StepGWR_gaussian {StepGWR}

StepGWR: a hybrid spatial model that combines the variable selection capabilities of stepwise regression with the predictive power of Geographically Weighted Regression (GWR) model

Description

StepGWR: a hybrid spatial model that combines the variable selection capabilities of stepwise regression with the predictive power of Geographically Weighted Regression (GWR) model

Usage

StepGWR_gaussian(data_sp, bw, split_value, gaussian_kernel)

Arguments

data_sp

A dataframe containing a response variable and the predictor variables, as well as the coordinates of the locations. In the dataframe, first column is the response variable (y), last two columns are coordinates i.e., Latitude and Longitudes and in between them is the set of predictor variables(X's).

bw

A numeric value specifying the bandwidth parameter for the GWR model. It can be noted that, optimum bandwidth parameter value can vary and depends on the spatial pattern of the dataset.

split_value

Splitting value for dividing the dataset into training and testing set, e.g. 0.8 or 0.7

gaussian_kernel

Spatial weight function of the GWR model, e.g. gaussian_kernel

Value

A list with the following components: - 'Important_vars ': Selected important variables based on stepwise regression - 'GWR_y_pred_test': The predicted values based on GWR at test locations - 'rrmse': root means square error - 'R_squared': R square value - 'mse': mean squared error - 'mae': mean absolute error

References

1. Leung, Y., Mei, C. L. and Zhang, W. X. (2000). Statistical tests for spatial non-stationarity based on the geographically weighted regression model. Environment and Planning A, 32(1),9-32.<DOI:10.1068/a3162>. 2. Brunsdon, C., Fotheringham, A.S. and Charlton, M,E. (1996).Geographically weighted regression: a method for exploring spatial non-stationarity. Geogr Anal.28(4),281-298.<DOI:10.1111/j.1538-4632.1996.tb00936.x>.

Examples

n<- 100
p<- 7
m<-sqrt(n)
id<-seq(1:n)
x<-matrix(runif(n*p), ncol=p)
e<-rnorm(n, mean=0, sd=1)
xy_grid<-expand.grid(c(1:m),c(1:m))
Latitude<-xy_grid[,1]
Longitude<-xy_grid[,2]
B0<-(Latitude+Longitude)/6
B1<-(Latitude/3)
B2<-(Longitude/3)
B3<-(2*Longitude)
B4<-2*(Latitude+Longitude)/6
B5<-(4*Longitude/3)
B6<-2*(Latitude+Longitude)/18
B7<-(4*Longitude/18)
y<-B0+(B1*x[,1])+(B2*x[,2])+(B3*x[,3])+(B4*x[,4])+(B5*x[,5])+(B6*x[,6])+(B7*x[,7])+e
data_sp<-data.frame(y,x,Latitude,Longitude)
StepGWR_gau<-StepGWR_gaussian(data_sp,0.8,0.7,gaussian_kernel)