified that the adjacent regions tend to group in 8 clusters containing the same significant determinants. Through MGWNBR, the comorbid prevalences (acute respiratory infection, pneumonia, and diabetes) were positively associated with the Covid-19 increasing cases in most regions. The unemployment rate and the number of health care facilities were negatively related to the increase of Covid-19 cases in some regions. MGWNBR was better than GWNBR in terms of AIC, deviance, and pseudo R-sq. The residual map also suggested that MGWNBR produced a more accurate projection than GWNBR. HIGHLIGHTS The statistical models for two Kalimantan provinces of Indonesia during early stage of Covid-19 pandemic Those models consisting of global, local, and mixed models estimated the effect of various social, economical, and health determinants on Covid-19 cases Mixed model parameters are estimated iteratively using L-BFGS-B weighted by adaptive bisquare kernel weight Comparison of models’ performance are applied using deviance, AIC, and pseudo R-sq GRAPHICAL ABSTRACT

Graphical interface of geographically weighted negative binomial regression (GWNBR) model using R-Shiny

In regression analysis, the spatial aspects need to be considered because each region has different characteristics as well as the Poisson regression model. In this method, some assumptions must be fulfilled, namely that the variance and the mean of the response variable are equal. However, counted data often have a greater variance than the mean, or what is generally called the over-dispersion phenomenon. If over-dispersion occurs, the Poisson regression is not suitable for modeling data, and that will produce biases in the parameter estimates. One method used to overcome over-dispersion in Poisson regression is negative binomial regression. The negative binomial regression model is more flexible than the Poisson regression model because it assumes that the mean and variance are not necessarily equal. Therefore, if the spatial aspect is considered, the Geographically Weighted Negative Binomial Regression (GWNBR) method is used. This study aims to compile a computational application to model spatial data using GWNBR Model using R-Shiny Web Application. And, the GWNBR model will be applied to modeling the number of dengue cases in Central Java province. The GWNBR model with Adaptive Boxcar weight is the best model because it has the smallest AIC. Using this model, two groups of districts/cities are obtained based on significant variables.

Non-Stationary Modeling of Microlevel Road-Curve Crash Frequency with Geographically Weighted Regression

Vehicle crashes on roads are caused by many factors. However, the influence of these factors is not necessarily homogenous across locations, which is a challenge for non-stationary modeling approaches. To address this problem, this paper adopts two types of methods allowing parameters to fluctuate among observations, that is, the random parameter approach and the geographically weighted regression (GWR) approach. With road curvature, curve length, pavement friction, and traffic volume as independent variables, vehicle crash frequencies are modeled by two non-spatial methods, including the negative binomial (NB) model and random parameter negative binomial (RPNB), as well as three spatial methods (GWR approach). These models are calibrated in microlevel using a dataset of 9415 horizontal curve segments with a total length of 1545 kilometers for a period of three years (2016–2018) over the State of Indiana. The results revealed that the GWR approach can capture spatial heterogeneity and therefore significantly outperforms the conventional non-spatial approach. Based on the Akaike Information Criterion (AICc), geographically weighted negative binomial regression (GWNBR) was proved to be a superior approach for statewide microlevel crash analysis.

PEMODELAN JUMLAH KASUS DEMAM BERDARAH DENGUE (DBD) DI JAWA TENGAH DENGAN GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION (GWNBR)

Dengue Hemorrhagic Fever (DHF) is one of the diseases with unsual occurrence in Central Java and spread throughout the regency/city. The number sufferers of this disease is still high because the mortality rate is still above the national target. Regarding the less handling of DHF spread, it is necessary to make a plan by identify the factors that allegedly affect that case. Characteristics of data the DHF cases is count data, so this research is carried out using poisson regression. If in poisson regression there is overdispersion, it can be overcome using negative binomial regression. Meanwhile to see the spatial effect, we can use the Geographically Weighted Negative Binomial Regression (GWNBR) method. GWNBR modeling uses a fixed exponential kernel for weighting function. GWNBR is better at modeling the number of DHF cases because it has the smallest AIC value than poisson regression and negative binomial regression. The results of research with poisson regression obtained three variables that have a significant effect on dengue cases. For negative binomial regression, two variables have a significant effect on DHF cases. While the GWNBR method obtained two groups of districts/cities based on significant variables. The variables affecting the number of DHF cases in all districts/cities in Central Java are the percentage of healthy houses, the percentage of clean water quality, and the ratio of medical personnel.Keywords: DHF, GWNBR, Poisson Regression, Binomial Negative Regression, Fixed Exponential Kernel