Geographically and Temporally Weighted Regression in Assessing Dengue Fever Spread Factors in Yunnan Border Regions

Objective This study employs the Geographically and Temporally Weighted Regression(GTWR)model to assess the impact of meteorological elements and imported cases on dengue fever outbreaks,emphasizing the spatial-temporal variability of these factors in border regions.Methods We conducted a descriptive analysis of dengue fever’s temporal-spatial distribution in Yunnan border areas.Utilizing annual data from 2013 to 2019,with each county in the Yunnan border serving as a spatial unit,we constructed a GTWR model to investigate the determinants of dengue fever and their spatio-temporal heterogeneity in this region.Results The GTWR model,proving more effective than Ordinary Least Squares(OLS)analysis,identified significant spatial and temporal heterogeneity in factors influencing dengue fever’s spread along the Yunnan border.Notably,the GTWR model revealed a substantial variation in the relationship between indigenous dengue fever incidence,meteorological variables,and imported cases across different counties.Conclusion In the Yunnan border areas,local dengue incidence is affected by temperature,humidity,precipitation,wind speed,and imported cases,with these factors’influence exhibiting notable spatial and temporal variation.

Exploring spatial non-stationarity of near-miss ship collisions from AIS data under the influence of sea fog using geographically weighted regression:A case study in the Bohai Sea,China

Sea fog is a disastrous weather phenomenon,posing a risk to the safety of maritime transportation.Dense sea fogs reduce visibility at sea and have frequently caused ship collisions.This study used a geographically weighted regression(GWR)model to explore the spatial non-stationarity of near-miss collision risk,as detected by a vessel conflict ranking operator(VCRO)model from automatic identification system(AIS)data under the influence of sea fog in the Bohai Sea.Sea fog was identified by a machine learning method that was derived from Himawari-8 satellite data.The spatial distributions of near-miss collision risk,sea fog,and the parameters of GWR were mapped.The results showed that sea fog and near-miss collision risk have specific spatial distribution patterns in the Bohai Sea,in which near-miss collision risk in the fog season is significantly higher than that outside the fog season,especially in the northeast(the sea area near Yingkou Port and Bayuquan Port)and the southeast(the sea area near Yantai Port).GWR outputs further indicated a significant correlation between near-miss collision risk and sea fog in fog season,with higher R-squared(0.890 in fog season,2018),than outside the fog season(0.723 in non-fog season,2018).GWR results revealed spatial non-stationarity in the relationships between-near miss collision risk and sea fog and that the significance of these relationships varied locally.Dividing the specific navigation area made it possible to verify that sea fog has a positive impact on near-miss collision risk.

Exploring the drivers of urban expansion in a medium-class urban agglomeration in India using the remote sensing techniques and geographically weighted models

Rapid urbanization urges the immediate attention of policymakers to ensure sustainable city development.Under-standing the urban growth drivers is essential to address effective strategies for urbanization-related challenges.This work aims to study Raiganj’s urban development and the factors associated with this expansion.This study employed global logistic regression(LR)and geographical weighted logistic regression(GWLR)to explore the role of different factors.The results showed that the role of the central business district(covariate>-1),commercial market(covariate>-3),and police station(covariate>-4)were significant to the development of new built-up areas.In the second period,major roads(covariate>-2)and new infrastructures(covariate>-4)became more relevant,particularly in the eastern and southern areas.GWLR was more accurate in assessing the different fac-tors’impact than LR.The results obtained are essential to understanding urban expansion in India’s medium-class cities,which is critical to effective policies for sustainable urbanization.

Exploration of the spatial pattern of urban residential land use with geographically weighted regression technique: a case study of Nanjing,China

As the traditional methods and technical means cannot meet the quantitative research needs of the urban land use patterns, quantitative research methods for the urban land use pattern are established via the GIS （geographic information system ） technique combined with the related theories and models. Taking the city of Nanjing as an example, a spatial database of urban land use and other environmental and socio-economic data is constructed. A multiple linear regression model is developed to determine the statistically significant factors affecting the residential land use distributions. To explain the spatial variations of urban land use patterns, the geographically weighted regression （GWR） is employed to establish spatial associations between these significant factors and the distribution of urban residential land use. The results demonstrate that the GWR can provide an effective approach to the exploration of the urban land use spatial patterns and also provide useful spatial information for planning residential development and other types of urban land use.

Comparison of Artificial Neural Networks,Geographically Weighted Regression and Cokriging Methods for Predicting the Spatial Distribution of Soil Macronutrients(N,P,and K)

Soil macronutrients(i.e. nitrogen(N), phosphorus(P), and potassium(K)) are important soils components and knowing the spatial distribution of these parameters are necessary at precision agriculture. The purpose of this study was to evaluate the feasibility of different methods such as artificial neural networks(ANN) and two geostatistical methods(geographically weighted regression(GWR) and cokriging(CK)) to estimate N, P and K contents. For this purpose, soil samples were taken from topsoil(0–30 cm) at 106 points and analyzed for their chemical and physical parameters. These data were divided into calibration(n = 84) and validation(n = 22). Chemical and physical variables including clay, p H and organic carbon(OC) were used as auxiliary soil variables to estimate the N, P and K contents. Results showed that the ANN model(with coefficient of determination R^2 = 0.922 and root mean square error RMSE = 0.0079%) was more accurate compared to the CK model(with R^2 = 0.612 and RMSE = 0.0094%), and the GWR model(with R^2 = 0.872 and RMSE = 0.0089%) to estimate the N variable. The ANN model estimated the P with the RMSE of 3.630 ppm, which was respectively 28.93% and 20.00% less than the RMSE of 4.680 ppm and 4.357 ppm from the CK and GWR models. The estimated K by CK, GWR and ANN models have the RMSE of 76.794 ppm, 75.790 ppm and 52.484 ppm. Results indicated that the performance of the CK model for estimation of macro nutrients(N, P and K) was slightly lower than the GWR model. Also, the accuracy of the ANN model was higher than CK and GWR models, which proved to be more effective and reliable methods for estimating macro nutrients.

Spatial Downscaling of the Tropical Rainfall Measuring Mission Precipitation Using Geographically Weighted Regression Kriging over the Lancang River Basin, China

Satellite-based precipitation products have been widely used to estimate precipitation, especially over regions with sparse rain gauge networks. However, the low spatial resolution of these products has limited their application in localized regions and watersheds.This study investigated a spatial downscaling approach, Geographically Weighted Regression Kriging(GWRK), to downscale the Tropical Rainfall Measuring Mission(TRMM) 3 B43 Version 7 over the Lancang River Basin(LRB) for 2001–2015. Downscaling was performed based on the relationships between the TRMM precipitation and the Normalized Difference Vegetation Index(NDVI), the Land Surface Temperature(LST), and the Digital Elevation Model(DEM). Geographical ratio analysis(GRA) was used to calibrate the annual downscaled precipitation data, and the monthly fractions derived from the original TRMM data were used to disaggregate annual downscaled and calibrated precipitation to monthly precipitation at 1 km resolution. The final downscaled precipitation datasets were validated against station-based observed precipitation in 2001–2015. Results showed that: 1) The TRMM 3 B43 precipitation was highly accurate with slight overestimation at the basin scale(i.e., CC(correlation coefficient) = 0.91, Bias = 13.3%). Spatially, the accuracies of the upstream and downstream regions were higher than that of the midstream region. 2) The annual downscaled TRMM precipitation data at 1 km spatial resolution obtained by GWRK effectively captured the high spatial variability of precipitation over the LRB. 3) The annual downscaled TRMM precipitation with GRA calibration gave better accuracy compared with the original TRMM dataset. 4) The final downscaled and calibrated precipitation had significantly improved spatial resolution, and agreed well with data from the validated rain gauge stations, i.e., CC = 0.75, RMSE(root mean square error) = 182 mm, MAE(mean absolute error) = 142 mm, and Bias = 0.78%for annual precipitation and CC = 0.95, RMSE = 25 mm, MAE = 16 mm, and Bias = 0.67% for monthly precipitation.

Travel Behaviours of Sharing Bicycles in the Central Urban Area Based on Geographically Weighted Regression: The Case of Guangzhou, China

Mobile information and communication technologies(MICTs) have fully penetrated everyday life in smart societies;this has greatly compressed time, space, and distance, and consequently, reshaped residents’ travel behaviour patterns. As a new mode of shared mobility, the sharing bicycle offers a variety of options for the daily travel of urban residents. Extant studies have mainly examined the travel characteristics and influencing factors of public bicycles with piles, while the travel patterns for sharing bicycles and their driving mechanisms have been largely ignored. Using one week’s travel data for Mobike, this study investigated the spatial and temporal distribution patterns of sharing bicycle travel behaviours in the central urban area of Guangzhou, China;furthermore, it identified the influences of built environment density factors on sharing bicycle travel behaviours based on the geographically weighted regression method. Obvious morning and evening peaks were observed in the sharing bicycle travel patterns for both weekdays and weekends. The old urban area, which had a high degree of mixed function, dense road networks, and cycling-friendly built environments, was the main travel area that attracted sharing bicycles on both weekdays and weekends. Furthermore, factors including the point of interest(POI) for the density of public transport stations, the functional mixing degree, and the density of residential POIs significantly affected residents’ travel behaviours. These findings could enrich discourse regarding shared mobility with a Chinese case characterised by rapidly developing MICTs and also provide references to local authorities for improving slow traffic environments.

Impact of Accessibility on Housing Prices in Dalian City of China Based on a Geographically Weighted Regression Model

This paper studies the relationship between accessibility and housing prices in Dalian by using an improved geographically weighted regression model and house prices, traffic, remote sensing images, etc. Multi-source data improves the accuracy of the spatial differentiation that reflects the impact of traffic accessibility on house prices. The results are as follows: first, the average house price is 12 436 yuan(RMB)/m^2, and reveals a declining trend from coastal areas to inland areas. The exception was Guilin Street, which demonstrates a local peak of house prices that decreases from the center of the street to its periphery. Second, the accessibility value is 33 minutes on average, excluding northern and eastern fringe areas, which was over 50 minutes. Third, the significant spatial correlation coefficient between accessibility and house prices is 0.423, and the coefficient increases in the southeastern direction. The strongest impact of accessibility on house prices is in the southeastern coast, and can be seen in the Lehua, Yingke, and Hushan communities, while the weakest impact is in the northwestern fringe, and can be seen in the Yingchengzi, Xixiaomo, and Daheishi community areas.

Modeling of Spatial Distributions of Farmland Density and Its Temporal Change Using Geographically Weighted Regression Model

This study used spatial autoregression(SAR)model and geographically weighted regression(GWR)model to model the spatial patterns of farmland density and its temporal change in Gucheng County,Hubei Province,China in 1999 and 2009,and discussed the difference between global and local spatial autocorrelations in terms of spatial heterogeneity and non-stationarity.Results showed that strong spatial positive correlations existed in the spatial distributions of farmland density,its temporal change and the driving factors,and the coefficients of spatial autocorrelations decreased as the spatial lag distance increased.SAR models revealed the global spatial relations between dependent and independent variables,while the GWR model showed the spatially varying fitting degree and local weighting coefficients of driving factors and farmland indices(i.e.,farmland density and temporal change).The GWR model has smooth process when constructing the farmland spatial model.The coefficients of GWR model can show the accurate influence degrees of different driving factors on the farmland at different geographical locations.The performance indices of GWR model showed that GWR model produced more accurate simulation results than other models at different times,and the improvement precision of GWR model was obvious.The global and local farmland models used in this study showed different characteristics in the spatial distributions of farmland indices at different scales,which may provide the theoretical basis for farmland protection from the influence of different driving factors.

Selecting suitable sites for mountain ginseng(Panax ginseng)cultivation by using geographically weighted logistic regression

With the well-being trends to pursue a healthy life, mountain ginseng(Panax ginseng) is rising as one of the most profitable forest products in South Korea. This study was aimed at evaluating a new methodology for identifying suitable sites for mountain ginseng cultivation in the country. Forest vegetation data were collected from 46 sites and the spatial distribution of all sites was analyzed using GIS data for topographic position, landform, solar radiation, and topographic wetness. The physical and chemical properties of the soil samples, including moisture content, p H, organic matter, total nitrogen, exchangeable cations, available phosphorous, and soil texture, were analyzed. The cultivation suitability at each site was assessed based on the environmental conditions using logistic regression(LR) and geographically weighted logistic regression(GWLR) and the results of both methods were compared. The results show that the areas with northern aspect and higher levels of solar radiation, moisture content, total nitrogen, and sand ratio are more likely to be identified as suitable sites for ginseng cultivation. In contrast to the LR, the spatial modeling with the GWLR results in an increase in the model fitness and indicates that a significant portion of spatialautocorrelation in the data decreases. A higher value of the area under the receiver operating characteristic(ROC) curve presents a better prediction accuracy of site suitability by the GWLR. The geographically weighted coefficient estimates of the model are nonstationary, and reveal that different site suitability is associated with the geographical location of the forest stands. The GWLR increases the accuracy of selecting suitable sites by considering the geographical variations in the characteristics of the cultivation sites.

Spatial distribution of snow depth based on geographically weighted regression kriging in the Bayanbulak Basin of the Tianshan Mountains, China

Snow depth is a general input variable in many models of agriculture,hydrology,climate and ecology.This study makes use of observational data of snow depth and explanatory variables to compare the accuracy and effect of geographically weighted regression kriging(GWRK)and regression kriging(RK)in a spatial interpolation of regional snow depth.The auxiliary variables are analyzed using correlation coefficients and the variance inflation factor(VIF).Three variables,Height,topographic ruggedness index(TRI),and land surface temperature(LST),are used as explanatory variables to establish a regression model for snow depth.The estimated spatial distribution of snow depth in the Bayanbulak Basin of the Tianshan Mountains in China with a spatial resolution of 1 km is obtained.The results indicate that 1)the result of GWRK's accuracy is slightly higher than that of RK(R^2=0.55 vs.R^2=0.50,RMSE(root mean square error)=0.102 m vs.RMSE=0.077 m);2)for the subareas,GWRK and RK exhibit similar estimation results of snow depth.Areas in the Bayanbulak Basin with a snow depth greater than 0.15m are mainly distributed in an elevation range of 2632.00–3269.00 m and the snow in this area comprises 45.00–46.00% of the total amount of snow in this basin.However,the GWRK resulted in more detailed information on snow depth distribution than the RK.The final conclusion is that GWRK is better suited for estimating regional snow depth distribution.

Association between Macroscopic-factors and Identified HIV/AIDS Cases among Injecting Drug Users: An Analysis Using Geographically Weighted Regression Model

Drug use （DU）, particularly injecting drug use （IDU） has been the main route of transmission and spread of Human Immunodeficiency Virus （HIV）/Acquired Immune Deficiency Syndrome （AIDSJ among injecting drug users （IDUs）[1]. Previous studies have proven that needles or cottons sharing during drug injection were major risk factors for HIV/AIDS transmission at the personal level[z4]. Being a social behavioral issue, HIV/AIDS related risk factors should be far beyond the personal level. Therefore, studies on HIV/AIDS related risk factors should focus not only on the individual factors, but also on the association between HIV/AIDS cases and macroscopic-factors, such as economic status, transportation, health care services, etc[1]. The impact of the macroscopic-factors on HIV/AIDS status might be either positive or negative, which are potentially reflected in promoting, delaying or detecting HIV/AIDS epidemics.

GIS-Based Local Spatial Statistical Model of Cholera Occurrence: Using Geographically Weighted Regression

Global statistical techniques often assume homogeneity of relationships between dependent variable and predictors across space. This assumption has been criticized by statistical geographers as a fundamental weakness that may yield misleading result when it is applied to dataset with spatial context. To strengthen this weakness, a new method that accounts for heterogeneity in relationships across geographic space has been presented. This is one of the family of local spatial statistical techniques referred to as geographically weighted regression (GWR). The method captures non-stationarity of relationship in spatial data that the ordinary least square (OLS) regression fails to account for. Thus, the paper is designed to explore and analyze the spatial relationships between cholera occurrence and household sources of water supply using GIS-based GWR, also to compare the modeling fitness of OLS and GWR. Vector dataset (spatial) of the study region by state levels and statistical data (non-spatial) on cholera cases, household sources of water supply and population data were used in this exploratory analysis. The result shows that GWR is a significant improvement on the global model. Comparing both models with the AICc value and the R2 value revealed that for the former, the value is reduced from 698.7 (for OLS model) to 691.5 (for GWR model). For the latter, OLS explained 66.4 percent while GWR explained 86.7 percent. This implies that local model’s fitness is higher than global model. In addition, the empirical analysis revealed that cholera occurrence in the study region is significantly associated with household sources of water supply. This relationship, as detected by GWR, largely varies across the region.

Analysis of Geographically Anomalous 2019 Novel Coronavirus Transmission in China

Approximately in the late-December of 2019, the coronavirus disease outbreak took place in China. COVID-19 (Coronavirus Disease 2019) is contagious and detrimental to the human body, which can even lead to death. As a result, the understanding of COVID-19 has become especially important. This paper studies four cases of anomalous disease-spreading in China (Guangdong Province, Heilongjiang province, Tianjin municipality, and Guizhou province) and analyzes four influencing factors of the transmission (temperature, transportation and passenger traffic volume, household size and distribution, and awareness). Major conclusions in this paper are as follows. Transportation and passenger traffic volume and the number of larger households are positively related to the extent of disease-spreading;the degree of awareness is negatively associated with the extent of disease-spreading. Provinces, municipalities, and autonomous regions with a more urbanized distribution of households are prone to experience a greater extent of disease transmission. Although the novel coronavirus prefers colder environment, temperature appears to be a secondary influencing factor, as regions with negative temperatures have fewer diagnoses. Disease transmission in Guangdong province is caused by a high volume of passenger traffic, large and urbanized households, and low awareness. Heilongjiang province is mainly a result of high passenger traffic volume, long travelling trips, and low public awareness. Guizhou province is benefited from high awareness, limited passenger volume, and scattered households. Tianjin municipality is protected from the severe disease-spreading owe to its beneficial temperature, low land transportation volume, and high public and government awareness.

Review of the Water Footprint Project within Geographically Delineated Area

During the last decade, there has been an intensive research activity concerning the concept of the Water Footprint （WF） approach, which was firstly introduced by Arjen Hoekstra in 2002. WF is an indicator of direct and indirect freshwater use of a consumer or producer that takes into account water consumption in every step （intermediate and final） along the production chain and services. The concept can be implemented in various levels such as products, consumers, producers, nations and river basins etc.. The water footprint within a geographically delineated area equals the sum of the process water footprints of all processes taking place in the area. The aim of current research is a review of the most important WF studies, with a special focus on applications within regional, basin and administrative unit level. National and global scales are not included in the current paper. The article presents the most widespread methodologies and approaches that attempt to evaluate water footprints of specific defined areas and highlights their recent advances as well as shortcomings in the constantly evolving research efforts.

Comparison of Geographically Weighted Regression of Benthic Substrate Modeling Accuracy on Large and Small Wadeable Streams

Aquatic habitat assessments encompass large and small wadeable streams which vary from many meters wide to ephemeral. Differences in stream sizes within or across watersheds, however, may lead to incompatibility of data at varying spatial scales. Specifically, issues caused by moving between scales on large and small streams are not typically addressed by many forms of statistical analysis, making the comparison of large (>30 m wetted width) and small stream (<10 m wetted width) habitat assessments difficult. Geographically weighted regression (GWR) may provide avenues for efficiency and needed insight into stream habitat data by addressing issues caused by moving between scales. This study examined the ability of GWR to consistently model stream substrate on both large and small wadeable streams at an equivalent resolution. We performed GWR on two groups of 60 randomly selected substrate patches from large and small streams and used depth measurements to model substrate. Our large and small stream substrate models responded equally well to GWR. Results showed no statistically significant difference between GWR R2 values of large and small stream streams. Results also provided a much needed method for comparison of large and small wadeable streams. Our results have merit for aquatic resource managers, because they demonstrate ability to spatially model and compare substrate on large and small streams. Using depth to guide substrate modeling by geographically weighted regression has a variety of applications which may help manage, monitor stream health, and interpret substrate change over time.

Geographically Weighted Regression and Secondary Variables for Mapping of Meteorological Data

GA （geostatistical analyst） is an indispensable tool to analyze various and plenty of data in GIS （geographic information system）. Spatial distribution is the most effective factor for predicting of meteorological maps at the point of performance or reliability of the model. Generally, classical interpolation methods may not be sufficient to produce accurate maps. GA is more considerable in this state. Secondary variables affect the precious of prediction models especially meteorological data mapping. In this study 245 meteorological data stations have been evaluated to produce precipitation model maps in Turkey. Long term （25 years） mean annual and monthly precipitation data from Turkish State Meteorological Service and elevation, slope and aspect values from DEM （Digital Elevation Model） were registered. OK （Ordinary Kriging）, OCK （Ordinary Co-Kriging） and GWR （Geographically Weighted Regression） have been used as a method to compare the models. With the study if there are effects of secondary variables to precipitation models have been illustrated on the prediction maps. Besides comparing statistical values, regional effects of secondary variables have been determined and illustrated on the maps numerically. As a result to define precipitation distribution spatially R2 values between measured and predicted values have been calculated 0.55 for Kriging, 0.67 for OCK and 0.86 for GWR. Cross validation indicated that GWR interpolation yields the smallest prediction error with elevation, slope and aspect. Spatial distribution of meteorological stations is also other important factor for similar studies.

Compositional Shifts in Ammonia-Oxidizing Microorganism Communities of Eight Geographically Different Paddy Soils —Biogeographical Distribution of Ammonia-Oxidizing Microorganisms

Soil nitrification is mediated by ammonia-oxidizing archaea (AOA) and bacteria (AOB), which occupy different specialized ecological niches. However, little is known about the diversification of AOA and AOB communities in a large geographical scale. Here, eight paddy soils collected from different geographic regions in China were selected to investigate the spatial distribution of AOA and AOB, and their potential nitrification activity (PNA). The result showed that the abundance of AOA was predominant over AOB, indicating that the rice fields favor the growth of AOA. PNA highly varied from 0.43 to 3.57 μg NOX-N·g·dry·soil·h-1, and was positively related with soil NH3 content, the abundance of AOA community, and negatively related with the diversity of AOB community (P amoA genes revealed remarkable differences in the compositions of AOA and AOB community. Phylogenetic analyses of amoA genes showed that Nitrosospiracluster-3-like and Nitrosomonas cluster 7-like AOB extensively dominated the AOB communities, and 54d9-like AOA within the soil group 1.1b predominated in AOA communities in paddy soils. Redundancy analysis suggested that the spatial variations of AOA community structure were influenced by soil TN content (P < 0.01), while no significant correlation between AOB community structure and soil properties was found. Findings highlight that ammonia oxidizers exhibit spatial variations in complex paddy fields due to the joint influence of soil variables associated with N availability.

Diversification of ammonia-oxidizing microorganisms in seven geographically different paddy soils in Sichuan

The diversification of ammonia-oxidizing bacteria (AOB) and ammonia-oxidizing archaea (AOA) communities and their potential nitrification activity (PNA) on a large scale have not been well documented. In this work, seven paddy soils from different geographic regions in Sichuan, P. R. China were selected to determine the spatial distribution of the activities, abundances and community compositions of AOB and AOA. PNA varied greatly among paddy soils, and was positively correlated with soil pH (P< 0.05). The abundance of AOA was 81.1 to 1 670.0 times more than that of AOB, which indicates paddy soil environments favor the growth of AOA. Denaturing gradient gel electrophoresis fingerprints of amoA genes exhibited distinct spatial differences in AOA compositions rather than in AOB compositions. Sequencing analysis revealed that acidic soils were dominated by AOA within marine group 1.1 a-associated lineage, whereas the soil group 1.1b lineage AOA predominated in neutral and alkaline soils. Both nitrosopira cluster 3-like and Nitrosomonas cluster 7-like AOB dominated the AOB communities in the paddy soils. Redundancy analysis suggested that soil NH4^+-N content was the most significant driver determining the AOB community structure, while no significant correlation between AOA community structure and soil properties was found. The findings highlight that the activity and composition of ammonia oxidizers exhibit spatial variations in complex paddy fields due to the joint influence of soil variables associated with pH and N availability.

Hierarchical Geographically Weighted Regression Model

In spatial analysis, two problems of the scale effect and the spatial dependencehave been plagued scholars, the first law of geography presented to solve the spatialdependence has played a good role in the guidelines, forming the Geographical WeightedRegression (GWR). Based on classic statistical techniques, GWR model has ascertainsignificance in solving spatial dependence and spatial non-uniform problems, but it hasno impact on the integration of the scale effect. It does not consider the interactionbetween the various factors of the sampling scale observations and the numerous factorsof possible scale effects, so there is a loss of information. Crossing a two-stage analysisof “return of regression” to establish the model of Hierarchical Geographically WeightedRegression (HGWR), the first layer of regression analysis reflects the spatial dependenceof space samples and the second layer of the regression reflects the spatial relationshipsscaling. The combination of both solves the spatial scale effect analysis, spatialdependence and spatial heterogeneity of the combined effects.