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.

A General Framework for Estimation and Inference of Geographically Weighted Regression Models: 1. Location-Specific Kernel Bandwidths and a Test for Locational Heterogeneity

2002 ◽  
Vol 34 (4) ◽  
pp. 733-754 ◽  
Author(s):  
Antonio Páez ◽  
Takashi Uchida ◽  
Kazuaki Miyamoto
Keyword(s):  
Geographically Weighted Regression ◽  
Degrees Of Freedom ◽  
Likelihood Function ◽  
Error Variance ◽  
Model Specification ◽  
Weighted Regression ◽  
Regularity Conditions ◽  
Local Regression ◽  
Specification Tests ◽  
Geographically Weighted Regression Model

Geographically weighted regression (GWR) has been proposed as a technique to explore spatial parametric nonstationarity. The method has been developed mainly along the lines of local regression and smoothing techniques, a strategy that has led to a number of difficult questions about the regularity conditions of the likelihood function, the effective number of degrees of freedom, and in general the relevance of extending the method to derive inference and model specification tests. In this paper we argue that placing GWR within a different statistical context, as a spatial model of error variance heterogeneity, or what might be termed locational heterogeneity, solves these difficulties. A maximum-likelihood-based framework for estimation and inference of a general geographically weighted regression model is presented that leads to a method to estimate location-specific kernel bandwidths. Moreover, a test for locational heterogeneity is derived and its use exemplified with a case study.

scholarly journals Key Factors Assessment on Bird Strike Density Distribution in Airport Habitats: Spatial Heterogeneity and Geographically Weighted Regression Model

2020 ◽  
Vol 12 (18) ◽  
pp. 7235
Author(s):  
Quan Shao ◽  
Yan Zhou ◽  
Pei Zhu ◽  
Yan Ma ◽  
Mengxue Shao
Keyword(s):  
Spatial Heterogeneity ◽  
Density Distribution ◽  
Geographically Weighted Regression ◽  
Spatial Variations ◽  
Least Square ◽  
Civil Aviation ◽  
Weighted Regression ◽  
Bird Strike ◽  
Key Factors ◽  
Geographically Weighted Regression Model

Although the factors influencing bird strikes have been studied extensively, few works focused on the spatial variations in bird strikes affected by factors due to the difference in the geographical environment around the airport. In this paper, the bird strike density distribution of different seasons affected by factors in a rectangular region of 800 square kilometers centered on the Xi’an Airport runway was investigated based on collected bird strike data. The ordinary least square (OLS) model was used to analyze the global effects of different factors, and the Geographically Weighted Regression (GWR) model was used to analyze the spatial variations in the factors of bird strike density. The results showed that key factors on the kernel density of bird strikes showed evident spatial heterogeneity and the seasonal difference in the different habitats. Based on the results of the study, airport managers are provided with some specific defense measures to reduce the number of bird strikes from the two aspects of expelling birds on the airfield area and reducing the attractiveness of habitats outside the airport to birds, so that achieve the sustainable and safe development of civil aviation and the ecological environment.

scholarly journals Spatiotemporal Changes in Vegetation Cover and Its Influencing Factors in the Loess Plateau of China Based on the Geographically Weighted Regression Model

Forests ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 673
Author(s):  
Chen Yang ◽  
Meichen Fu ◽  
Dingrao Feng ◽  
Yiyu Sun ◽  
Guohui Zhai
Keyword(s):  
Regression Model ◽  
Influencing Factors ◽  
Loess Plateau ◽  
Geographically Weighted Regression ◽  
Vegetation Cover ◽  
Weighted Regression ◽  
Vegetation Coverage ◽  
The Loess Plateau ◽  
Geographically Weighted Regression Model ◽  
Spatiotemporal Changes

Vegetation plays a key role in ecosystem regulation and influences our capacity for sustainable development. Global vegetation cover has changed dramatically over the past decades in response to both natural and anthropogenic factors; therefore, it is necessary to analyze the spatiotemporal changes in vegetation cover and its influencing factors. Moreover, ecological engineering projects, such as the “Grain for Green” project implemented in 1999, have been introduced to improve the ecological environment by enhancing forest coverage. In our study, we analyzed the changes in vegetation cover across the Loess Plateau of China and the impacts of influencing factors. First, we analyzed the latitudinal and longitudinal changes in vegetation coverage. Second, we displayed the spatiotemporal changes in vegetation cover based on Theil-Sen slope analysis and the Mann-Kendall test. Third, the Hurst exponent was used to predict future changes in vegetation coverage. Fourth, we assessed the relationship between vegetation cover and the influence of individual factors. Finally, ordinary least squares regression and the geographically weighted regression model were used to investigate the influence of various factors on vegetation cover. We found that the Loess Plateau showed large-scale greening from 2000 to 2015, though some regions showed decreasing vegetation cover. Latitudinal and longitudinal changes in vegetation coverage presented a net increase. Moreover, some areas of the Loess Plateau are at risk of degradation in the future, but most areas showed a sustainable increase in vegetation cover. Temperature, precipitation, gross domestic product (GDP), slope, cropland percentage, forest percentage, and built-up land percentage displayed different relationships with vegetation cover. Geographically weighted regression model revealed that GDP, temperature, precipitation, forest percentage, cropland percentage, built-up land percentage, and slope significantly influenced (p < 0.05) vegetation cover in 2000. In comparison, precipitation, forest percentage, cropland percentage, and built-up land percentage significantly affected (p < 0.05) vegetation cover in 2015. Our results enhance our understanding of the ecological and environmental changes in the Loess Plateau.

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.

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