Parameter Estimation of Locally Compensated Ridge-Geographically Weighted Regression Model

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 ^ ( u i , v i , λ i ) = [ X ∗ T W * ( u i , v i ) X ∗ + λ I ( u i , v i ) ] − 1 X ∗ T W * ( u i , v i ) 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 = t = β ^ k ( u i , v i , λ i ) σ ^ v k k .