Geographically Weighted Regression Model Research Articles

Exploring the Spatiotemporal Heterogeneities in Urban Vitality Through Scalable Proxies from Mobile Data

Jane Jacob’s concepts of urban vitality and diversity have become prevailing urban planning philosophies in most countries for making cities more livable. Recent changes in demographics and the impacts of COVID-19 have exacerbated the economic and social challenges that cities commonly face, particularly spatiotemporal heterogeneities. Being able to understand these heterogeneities in scalable approaches is fundamental to tackling these challenges in cities. Therefore, this article aims to provide a new form of scalable estimation of urban vitality by using the de facto population. Instead of merely adopting static statistical information such as morphological characteristics in areas, we leverage dynamic factors such as internal mobility flows and energy use intensity as proxies for the spatiotemporal dynamics of indoor and outdoor behaviors of crowds. In this way, we combine dynamic attributes and static features to describe the patterns of urban vitality, which are directly related to spatiotemporal dynamics in urban places. We utilize GNSS-based mobile data and building energy usage intensity as dynamic proxies along with static data such as land use mix and age distribution. To better capture spatial heterogeneity, we use a Multiscale Geographically Weighted Regression (MGWR) model to identify the relationships between the de facto population and the dynamic and static factors. Drawing from the factors determining urban vitality, this article provides policy implications for alleviating spatiotemporal urban imbalances. These data-driven implications can fill the technical knowledge gaps in establishing planning strategies for achieving urban sustainability while enhancing overall subjective livability.

Spatial distribution characteristics and influencing factors of soil organic carbon based on the geographically weighted regression model.

Quantifying the effects of environmental factors on soil organic carbon and spatial distribution is fundamental to soil quality regulation, restoration, and response to climate change. The present study aims to explore the spatial distribution characteristics of the soil organic carbon (SOC) contents in Anhui Province, China, based on national soil data. In addition, we used the geographically weighted regression (GWR) model to quantify the influence degrees of environmental factors on the soil organic carbon density (SOCD). The results showed that the spatial distribution of SOCD in Anhui Province in both 1985 and 2018 was characterized by high in the south and low in the north. The GWR model prediction results of the 0-30cm SOCD showed local coefficients of determination (local R2) ranging from 0.21 to 0.96 and 0.14 to 0.96 in 1985 and 2018, respectively. Therefore, the predicted results were effective in evaluating the overall spatial distribution of the SOCD in Anhui Province. The regression coefficients of the normalized difference vegetation index (NDVI) and air temperature ranged from - 0.39 to 5.67 and - 0.17 to 3.11, respectively, demonstrating their strong controlling effects on the spatiotemporal variations in the 0-30cm SOCD in Anhui Province.

Urban Heat Island Differentiation and Influencing Factors: A Local Climate Zone Perspective

With the acceleration of urbanization, the urban heat island (UHI) effect has become a major environmental challenge, severely affecting the quality of life of residents and the ecological environment. Quantitative analysis of the factors influencing urban heat island intensity (UHII) is crucial for precise urban planning. Although extensive research has investigated the causes of UHI effects and their spatial variability, most studies focus on macro-scale analyses, overlooking the spatial heterogeneity of thermal characteristics within local climate zones (LCZs) under rapid urbanization. To address this gap, this study took the central urban area of Chengdu, constructing a LCZ map using multisource remote sensing data. Moran’s Index was employed to analyze the spatial clustering effects of UHI across different LCZs. By constructing Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR) models, the study further explored the influencing factors within these climate zones. The results showed that: (1) Chengdu’s built and natural environments had comparable proportions, with the scattered building zone comprising the highest proportion at 22.12% in the built environment, and the low vegetation zone accounting for 21.8% in the natural environment. The UHII values in this study ranged from 10.2 °C to −1.58 °C, based on specific measurement conditions. Since UHII varied with meteorological conditions, time, seasons, and the selection of rural reference points, these values represented dynamic results during the study period and were not constant. (2) Chengdu’s urban spatial morphology and UHII exhibited significant spatial heterogeneity, with a global Moran’s I index of 0.734, indicating a high degree of spatial correlation. The highest local Moran’s I value was found in the proportion of impervious surfaces (0.776), while the lowest is in the floor area ratio (0.176). (3) The GWR model demonstrated greater explanatory power compared to the OLS model, with a fit of 0.827. The impact of spatial morphological factors on UHII varied significantly across different environments, with the most substantial difference observed in the sky view factor, which has a standard deviation of 13.639. The findings provide precise recommendations for ecological spatial planning, aiming to mitigate the UHI effect and enhance the quality of life for urban residents.

Spatial and temporal evolution patterns and driving mechanisms of rural settlements: a case study of Xunwu County, Jiangxi Province, China

Urbanization and industrialization have driven rapid socio-economic development, leading to a significant population shift from rural areas to cities. This demographic transition has resulted in substantial changes in rural settlements, presenting considerable challenges for rural revitalization. Given the spatial differentiation, it is crucial to analyze the spatiotemporal evolution patterns and driving mechanisms of rural settlements under various development scenarios and at multiple scales within a county. Such analysis is essential for rational planning and sustainable development. This study analyzes the spatial and temporal evolution patterns and driving mechanisms of rural settlements in Xunwu County, Jiangxi Province, China, using land use dynamics, hot and cold spot analysis, and center of gravity migration models. The Multiscale Geographically Weighted Regression Model (MGWR) is employed to explore their transformation driving mechanisms. The results show that during 2010–2020 in the study area, the total change rate of rural settlements was 39.82%, with a dynamic degree of 2.87%. The average centroid of the settlements is located in Wenfeng Township, gradually migrating southeastward by 3.7 km. Cold spots are shrinking northward, while hotspots are gathering in Chengjiang Town. Socio-economic conditions dominate the evolution of rural clusters in this region, showing obvious spatial heterogeneity. This is followed by locational conditions that are weakening in influence, while the impact of natural geographical conditions exists in the northeast region. The research findings offer a scientifically rigorous and well-founded analysis of the evolution and driving mechanisms of rural settlements. This analysis provides a solid theoretical basis for policy planning in urban-rural integrated development and supports the sustainable growth of rural communities.

Towards socially equitable public transport systems: The effect of COVID-19 on taxi trip behavior

The COVID-19 pandemic emerged as a very influential occurrence with a profound impact on a global scale. The onset of the pandemic abruptly disrupted the regular course of everyday activities, primarily impacting urban regions. Hence, it is imperative to understand the effects of the COVID-19 pandemic on modern urban areas. This study seeks to analyze the effect of the pandemic on travel behavior by utilizing GPS data obtained from taxis, with a specific focus on spatial socioeconomic features. The M2 metro line in Istanbul has been selected for evaluation. In this analysis, four distinct periods are considered: total, off-peak, morning, and evening peaks. The stations are categorized using K-means clustering. The estimation models are constructed using ordinary least squares (OLS), spatial autoregression (SAR), and geographically weighted regression (GWR) techniques, which are applied to the variation in daily average cab trips and the characteristics of stations. The GWR models provide superior performance in comparison to the other two models, with notable distinctions observed in peak times, particularly morning peak when compared to total and off-peak counts. The findings indicate that factors such as population, population density, socioeconomic status, and the quantity of shopping malls are influential variables in elucidating and forecasting the fluctuations in taxi trip counts.

Spatiotemporal distribution and ecological factors of brucellosis among children from 2016 to 2020 in Inner Mongolia, China

ObjectiveIn recent years, the increasing incidence of brucellosis in children has become more serious. However, relatively few studies have been conducted to characterize the spatialtemporal distribution of brucellosis in children. This study aimed to analyze the spatiotemporal distribution characteristics and ecological influencing factors of brucellosis incidence among children in Inner Mongolia.MethodsThis study used data on brucellosis incidence in children aged 0–14 years reported in Inner Mongolia from 2016 to 2020. A Bayesian model was used to analyze the spatial and temporal distribution of brucellosis in children from 2016 to 2020 in Inner Mongolia. Geographical weighted regression model was used to analyze the ecological factors related to the incidence of brucellosis in children.ResultBayesian spatiotemporal analysis indicated that the highest brucellosis risk and increased disease incidence were observed in Hinggan, Inner Mongolia, in children aged 0–14 years. Alxa had the lowest risk but the incidence rate increased rapidly. The incidence of childhood brucellosis was positively associated with the number of sheep at the year-end (β: 2.5909 ~ 2.5926, P < 0.01), average temperature (β: 2.8978 ~ 2.9030, P < 0.05), and precipitation level (β: 3.3261 ~ 3.3268, P < 0.01).ConclusionFrom 2016 to 2020, the overall incidence of brucellosis in children in Inner Mongolia showed an upward trend, with cases exhibiting spatial aggregation. We should focus on areas where the incidence of brucellosis in children is rising rapidly. The incidence of childhood brucellosis was associated with the number of sheep at the year-end, average temperature and precipitation level.Implications and contributionThe findings suggest that brucellosis in children is not to be taken lightly. For children should also focus on protection, take corresponding protective measures. While we focus on high-risk areas, we must also monitor areas where the risk of disease is low, but the incidence is rising fast, to prevent outbreaks in low-risk areas from becoming high-risk areas.

Unraveling nonlinear and spatial non-stationary effects of urban form on surface urban heat islands using explainable spatial machine learning

Under global warming, surface urban heat islands (SUHI) threaten human health and urban ecosystems. However, scant research focused on exploring the complex associations between urban form factors and SUHI at the county scale, compared with rich studies at the city scale. Therefore, this study simultaneously examined the nonlinear and spatial non-stationary association between SUHI and urban form factors (e.g., landscape structure, built environment, and industrial pattern) across 2321 Chinese counties. An explainable spatial machine learning method, combining the Geographically Weighted Regression, Random Forest, and Shapley Additive Explanation model, was employed to deal with nonlinearity, spatial non-stationary, and interpretability of modeling. The results indicate the remarkable spatial disparities in the relationship between urban form factors and SUHI. Landscape structure contributes the most in southern counties, while the built environment is more important in northeastern counties. The impact of building density and building height increases with the county size and becomes the main driver of urban heat in mega counties. Most urban form factors exhibit nonlinear impacts on SUHI. For example, urban contiguity significantly affects SUHI beyond a threshold of 0.93, while building density does so at 0.17. By comparison, the influence of shape complexity remains stable above a value of 7. Factors such as industrial density and diversity have a varied influence on SUHI between daytime and nighttime. The results of local explanations and nonlinear effects provide targeted regional mitigation strategies for urban heat.

Diagnosis of ecological security and the spatial heterogeneity of its driving factors in the mining-impacted watershed, based on ecosystem health-risk-services framework

A comprehensive diagnosis of ecological security (ES) and its driving mechanisms in the watershed under mining influence is essential for the conservation and restoration of watershed ecosystems. Few studies have comprehensively evaluated ES by considering the condition of the ecosystem itself, the ecological function it provides, and the risk it faces. Therefore, by innovatively synthesizing ecosystem health (EH), ecological risk (ER), and ecosystem services (ESs), an ES evaluation framework based on EH-ER-ESs was constructed. Based on quantifying the ES of a typical watershed with mines clustered in China’s Northern Sand Prevention Belt, a spatial correlation analysis was used to elucidate the spatial differentiation characteristic of ES and verify the necessity of the evaluation framework. The driving mechanism of ES and the spatial heterogeneity of its key driving factors were explored using the Geodetector model and the geographically-weighted regression model. The results show that (1) ES was generally medium-security, and very low-security areas (8.16%) were mainly concentrated in the eastern mining aggregation areas. (2) ES showed high-high and low-low spatial clusters. Overall, ES was positively correlated with EH and ESs, while negatively correlated with ER, but there were individual cases of “high health-low security” and “high services-low security”, and combining EH, ER, and ESs to diagnose ES comprehensively was necessary. (3) Drought index, vegetation cover, distance from mining land, population density, and CONTAG were the key driving factors of ES. The explanatory power of factor interactions was higher than that of single factors. The impact of driving factors showed significant spatial heterogeneity, with the effects of mine agglomeration on ES primarily concentrated in the east. The EH-ER-ESs framework can be used for ES evaluation in other ecosystems, and the findings provide important guidance for conducting integrated watershed management.

Decoding Socio-Economic Demographic Trends: The Power of Spatial Econometrics and Geographic Analysis

Greece is experiencing a steady population decline caused by the declining migratory and natural balance. This research investigates the spatial impact of socio-economic and demographic factors on the natural population balance in Greece for the spatial zoning of municipal administrative units. Using geographically weighted regression (GWR) on data from the 2011 Greek census, the research explores the local impacts of factors like housing repair permits, vacant housing, employment rates, population inflows, distance from regional centers, aging, gender ratios, and education levels. An initial ordinary least squares (OLS) regression was conducted, revealing significant spatial variation and emphasizing the necessity of spatial econometric methods. The GWR model proved to be more effective in accounting for the variance in the data, removing spatial autocorrelation and revealing high local variation. Results show the high negative impact of the aging index in Western Greece and the Ionian islands, the counterintuitive positive effect of the gender ratio in urban areas, and the positive influence of population inflows in high-migration regions like Northern Greece and Crete. The results of this study underline the need to utilize spatial econometric methods for a precise and detailed understanding of demographic trends and provide valuable insights for localized strategies to address demographic challenges.

A Geographically Weighted Regression–Compute Unified Device Architecture Approach to Explore the Spatial Agglomeration and Heterogeneity in Arable Land Consumption in Southwest China

Arable land loss has become a critical issue in China because of rapid urbanization, industrial expansion, and unsustainable agricultural practices. While previous studies have explored the factors contributing to this loss, they often fall short in addressing the challenges of spatial heterogeneity and large-scale dataset analysis. This research introduces an innovative approach to geographically weighted regression (GWR) for assessing arable land loss in China, effectively addressing these challenges. Focusing on Chongqing, Guizhou, and Yunnan Provinces over the past two decades, it examines spatial autocorrelation with R-squared values exceeding 0.6 and residuals. Eight factors, including environmental elements (rain, evaporation, slope, digital elevation model) and human activities (distance to city, distance to roads, population, GDP), were analyzed. By visualizing and analyzing R² spatial patterns, the results reveal a clear spatial agglomeration distribution, primarily in urban areas with industries, highly urbanized cities, and flat terrains near rivers, influenced by GDP, population, rain, and slope. The novelty of this study is that it significantly enhances GWR computational capabilities for handling extensive datasets by utilizing Compute Unified Device Architecture (CUDA) on a high-performance GPU cloud server. Simultaneously, it conducts comprehensive analyses of the GWR model’s local results through visualization and spatial autocorrelation tools, enhancing the interpretability of the GWR model. Through spatial clustering analysis of local results, this study enables targeted exploration of factors influencing arable land changes in various temporal and spatial dimensions while also evaluating the reliability of the model results.

Improved Population Mapping for China Using the 3D Building, Nighttime Light, Points-of-Interest, and Land Use/Cover Data within a Multiscale Geographically Weighted Regression Model

Large-scale gridded population product datasets have become crucial sources of information for sustainable development initiatives. However, mainstream modeling approaches (e.g., dasymetric mapping based on Multiple Linear Regression or Random Forest Regression) do not consider the heterogeneity and multiscale characteristics of the spatial relationships between influencing factors and populations, which may seriously degrade the accuracy of the prediction results in some areas. This issue may be even more severe in large-scale gridded population products. Furthermore, the lack of detailed 3D human settlement data likewise poses a significant challenge to the accuracy of these data products. The emergence of the unprecedented Global Human Settlement Layer (GHSL) data package offers a possible solution to this long-standing challenge. Therefore, this study proposes a new Gridded Population Mapping (GPM) method that utilizes the Multiscale Geographically Weighted Regression (MGWR) model in conjunction with GHSL-3D Building, POI, nighttime light, and land use/cover datasets to disaggregate population data for third-level administrative units (districts and counties) in mainland China into 100 m grid cells. Compared to the WorldPop product, the new population map reduces the mean absolute error at the fourth-level administrative units (townships and streets) by 35%, 51%, and 13% in three test regions. The proposed mapping approach is poised to become a crucial reference for generating next-generation global demographic maps.

Spatiotemporal Differentiation of Carbon Emissions from Logistics Industry at Provincial Scale in China Under the Background of High-quality Economic Development

Since 2010, the Chinese economy has transitioned from a high-speed growth model to a high-quality development model. During this period, the logistics industry has witnessed rapid growth, leading to significant carbon emissions and posing severe threats to the ecological environment. To investigate the spatiotemporal variations in carbon emissions in China's logistics industry, we conducted a correlation analysis using Moran's I index and a bivariate spatial autocorrelation model from 2010 to 2021. Additionally, we employed a geographically and temporally weighted regression model （GTWR） to examine the spatial heterogeneity of factors influencing provincial-level logistics-related carbon emissions. The results indicated that over the study period, there was a shift from insignificant spatial relationships to significant positive spatial correlations among provincial-level logistics carbon emissions in China. Furthermore, varying degrees of spatial clustering were observed. The findings regarding factor heterogeneity revealed that freight turnover volume, per capita GDP of the logistics industry, and infrastructure level exhibited positive spatial correlations with logistics-related carbon emissions, whereas energy intensity showed negative spatial correlations with such emissions. Comparing the results from the geographically weighted regression （GWR） and ordinary least squares regression （OLS）, it was evident that the adjusted R-squared values for the OLS, GWR, and GTWR models were 0.541, 0.567, and 0.838, respectively. This suggests that our adopted GTWR model provided a superior fit and offered better explanations for spatiotemporal heterogeneity between various influencing factors and logistics-related carbon emissions. These research findings can serve as valuable references for formulating province-specific strategies to reduce carbon emissions within China's economy under its high-quality development context.

Does the spatial distribution of afforestation by government and farmers in Beijing follow a random pattern?

The forestland expansion is the joint efforts by various behavioral actors, and among them governments and farmers play a more important role in it. However, their afforestation behaviors haven't be together investigated. Examining Beijing metropolitan area, this research distinguishes between government-led (GA) and farmer-led (FA) afforestation on arable land, and analyzes their spatial characteristics and the influencing factors using Ordinary Least Squares and Geographically Weighted Regression models. Our findings show: (1) Spatial distributions of GA and FA are non-random and systematically organized. GA dominates both in the areas close to the central city and at the outermost edge of the metropolitan area. FA leads in intermediate zones between GA dominant areas. (2) Both GA and FA are rational strategies for land allocation. GA in areas close to the central city is regarded as a trade-off between public benefits of afforestation and potential loss of fiscal revenue, while GA at the metropolitan area's outermost edge prioritizes ecological gains and lower land costs. FA, however, is driven by maximizing household welfare amidst the challenges brought by rural exodus and a rapid aging society. The findings deepen the existing investigations and provide a guidance for spatially organizing GA and synthetically regulating FA.

Spatially clustered patterns of suicide mortality rates in South Korea: a geographically weighted regression analysis

BackgroundSuicide mortality remains a global health concern, and community characteristics affect regional variations in suicide. This study investigated spatially clustered patterns of suicide mortality rates in South Korea and evaluated the impact of community factors on suicide.MethodsSuicide mortality rates were estimated by sex, age group, and district, using the 2021 Cause of Death Statistics in South Korea from the MicroData Integrated Service. Community-determinant data for 2021 or the nearest year were collected from the Korean Statistical Information Service. The spatial autocorrelation of suicide by sex and age was examined based on Global Moran’s I index. Geographically weighted regression (GWR) was used to discern the influence of community determinants on suicide.ResultsSuicide mortality rates were significantly higher among men (40.64 per 100,000) and adults over the age of 65 years (43.18 per 100,000). The male suicide mortality rates exhibited strong spatial dependence, as indicated by a high global Moran’s I with p < 0.001, highlighting the importance of conducting spatial analysis. In the GWR model calibration, a subset of the community’s age structure, single-person household composition, access to mental healthcare centers, and unmet medical needs were selected to explain male suicide mortality. These determinants disproportionately increased the risk of male suicide, varying by region. The GWR coefficients of each variable vary widely across 249 districts: aging index (Q1:0.06–Q3:0.46), single-person households (Q1:0.22–Q3:0.35), psychiatric clinics (Q1:-0.20–Q3:-0.01), and unmet medical needs (Q1:0.09–Q3:0.14).ConclusionsCommunity cultural and structural factors exacerbate regional disparities in suicide among men. The influencing factors exhibit differential effects and significance depending on the community, highlighting the need for efficient resource allocation for suicide. A regionally tailored approach is crucial for the effective control of the community’s mental health management system.

Analysis of Taxi Demand and Traffic Influencing Factors in Urban Core Area Based on Data Field Theory and GWR Model: A Case Study of Beijing

Urban transportation constitutes a complex and dynamic system influenced by various factors, including population density, infrastructure, economic activities, and individual travel behavior. Taxis, as a widespread mode of transportation in many cities, play a crucial role in meeting the transportation needs of urban residents. By using data field theory and the Geographically Weighted Regression (GWR) modeling method, this study explored the complex relationship between taxi demand and traffic-related factors in urban core areas and revealed the potential factors affecting taxi starting and landing points. This research reveals that during the morning peak hours (7:00–9:00), at locations such as long-distance bus terminals, bus stations, parking areas, train stations, and bike-sharing points, taxi demand significantly increases, particularly in the central and southeastern regions of the urban core. Conversely, demand is lower in high-density intersection areas. Additionally, proximity to train stations is positively correlated with higher taxi demand, likely related to the needs of long-distance travelers. During the evening peak hours (17:00–19:00), the taxi demand pattern resembles that of the morning peak, with long-distance bus terminals, bus stations, and parking and bike sharing areas remaining key areas of demand. Notably, parking areas frequently serve as pick-up points for passengers during this time, possibly associated with evening activities and entertainment. Moreover, taxi demand remains high around train stations. In summary, this study enhances our understanding of the dynamics of urban taxi demand and its relationship with various transportation-related influencing factors within the core urban areas. The proposed grid partitioning and GWR modeling methods provide valuable insights for urban transportation planners, taxi service providers, and policymakers, facilitating service optimization and improved urban mobility.

Understanding the drivers of PM2.5 concentrations in Chinese cities: A comprehensive study of anthropogenic and environmental factors

Understanding the factors that drive PM2.5 concentrations in cities with varying population and land areas is crucial for promoting sustainable urban population health. This knowledge is particularly important for countries where air pollution is a significant challenge. Most existing studies have investigated either anthropogenic or environmental factors in isolation, often in limited geographic contexts; however, this study fills this knowledge gap. We employed a multimethodological approach, using both multiple linear regression models and geographically weighted regression (GWR), to assess the combined and individual effects of these factors across different cities in China. The variables considered were urban built-up area, land consumption rate (LCR), population size, population growth rate (PGR), longitude, and latitude. Compared with other studies, this study provides a more comprehensive understanding of PM2.5 drivers. The findings of this study showed that PGR and population size are key factors affecting PM2.5 concentrations in smaller cities. In addition, the extent of urban built-up areas exerts significant influence in medium and large cities. Latitude was found to be a positive predictor for PM2.5 concentrations across all city sizes. Interestingly, the northeast, south, and southwest regions demonstrated lower PM2.5 levels than the central, east, north, and northwest regions. The GWR model underscored the importance of considering spatial heterogeneity in policy interventions. However, this research is not without limitations. For instance, international pollution transfers were not considered. Despite the limitation, this study advances the existing literature by providing an understanding of how both anthropogenic and environmental factors, in conjunction with city scale, shape PM2.5 concentrations. This integrated approach offers invaluable insights for tailoring more effective air pollution management strategies across cities of different sizes and characteristics.

A backfitting maximum likelihood estimator for hierarchical and geographically weighted regression modelling, with a case study of house prices in Beijing

Geographically weighted regression (GWR) and its extensions are important local modelling techniques for exploring spatial heterogeneity in regression relationships. However, when dealing with spatial data of overlapping samples – for example, when precise locational information is aggregated to a shared neighbourhood to avoid revealing the addresses of individual survey respondents – GWR-based models can encounter several problems, including obtaining reliable bandwidths. Because data with this characteristic exhibit spatial hierarchical structures, we propose combining hierarchical linear modelling (HLM) with GWR to give a hierarchical and geographically weighted regression (HGWR) model that divides coefficients into sample-level fixed effects, group-level fixed effects, sample-level random effects, and group-level spatially weighted effects. This paper presents a back-fitting likelihood estimator to fit the model, a simulation experiment that suggests that HGWR is better able to capture these effects and the spatial heterogeneity within them than are traditional HLM or GWR models, and a case study looking at predictors of housing price in Beijing, China. The ability of HGWR to tackle both spatial and group-level heterogeneity simultaneously suggests its potential as a promising data modelling tool for handling spatio-temporal big data with spatially hierarchical structures.

Spatial clustering based on geographically weighted multivariate generalized gamma regression

Geographically Weighted Regression (GWR) is one of the local statistical models that can capture the effects of spatial heterogeneity. This model can be used for both univariate and multivariate responses. However, it should be noted that GWR models require the assumption of error normality. To overcome this problem, we propose a GWR model for generalized gamma distributed responses that can capture the phenomenon of some special continuous distributions. The proposed model is known as Geographically Weighted Multivariate Generalized Gamma Regression (GWMGGR). Parameter estimation is performed using the Maximum Likelihood Estimation (MLE) method optimized with the Bernt-Hall-Hall-Haussman (BHHH) algorithm. To determine the significance of the spatial heterogeneity effect, a hypothesis test was conducted using the Maximum Likelihood Ratio Test (MLRT) approach. We made a spatial cluster based on the estimated model parameters for each response using the k-means clustering method to interpret the obtained results. Some highlights of the proposed method are:•A new model for GWR with multivariate generalized gamma distributed responses to overcome the assumption of normally distributed errors.•Goodness of fit test to test the spatial effects in GWMGGR model.•Spatial clustering of districts/cities in Central Java based on three dimensions of educational indicators.

Exploring spatial non-stationarity of child labour and its related factors: A multiscale geographically weighted regression study of India

The relationships between various factors and child labour have been explored in the literature but, despite findings that suggest the predictive factors of child labour can vary according to context, there has been little research that has used spatial methods of analysis or attempted to estimate local relationships between covariates and the prevalence of child labour. This paper seeks to address this knowledge gap by using geographically weighted regression (GWR) and multiscale geographically weighted regression (MGWR) models. Using India 2011 Census Data as a case study, the findings show that GWR and MGWR models both perform significantly better than a global regression model across the whole of India. The study also finds significant spatial non-stationarity in the relationships between child labour and its covariates, with the association between district-level child labour rates and both the Muslim population and the child sex ratio found to have opposite directions in different parts of the country. Using MGWR, it was also possible to demonstrate that different covariates interact with child labour at various spatial scales, suggesting that interventions aiming to address varying aspects of the child labour problem may need to be deployed at different administrative levels to maximise their efficacy.

ANALISIS SPASIAL BERBASIS PEMETAAN MENGGUNAKAN GEOGRAPHICALLY WEIGHTED REGRESSION (GWR) PADA SEBARAN JUMLAH WISMA DI KABUPATEN LOMBOK BARAT

This research aims to analyze the effect of population density, number of food stalls, and population on the number of homesteads using the Geographically Weighted Regression (GWR) model. GWR modeling is carried out based on spatial data using secondary data sourced from the Central Statistics Agency (BPS). First, multiple linear regression analysis was carried out to evaluate the relationship between variables. The results of multiple linear regression show that only the variable number of food stalls has a significant effect on the number of homesteads. Next, spatial aspects were tested, including spatial autocorrelation tests and spatial heterogeneity tests. Testing spatial aspects shows the existence of spatial autocorrelation and spatial heterogeneity in the data. Therefore, we continued with GWR modeling to obtain a more in-depth picture of the distribution of the number of homesteads in West Lombok Regency. The results of modeling with GWR show that the variables used have a spatially varying influence throughout the West Lombok Regency area. Mapping GWR results produces better modeling of the factors that influence the number of homesteads in each village. A comparison between the multiple linear regression model and the GWR shows that the GWR model is able to explain variations in the number of homesteads with a higher R-square and a smaller AIC value