Parameter Estimation of Locally Compensated Ridge-Geographically Weighted Regression Model

9th Annual Basic Science International Conference 2019

自然科学（总论）

Fadliana, Alfi^1 ; Pramoedyo, Henny^2 ; Fitriani, Rahma^2

Statistics Master Study Program, Department of Statistics, Faculty of Mathematics and Natural Sciences, Brawijaya University, East Java, Malang, Indonesia^1

Department of Statistics, Faculty of Mathematics and Natural Sciences, Brawijaya University, East Java, Malang, Indonesia^2

关键词: Collinearity;    Explanatory variables;    Geographically weighted regression;    Geographically weighted regression models;    Locally Compensated Ridge;    Spatial data analysis;    Spatially varying coefficients;    Weighted least square method;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/546/5/052022/pdf
DOI  :  10.1088/1757-899X/546/5/052022

学科分类：自然科学（综合）

来源: IOP

【 摘 要 】

Geographically weighted regression (GWR) is a spatial data analysis method where spatially varying relationships are explored between explanatory variables and a response variable. One unresolved problem with spatially varying coefficient regression models is local collinearity in weighted explanatory variables. The consequence of local collinearity is: estimation of GWR coefficients is possible but their standard errors tend to be large. As a result, the population values of the coefficients cannot be estimated with great precision or accuracy. In this paper, we propose a recently developed method to remediate the collinearity effects in GWR models using the Locally Compensated Ridge Geographically Weighted Regression (LCR-GWR). Our focus in this study was on reviewing the estimation parameters of LCR-GWR model. And also discussed an appropriate statistic for testing significance of parameters in the model. The result showed that Parameter estimation of LCR-GWR model using weighted least square method is β(ui,vi,λi) = [X∗TW(ui,vi)X∗+λI(ui,vi)]-1X∗TW)(ui,vi)y∗, where the ridge parameter, λ, varies across space. The LCR-GWR is not necessarily calibrates the ridge regressions everywhere; only at locations where collinearity is likely to be an issue. And the parameter significance test using t-test, t = (equation presented).