MARSGWR_exponential {MARSGWR}

MARSGWR: a hybrid model that uses the MARS model for important variable selection and the GWR model for prediction at an unknown location based on the selected variables.

Description

MARSGWR: a hybrid model that uses the MARS model for important variable selection and the GWR model for prediction at an unknown location based on the selected variables.

Usage

MARSGWR_exponential(sp_data, bw, deg, sv, exponential_kernel)

Arguments

sp_data

A dataframe containing the response variables and the predictor variable, 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

deg

The degree of interactions to be considered in the MARS model

sv

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

exponential_kernel

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

Value

A list with the following components: - 'Selected_variables': The selected variables from the MARS model - 'GWR_y_pred_train': The GWR predictions at the training locations - 'GWR_y_pred_test': The GWR predictions at testing locations - 'In_sample_accuracy': In sample accuracy measures - 'Out_of_sample_accuracy': Out of sample accuracy measures

References

1. Friedman, J.H. (1991).Multivariate Adaptive Regression Splines. Ann. Statist. 19(1),1-67. <DOI:10.1214/aos/1176347963>. 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<- 5
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)
y<-B0+(B1*x[,1])+(B2*x[,2])+(B3*x[,3])+(B4*x[,4])+(B5*x[,5])+ e
sp_data<-data.frame(y,x,Latitude,Longitude)
MARSGWR_exp<-MARSGWR_exponential(sp_data,5,3,0.7,exponential_kernel)