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 Robust Geographically Weighted Regression Modeling using Least Absolute Deviation and M-Estimator

2019 ◽  
pp. 238-245
Author(s):  
Puteri Pekerti Wulandari ◽  
Anik Djuraidah ◽  
Aji Hamim Wigena
Keyword(s):  
Parameter Estimation ◽  
Geographically Weighted Regression ◽  
Location Parameter ◽  
Least Square Method ◽  
Least Square ◽  
Weighted Regression ◽  
Absolute Deviation ◽  
Estimated Parameters ◽  
M Estimator ◽  
Better Than

Geographically weighted regression (GWR) is development of multiple regression that has spatial varying, so that the estimator of GWR is different for each location. Parameter estimation in GWR uses weighted least square method which is vulnerable to outlier and can cause biased parameter estimation. The robust GWR (RGWR) with LAD and M-estimator is resistance to outliers. This research estimated parameters on RGWR using LAD and M-estimator method and uses data of Java gross domestic product (GRDP) in 2015 containing several outliers. The result showed that RGWR model was better than GWR with M-estimator, and the predictions were closer to the actual values.

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.

Second-hand housing batch evaluation model of zhengzhou city based on big data and MGWR model

2021 ◽  
pp. 1-20
Author(s):  
Chaojie Liu ◽  
Jie Lu ◽  
Wenjing Fu ◽  
Zhuoyi Zhou
Keyword(s):  
Real Estate ◽  
Geographically Weighted Regression ◽  
Euclidean Distance ◽  
Evaluation Model ◽  
Housing Prices ◽  
Information Criterion ◽  
Access Point ◽  
Least Square ◽  
Weighted Regression ◽  
Spatial Error

How to better evaluate the value of urban real estate is a major issue in the reform of real estate tax system. So the establishment of an accurate and efficient housing batch evaluation model is crucial in evaluating the value of housing. In this paper the second-hand housing transaction data of Zhengzhou City from 2010 to 2019 was used to model housing prices and explanatory variables by using models of Ordinary Least Square (OLS), Spatial Error Model (SEM), Geographically Weighted Regression (GWR), Geographically and Temporally Weighted Regression (GTWR), and Multiscale Geographically Weighted Regression (MGWR). And a correction method of Barrier Line and Access Point (BLAAP) was constructed, and compared with three correction methods previously studied: Buffer Area (BA), Euclidean Distance (ED), and Non-Euclidean Distance, Travel Distance (ND, TT). The results showed: The fitting degree of GWR, MGWR and GTWR by BLAAP was 0.03–0.07 higher than by ND. The fitting degree of MGWR was the highest (0.883) by BLAAP but the smallest by Akaike Information Criterion (AIC), and 88.3% of second-hand housing data could be well interpreted by the model.

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 Estimation of Error Variance-Covariance Parameters Using Multivariate Geographically Weighted Regression Model

2020 ◽  
Vol 2020 ◽  
pp. 1-5 ◽  
Author(s):  
Sri Harini
Keyword(s):  
Statistical Inference ◽  
Geographically Weighted Regression ◽  
Weighting Function ◽  
Likelihood Estimation ◽  
Error Variance ◽  
Least Square ◽  
Weighted Regression ◽  
Inference Procedure ◽  
Geographically Weighted Regression Model ◽  
Estimated Error

The Multivariate Geographically Weighted Regression (MGWR) model is a development of the Geographically Weighted Regression (GWR) model that takes into account spatial heterogeneity and autocorrelation error factors that are localized at each observation location. The MGWR model is assumed to be an error vector ε that distributed as a multivariate normally with zero vector mean and variance-covariance matrix Σ at each location ui,vi, which Σ is sized qxq for samples at the i-location. In this study, the estimated error variance-covariance parameters is obtained from the MGWR model using Maximum Likelihood Estimation (MLE) and Weighted Least Square (WLS) methods. The selection of the WLS method is based on the weighting function measured from the standard deviation of the distance vector between one observation location and another observation location. This test uses a statistical inference procedure by reducing the MGWR model equation so that the estimated error variance-covariance parameters meet the characteristics of unbiased. This study also provides researchers with an understanding of statistical inference procedures.

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 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.

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