scholarly journals Computational improvements to multiscale geographically weighted regression

2019 ◽  
Author(s):  
Ziqi Li ◽  
Alexander Stewart Fotheringham
Keyword(s):  
Geographically Weighted Regression ◽  
Parallel Implementation ◽  
Additive Model ◽  
Large Datasets ◽  
Computational Method ◽  
Weighted Regression ◽  
Multi Scale ◽  
Single Scale ◽  
Gwr Model ◽  
Python Package

Geographically Weighted Regression (GWR) has been broadly used in various fields to model spatially non-stationary relationships. Multi-scale Geographically Weighted Regression (MGWR) is a recent advancement to the classic GWR model. MGWR is superior in capturing multi-scale processes over the traditional single-scale GWR model by using different bandwidths for each covariate. However, the multiscale property of MGWR brings additional computation costs. The calibration process of MGWR involves iterative back-fitting under the additive model (AM) framework. Currently, MGWR can only be applied on small datasets within a tolerable time and is prohibitive on moderately large datasets (greater than 5,000 observations). In this paper, we propose a parallel implementation that has crucial computational improvements to MGWR calibration. This improved computational method reduces both memory footprint and runtime to allow MGWR modelling to be applied to moderate-to-large datasets (up to 100,000 observations). These improvements are integrated into the mgwr python package and MGWR 2.0 software, both of which are freely available to download.

scholarly journals Measuring Bandwidth Uncertainty in Multiscale Geographically Weighted Regression Using Akaike Weights

2019 ◽  
Author(s):  
Ziqi Li ◽  
Alexander Stewart Fotheringham ◽  
Taylor M. Oshan ◽  
Levi John Wolf
Keyword(s):  
Geographically Weighted Regression ◽  
Regression Models ◽  
Bandwidth Selection ◽  
Information Criterion ◽  
Weighted Regression ◽  
Parameter Estimates ◽  
Multi Scale ◽  
Single Scale ◽  
Heterogeneous Processes ◽  
Key Parameter

Bandwidth, a key parameter in geographically weighted regression models, is closely related to the spatial scale at which the underlying spatially heterogeneous processes being examined take place. Generally, a single optimal bandwidth (geographically weighted regression) or a set of covariate-specific optimal bandwidths (multiscale geographically weighted regression) is chosen based on some criterion such as the Akaike Information Criterion (AIC) and then parameter estimation and inference are conditional on the choice of this bandwidth. In this paper, we find that bandwidth selection is subject to uncertainty in both single-scale and multi-scale geographically weighted regression models and demonstrate that this uncertainty can be measured and accounted for. Based on simulation studies and an empirical example of obesity rates in Phoenix, we show that bandwidth uncertainties can be quantitatively measured by Akaike weights, and confidence intervals for bandwidths can be obtained. Understanding bandwidth uncertainty offers important insights about the scales over which different processes operate, especially when comparing covariate-specific bandwidths. Additionally, unconditional parameter estimates can be computed based on Akaike weights accounts for bandwidth selection uncertainty.

scholarly journals Remote Sensing Estimation of Bamboo Forest Aboveground Biomass Based on Geographically Weighted Regression

2021 ◽  
Vol 13 (15) ◽  
pp. 2962
Author(s):  
Jingyi Wang ◽  
Huaqiang Du ◽  
Xuejian Li ◽  
Fangjie Mao ◽  
Meng Zhang ◽  
...  
Keyword(s):  
Aboveground Biomass ◽  
Geographically Weighted Regression ◽  
Local Variation ◽  
Zhejiang Province ◽  
Weighted Regression ◽  
Landsat 8 ◽  
Bamboo Forest ◽  
Prediction Ability ◽  
Gwr Model ◽  
Forest Aboveground Biomass

Bamboo forests are widespread in subtropical areas and are well known for their rapid growth and great carbon sequestration ability. To recognize the potential roles and functions of bamboo forests in regional ecosystems, forest aboveground biomass (AGB)—which is closely related to forest productivity, the forest carbon cycle, and, in particular, carbon sinks in forest ecosystems—is calculated and applied as an indicator. Among the existing studies considering AGB estimation, linear or nonlinear regression models are the most frequently used; however, these methods do not take the influence of spatial heterogeneity into consideration. A geographically weighted regression (GWR) model, as a spatial local model, can solve this problem to a certain extent. Based on Landsat 8 OLI images, we use the Random Forest (RF) method to screen six variables, including TM457, TM543, B7, NDWI, NDVI, and W7B6VAR. Then, we build the GWR model to estimate the bamboo forest AGB, and the results are compared with those of the cokriging (COK) and orthogonal least squares (OLS) models. The results show the following: (1) The GWR model had high precision and strong prediction ability. The prediction accuracy (R2) of the GWR model was 0.74, 9%, and 16% higher than the COK and OLS models, respectively, while the error (RMSE) was 7% and 12% lower than the errors of the COK and OLS models, respectively. (2) The bamboo forest AGB estimated by the GWR model in Zhejiang Province had a relatively dense spatial distribution in the northwestern, southwestern, and northeastern areas. This is in line with the actual bamboo forest AGB distribution in Zhejiang Province, indicating the potential practical value of our study. (3) The optimal bandwidth of the GWR model was 156 m. By calculating the variable parameters at different positions in the bandwidth, close attention is given to the local variation law in the estimation of the results in order to reduce the model error.

scholarly journals Geographically weighted regression modelling of the spatial association between malaria cases and environmental factors in Cameroon.

2020 ◽  
Author(s):  
Marlvin Anemey Tewara ◽  
Liu Yunxia ◽  
Weiqiang Ling ◽  
Binang Helen Barong ◽  
Prisca Ngetemalah Mbah-Fongkimeh ◽  
...  
Keyword(s):  
Environmental Factors ◽  
Spatial Variability ◽  
Geographically Weighted Regression ◽  
Environmental Variables ◽  
Vegetation Index ◽  
Spatial Association ◽  
Ordinary Least Squares ◽  
Variable Coefficients ◽  
Weighted Regression ◽  
Gwr Model

Abstract Background: Studies have illustrated the association of malaria cases with environmental factors in Cameroon but limited in addressing how these factors vary in space for timely public health interventions. Thus, we want to find the spatial variability between malaria hotspot cases and environmental predictors using Geographically weighted regression (GWR) spatial modelling technique.Methods: The global Ordinary least squares (OLS) in the modelling spatial relationships tool in ArcGIS 10.3. was used to select candidate explanatory environmental variables for a properly specified GWR model. The local GWR model used the global OLS candidate variables to examine, predict and explore the spatial variability between environmental factors and malaria hotspot cases generated from Getis-Ord Gi* statistical analysis. Results: The OLS candidate environmental variable coefficients were statistically significant (adjusted R2 = 22.3% and p < 0.01) for a properly specified GWR model. The GWR model identified a strong spatial association between malaria cases and rainfall, vegetation index, population density, and drought episodes in most hotspot areas and a weak correlation with aridity and proximity to water with an overall model performance of 0.243 (adjusted R2= 24.3%).Conclusion: The generated GWR maps suggest that for policymakers to eliminate malaria in Cameroon, there should be the creation of malaria outreach programs and further investigations in areas where the environmental variables showed strong spatial associations with malaria hotspot cases.

scholarly journals Parameter estimation of geographically weighted regression (GWR) model using weighted least square and its application

2018 ◽  
Author(s):  
Saskya Mary Soemartojo ◽  
Rima Dini Ghaisani ◽  
Titin Siswantining ◽  
Mariam Rahmania Shahab ◽  
Moch. Muchid Ariyanto
Keyword(s):  
Parameter Estimation ◽  
Geographically Weighted Regression ◽  
Least Square ◽  
Weighted Regression ◽  
Weighted Least Square ◽  
Gwr Model

scholarly journals Inference in multiscale geographically weighted regression

2018 ◽  
Author(s):  
Hanchen Yu ◽  
Stewart Fotheringham ◽  
Ziqi Li ◽  
Taylor Oshan ◽  
Wei Kang ◽  
...  
Keyword(s):  
Geographically Weighted Regression ◽  
Additive Model ◽  
Simulated Data ◽  
Weighted Regression ◽  
Parameter Estimates ◽  
Real World Data ◽  
Data Set ◽  
Smoothing Factor ◽  
Hat Matrix ◽  
Response Vector

A recent paper (Fotheringham et al. 2017) expands the well-known Geographically Weighted Regression (GWR) framework significantly by allowing the bandwidth or smoothing factor in GWR to be derived separately for each covariate in the model – a framework referred to as Multiscale GWR (MGWR). However, one limitation of the MGWR framework is that, until now, no inference about the local parameter estimates was possible. Formally, the so-called “hat matrix,” which projects the observed response vector into the predicted response vector, was available in GWR but not in MGWR. This paper addresses this limitation by reframing GWR as a Generalized Additive Model (GAM), extending this framework to MGWR and then deriving standard errors for the local parameters in MGWR. In addition, we also demonstrate how the effective number of parameters (ENP) can be obtained for the overall fit of an MGWR model and for each of the covariates within the model. This statistic is essential for comparing model fit between MGWR, GWR, and traditional global models, as well as adjusting for multiple hypothesis tests. We demonstrate these advances to the MGWR framework with both a simulated data set and a real-world data set.

scholarly journals An exploratory approach for enhancing vertical and horizontal equity tests for ad valorem property tax valuations using geographically weighted regression

2019 ◽  
Vol 24 (2) ◽  
pp. 231-250
Author(s):  
Paul Bidanset ◽  
Michael McCord ◽  
Peadar Davis ◽  
Mark Sunderman
Keyword(s):  
Geographically Weighted Regression ◽  
Local Level ◽  
Property Tax ◽  
Horizontal Equity ◽  
Weighted Regression ◽  
Horizontal Inequity ◽  
Content Type ◽  
Property Taxation ◽  
Gwr Model ◽  
Ad Valorem

Purpose The purpose of this study is to enhance the estimation of vertical and horizontal inequity within property valuation. Property taxation is a crucial source of finance for local government around the world – based on a presumptive tax base underpinned by estimates of property value, inaccurate real estate valuations used for such ad valorem or value-based property tax calculations potentially lead to a variety of costs, both financial and other, for tax payers and governments alike. More common are increased costs in time, staff and, in some cases, legal fees. Some governments are even bound by acceptability thresholds to promote fairness, equitability and overall government accountability with respect to valuation. Design/methodology/approach There exist a number of vertical inequity measurements that have undergone academic testing and scrutiny within the property tax industry since the 1970s. While these approaches have proved successful in detecting horizontal and vertical inequity, one recurring disadvantage pertains to measurement error/omitted variable bias, stemming largely from a failure to accurately account for location. A natural progression within property tax research is the application of a more spatially local weighted modelling approach to examine vertical and horizontal inequity. This research, therefore, specifies a geographically weighted regression (GWR) methodology to detect and measure vertical inequity in property valuations. Findings The findings show the efficacy of using more applied spatial approaches for vertical tax estimation and indeed the limitations of employing conditional mean estimates coupled with delineated boundaries for assessing property tax inequity. The GWR model findings highlight the more fluctuating nature of vertical inequity across the Belfast market for the apartment sector both in a progressive and regressive sense and at different magnitudes. Moreover, the results reveal spatial clustering in the effects and are indicative of systematic inequities related to location inferring that spatial (horizontal) tax inequities are not random. The findings further show increased GWR model predictability overall. Originality/value This research adds to the existing literature base for evaluating both vertical and horizontal inequity in value-based property taxation at the intra-neighbourhood level. This is accomplished by modifying the Birch–Sunderman approach by transforming the traditional OLS model architecture to a GWR model, thereby allowing coefficient estimates of inequity to vary not only across a jurisdiction, but also at a more local level, while incorporating property characteristic variables. This arguably allows assessors to identify specific geographical areas of concern, saving them money, time and resources on identifying, addressing and correcting for inequity.

scholarly journals PEMODELAN REGRESI BERGANDA DAN GEOGRAPHICALLY WEIGHTED REGRESSION PADA TINGKAT PENGANGGURAN TERBUKA DI JAWA TENGAH

2017 ◽  
Vol 9 (2) ◽  
pp. 133
Author(s):  
Tiani Wahyu Utami ◽  
Abdul Rohman ◽  
Alan Prahutama
Keyword(s):  
Labor Force ◽  
Unemployment Rate ◽  
Geographically Weighted Regression ◽  
Poor Performance ◽  
Predictor Variables ◽  
Weighted Regression ◽  
Residual Variance ◽  
Central Java ◽  
Gdp Growth Rate ◽  
Gwr Model

The problems in employment was the growing number of Open Unemployment Rate (OUR). The open unemployment rate is a number that indicates the number of unemployed to the 100 residents are included in the labor force. The purpose of this study is mapping the data OUR in Central Java and the suspect and identify linkages between factors that cause OUR in the District / City of Central Java in 2014. Factors that allegedly include population density (X1), Inflation (X2), the GDP value (X3), UMR Value (X4), the percentage of GDP growth rate (X5), Hope of the old school (X6), the percentage of the labor force by age (X7) and the percentage of employment (X8). Geographically Weighted Regression (GWR) is a method for modeling the response of the predictor variables, by including elements of the area (spatial) into the point-based model. This research resulted in the conclusion that the OLS regression models have poor performance because the residual variance is not homogeneous. There were no significant differences between GWR models with OLS model or in other words generally predictor variables did not affect the response variable (rate of unemployment in Central Java) spatially. However, GWR model could captured modelling in each region. Keywords: multiple linear regression, geographiically weighted regression, open unemployement rate in Central Java.

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

2021 ◽  
Vol 5 (1) ◽  
pp. 173-181
Author(s):  
Winda Nurpadilah ◽  
I Made Sumertajaya ◽  
Muhamad Nur Aidi
Keyword(s):  
Kernel Function ◽  
Geographically Weighted Regression ◽  
Spatial Regression ◽  
Spatial Diversity ◽  
Weighted Regression ◽  
Parameter Estimates ◽  
Spatial Effects ◽  
West Java ◽  
Exponential Kernel ◽  
Gwr Model

Spatial regression analysis is a form of regression model that considers spatial effects. Geographically weighted regression (GWR) is the spatial regression methods that can be used to deal with the problem of spatial diversity. This method generates local model parameter estimates for each observation location. The application of spatial statistics can be done in all areas such as the problem of poverty. Poverty can be influenced by factors of proximity between regions, so that in determining the poverty factor, the proximity factor of the region cannot be ignored. West Java Province is a province with the largest population, so this study aims to model the poverty data in West Java Province by incorporating spatial effects. The weighting function used for the GWR model is the function of the fixed and adaptive kernels. The analysis results show that the fixed exponential kernel function has the smallest cross validation (CV) value, so the weighting matrix used in the model is determined by the exponential kernel function. The largest  value and the smallest AIC value are owned by the GWR model with an exponential kernel function. Based on the results obtained by the the ANOVA table to test GWR's global goodness, the GWR model is more effective than global regression. Therefore, the GWR model is the best model when it used in West Java’s poverty cases. The effect of each explanatory variable on the percentage of poverty varies in each district/city in West Java Province.

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