Geographically Weighted Regression with Kernel Weighted Function on Poverty Cases in West Java Province

Geographically Weighted Regression (GWR) is an analytical method for data that contains spatial heterogeneity effects. However, parameter estimation in the GWR model has a weakness, namely it is prone to outliers and can cause the parameter estimation to be biased. This can be overcome by the Robust Geographically Weighted Regression (RGWR) method which is more robust against the presence of outliers. This method is suitable for Gross Regional Domestic Product (GRDP) data in West Java Province, which contains outliers and also has spatial effects. The data used in this study are secondary data obtained from the Central Statistics Agency (BPS) of West Java Province. The purpose of this study is to compare the Robust Geographically Weighted Regression (RGWR) method with the Least Absolute Deviation (LAD) Estimation and M-estimation and also to find out the factors that affect the Gross Regional Domestic Product (GRDP) in West Java Province in 2021 based on the model resulting from. Selection of the best model is seen based on the value of the coefficient of determination (R2) and Mean Squared of Error (MSE). The research results show that the Robust Geographically Weighted Regression (RGWR) method with M-estimation is much more effective in estimating the distribution of GRDP in West Java Province in 2021, seen from the larger coefficient of determination and the smaller Mean Square Error (MSE). The variables that have a significant influence on GRDP in West Java Province in 2021 are the variables of foreign investment and local income.

Geographically weighted regression (GWR) is a linear regression technique used to fit a regression equation to every observation in a dataset. In this study, both the global regression (multiple linear regression) and the GWR were calibrated for the 2019 Nigeria presidential election dataset, and diagnostics of each model were computed and compared. Experiments and analyses in the study were implemented in the R-environment, R-4.1.2. The GWR model outperforms the global regression model with an R^2 value of 0.776 exceeding that of the global regression of 0.513. The superiority of the GWR model is also confirmed by its much smaller RSS and AICc values (173.362 and 1372.8555 respectively), compared to those of the global regression (377.103 and 1662.316 respectively). The GWR model better fits the election dataset; it explains spatial variations in the dependent variable better than the global regression model does.

The geographically weighted regression (GWR) model is a local spatial regression technique used to determine and map spatial variations in the relationships between variables. In the GWR model, the bandwidth is very important as it can change the parameter estimates and affect the model performance. In this study, we applied the information complexity (ICOMP) type criteria in the selection of fixed bandwidth for the first time in the literature. The ICOMP‐type criteria use a complexity measure that measures how parameters in the model relate to each other. A real dataset example and a simulation study have been conducted. Results of the simulation demonstrate that GWR models created with the bandwidth selection by ICOMP‐type criteria show superior performance. In addition, when the bandwidth is selected according to the ICOMP‐type criteria and the GWR model is created for the actual total fertility rate data, it is seen that the spatial distribution of the total fertility rate estimates is quite compatible with the distribution of the actual total fertility rate. According to the results, ICOMP‐type criteria can be used effectively instead of the classical criteria in the literature in the selection of bandwidth in the GWR model.

Understanding the spatial distribution of land surface temperature (LST) and its impact factors is crucial for mitigating urban heat island effect. However, few studies have quantitatively investigated the spatial non-stationarity and spatial scale effects of the relationships between LST and its impact factors at multi-scales. The main purposes of this study are as follows: (1) to estimate the spatial distributions of urban heat island (UHI) intensity by using hot spots analysis and (2) to explore the spatial non-stationarity and scale effects of the relationships between LST and related impact factors at multiple resolutions (30–1200 m) and to find appropriate scales for illuminating the relationships in a plain city. Based on the LST retrieved from Landsat 8 OLI/TIRS images, the Geographically-Weighted Regression (GWR) model is used to explore the scale effects of the relationships in Zhengzhou City between LST and six driving indicators: The Fractional Vegetation Cover (FVC), the Impervious Surface (IS), the Population Density (PD), the Fossil-fuel CO2 Emission data (FFCOE), the Shannon Diversity Index (SHDI) and the Perimeter-area Fractal Dimension (PAFRAC),which indicate the vegetation abundance, built-up, social-ecological variables and the diversity and shape complexity of land cover types. Our findings showed that the spatial patterns of LST show statistically significant hot spot zones in the center of the study area, partly extending to the western and southern industrial areas, indicating that the intensity of the urban heat island is significantly spatial clustering in Zhengzhou City. In addition, compared with the Ordinary Least Squares (OLS) model, the GWR model has a better ability to characterize spatial non-stationarity and analyze the relationships between the LST and its impact factors by considering the space-varying relationships of different variables, especially at the fine spatial scales (30–480 m). However, the strength of GWR model has become relatively weak with the increase of spatial scales (720–1200 m). This reveals that the GWR model is recommended to be applied in the analysis of UHI problems and related impact factors at scales finer than 480 m in the plain city. If the spatial scale is coarser than 720 m, both OLS and GWR models are suitable for illustrating the correct relationships between UHI effect and its influence factors in the plain city due to their undifferentiated performance. These findings can provide valuable information for urban planners and researchers to select appropriate models and spatial scales seeking to mitigate urban thermal environment effect.

Regional disparity of economic development in China is always greatly concerned by investigators domestic and abroad, and sets of models have been used in the analysis. Spatial dependence, which is hidden in the data with spatial attributes, usually is not taken into account in classical statistics methods, such as ordinary linear regression(OLR) model. Along with the development of spatial statistics, more and more attentions are paid on spatial interactions between observations in the study of regional disparity. Geographically weighted regression (GWR) is a simple but effective model to recognize spatial variation and local difference, which considers the influence of the spatially non-stationarity of the variables. In this study, GWR model and Geo-Informatic Tupu were used to analyze the disparity of regional economic development in China, taking GDP per capita in 1999 and 2003 as a case, which is usually used to measure level of economic development. GDP per capita in the 338 cities in 1999 were selected to simulate GDP per capita in 2003 and to analysis non-stationarity of the growth of GDP per capita. Using Geo-Informatic Tupu, A series of maps were processed to display patterns of local parameter estimates, such as local r-squares, the residual sum of squares, local residual and so on, to gain a better understanding of the degree of spatial non-stationarity in a relationship over space. We tested for geographic heterogeneity in the parameters and compare them to estimates obtained from global regression approaches. The results suggested there was heterogeneity in the regression coefficients across broad regions of China, and a one-size fits all approach to describe growth processes appeared simplistic. The GWR model improved over the OLR model, and it was able to better explain the variation in the data and to simulate GDP per capita with smaller errors than the OLR models.

Newtown Business of Seoul had been performed to reduce deterioration of Gangbuk and economic inequality between Gangnam and Gangbuk. According to this, Eunpyeong-gu was set as test-bed for Newtown business and Newtown business had been completed until 2013. This study aims to analyze the influence of social and economical factors which affect land price using GWR (Geographically Weighted Regression) considered spatial effect. As a result of analysis, GWR model demonstrated a better goodness-of-fit than OLS (Ordinary least square) model typically used in most study. Furthermore, AIC value and Moran’s I of residual prove that GWR model is more suitable than OLS model. GWR model enable to explain more detailed than global regression model as coefficient and sign show different value locally. In future, this research will be helpful to develop Eunpyeong-gu considering spatial characters and strength effectiveness of development.Keywords : Eunpyeong Newtown, Newtown Projects, Land Value, Geographically Weighted Regression

Soil erosion is one of the most common types of land degradation. To provide useful information for proper management, quantitative soil erosion evaluation and identifying influential factors are needed. However, rare studies have been reported on spatial modeling of soil erosion in connection with affective factors to prioritize the locality and the type of erosion control measures. Hence, the aim of this study was to (1) assess erosion-prone areas in the Talar watershed, Iran, using the revised universal soil loss equation (RUSLE) model and (2) investigate the relationship between soil erosion variability and land-use changes. Toward that, the ordinary least squares (OLS), geographically weighted regression (GWR) models, and principal component analysis (PCA) were used to analyze spatial relationships between soil erosion, land-use, and the RUSLE factors. The results of the OLS and GWR models indicated that these relationships are spatially non-stationary. GWR models had a good predictive performance than OLS with lower Akaike’s Information Criterion (from 254.31 to 276.81 in OLS and from 247.87 to 269.42 in GWR) and higher adjusted R2 values (from 0.12 to 0.54 in OLS, and from 0.36 to 0.66 in GWR). Among the variables mentioned above, LS factor, P factor, forest, and irrigated land were the most influential variables in GWR models. The results of PCA showed that PC1 and PC2 explained 66.2% of the variation in soil erosion concerning land-use and the RUSLE factors. These results provided appropriate references for managers and experts properly planning the study watershed.Graphical abstract

Regression analysis is a statistical analysis method that is used to modeling the relationship between dependent variables and independent variables. In the linear regression model only produced parameter estimators are globally, so it’s often called global regression. While to analyze spatial data can be used Geographically Weighted Regression (GWR) method. Geographically and Temporally Weighted Regression (GTWR) is the development of GWR model to handle the instability of a data both from the spatial and temporal sides simultaneously. In this GWR modeling the weight function used is a Gaussian Kernel, which requires the bandwidth value as a distance parameter. Optimum bandwidth can be obtained by minimizing the CV (cross validation) coefficient value. By comparing the R-square, Mean Square Error (MSE) and Akaike Information Criterion (AIC) values in both methods, it is known that modeling the level of deforestation in protected forest areas in Indonesia in 2013 through 2016 uses the GTWR method better than global regression. With the R-square value the GTWR model is 25.1%, the MSE value is 0.7833 and AIC value is 349,6917. While the global regression model has R-square value of 15.8%, MSE value of 0.861 and AIC value of 361,3328. Keywords : GWR, GTWR, Bandwidth, Kernel Gaussian

Detailed information about spatial distribution of soil properties is important in ecological modelling, environmental prediction, precision agriculture, and natural resources management, as well as land-use planning. In the present study, a recently developed method called geographically weighted regression (GWR) is applied to predict spatial distribution of soil properties (pH, soil organic matter, available nitrogen, available potassium) based on topographical indicators, climate factors, and geological stratum at a regional scale. In total, 1914 soil samples collected from a depth of 0–20 cm were used to calibrate and validate the models. Performances of the GWR models were compared with the traditional, ordinary least-squares (OLS) regression. The results indicated that the GWR models made significant improvements to model performances over OLS regression, based on F-test, coefficient of determination, and corrected Akaike information criterion. GWR models also improved the reliability of the soil–environment relationships by reducing the spatial autocorrelations in model residuals. Meanwhile, the use of GWR models disclosed that the relationships between soil properties and environmental variables were not invariant over space but exhibited significant spatial non-stationarity. Accordingly, the GWR models remarkably improved the prediction accuracies over the corresponding OLS models. The results demonstrated that GWR could serve as a useful tool for digital soil mapping in areas with complex terrain.

Geographically Weighted Regression (GWR) is increasingly used in spatial analyses of social and environmental data. It allows spatial heterogeneities in processes and relationships to be investigated through a series of local regression models rather than a single global one. Standard GWR assumes that relationships between the response and predictor variables operate at the same spatial scale, which is frequently not the case. To address this, several GWR variants have been proposed. This paper describes a route map to decide whether to use a GWR model or not, and if so which of three core variants to apply: a standard GWR, a mixed GWR or a multiscale GWR (MS‐GWR). The route map comprises 3 primary steps that should always be undertaken: (1) a basic linear regression, (2) a MS‐GWR, and (3) investigations of the results of these in order to decide whether to use a GWR approach, and if so for determining the appropriate GWR variant. The paper also highlights the importance of investigating a number of secondary issues at global and local scales including collinearity, the influence of outliers, and dependent error terms. Code and data for the case study used to illustrate the route map are provided.

Research using a global regression model might not be appropriate to find out the factors that influence strategic food prices based on spatial characteristics. To analyze the spatial effect, Geographically Weighted Regression (GWR) was employed. GWR models are better than OLS, which is indicated by the higher R2 GWR and lower AIC values. The GWR analysis provides the following findings: (1) the wholesale price most influential on the retail price of medium rice and red chili both during the main harvest and non-harvest periods; (2) the harvest pattern results in the effect of production and producer prices on the retail prices of the major harvest and non-harvest periods. Management of inter-regional distribution must be carried out to maintain supply stability and disparity in food prices between regions; (3) producer prices are integrated with trader prices in the district of production centers and surrounding areas while the integration of food prices at the consumer level occurs in the main economic center area of the region. These aspects have different effects for each region and district because the estimated parameters can be positive or negative. Testing during the harvest season (April) and non-harvest can also produce estimates that vary according to the specific characteristics of each location. Keywords: spatial analysis, Geographically Weighted Regression (GWR), retail prices, wholesale price, spatial distribution patterns

BackgroundAngiostrongyliasis is a food-borne parasitic zoonosis. Human infection is caused by infection with the third-stage larvae of Angiostrongylus cantonensis. The life cycle of A. cantonensis involves rodents as definitive hosts and molluscs as intermediate hosts. This study aims to investigate on the infection status and characteristics of spatial distribution of these hosts, which are key components in the strategy for the prevention and control of angiostrongyliasis.MethodsThree villages from Nanao Island, Guangdong Province, China, were chosen as study area by stratified random sampling. The density and natural infection of Pomacea canaliculata and various rat species were surveyed every three months from December 2015 to September 2016, with spatial correlations of the positive P. canaliculata and the infection rates analysed by ArcGIS, scan statistics, ordinary least squares (OLS) and geographically weighted regression (GWR) models.ResultsA total of 2192 P. canaliculata specimens were collected from the field, of which 1190 were randomly chosen to be examined for third-stage larvae of A. cantonensis. Seventy-two Angiostrongylus-infected snails were found, which represents a larval infection rate of 6.1% (72/1190). In total, 110 rats including 85 Rattus norvegicus, 10 R. flavipectus, one R. losea and 14 Suncus murinus were captured, and 32 individuals were positive (for adult worms), representing an infection rate of 29.1% of the definitive hosts (32/110). Worms were only found in R. norvegicus and R. flavipectus, representing a prevalence of 36.5% (31/85) and 10% (1/10), respectively in these species, but none in R. losea and S. murinus, despite testing as many as 32 of the latter species. Statistically, spatial correlation and spatial clusters in the spatial distribution of positive P. canaliculata and positive rats existed. Most of the spatial variability of the host infection rates came from spatial autocorrelation. Nine spatial clusters with respect to positive P. canaliculata were identified, but only two correlated to infection rates. The results show that corrected Akaike information criterion, R2, R2 adjusted and σ2 in the GWR model were superior to those in the OLS model.ConclusionsP. canaliculata and rats were widely distributed in Nanao Island and positive infection has also been found in the hosts, demonstrating that there was a risk of angiostrongyliasis in this region of China. The distribution of positive P. canaliculata and rats exhibited spatial correlation, and the GWR model had advantage over the OLS model in the spatial analysis of hosts of A. cantonensis.

Two popular data science analyses are spatial analysis and machine learning. The most popular spatial analysis is geographically weighted regression (GWR), and the most popular of machine learning is random forest (classification dan regression). The paper used GWR and Random Forest Regression (RFR) to find the variables that significantly impact life expectancy and compare two methods using RMSE. Knowledge of life expectancy and determining factors on life expectancy is essential because the increase in life expectancy is linked to a country's economic and social prosperity. The researcher employed life expectancy data as the dependent variable (Y) and some independent variables. At each observation location in Sumatra Region, the GWR model and significant independent variables are different. The RMSE value in the GWR model is 64.99. There are three variables with significant influence in most areas are X3 (percentage of proper sanitation households), X5 (number of doctors), and X7 (average years of schooling). The RMSE value in the RFR model is 84.04 with three variables importance: X3 (percentage of proper sanitation households), X5 (number of doctors), and X7 (average years of schooling) have the most influence. Keywords: GWR, Life Expectancy, RFR, RMSE.

With the fast urbanization process, how does the vegetation environment change in one of the most economically developed metropolis, Shanghai in East China? To answer this question, there is a pressing demand to explore the non-stationary relationship between socio-economic conditions and vegetation across Shanghai. In this study, environmental data on vegetation cover, the Normalized Difference Vegetation Index (NDVI) derived from MODIS imagery in 2003 were integrated with socio-economic data to reflect the city’s vegetative conditions at the census block group level. To explore regional variations in the relationship of vegetation and socio-economic conditions, Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR) models were applied to characterize mean NDVI against three independent socio-economic variables, an urban land use ratio, Gross Domestic Product (GDP) and population density. The study results show that a considerable distinctive spatial variation exists in the relationship for each model. The GWR model has superior effects and higher precision than the OLS model at the census block group scale. So, it is more suitable to account for local effects and geographical variations. This study also indicates that unreasonable excessive urbanization, together with non-sustainable economic development, has a negative influence of vegetation vigor for some neighborhoods in Shanghai.

Spatial variations in active mode trip volume at intersections: a local analysis utilizing geographically weighted regression