mgwrsar (version 0.1-1)

bandwidths_mgwrsar: Select optimal kernel and bandwidth from a list of models, kernels and bandwidth candidates.

Description

Given a lm formula and a dataframe with coordinates, function bandwidths_mgwrsar optimizes the choice of a bandwidth value for each of the chosen models and kernel types using a leave-one-out cross validation criteria. A cross validated criteria is also used for selecting the best kernel type for a given model.

Usage

bandwidths_mgwrsar(formula, data,coord,
fixed_vars='Intercept',Models='GWR',Kernels='bisq',control=list(),control_search=list())

Arguments

formula

a formula.

data

a dataframe or a spatial dataframe (sp package).

coord

a dataframe or a matrix with coordinates, not required if data is a spatial dataframe, default NULL.

fixed_vars

a vector with the names of spatially constant coefficient. For mixed model, if NULL, the default #' is set to 'Intercept'.

Models

character containing the type of model: Possible values are "OLS", "SAR", "GWR" (default), "MGWR" , "MGWRSAR_0_0_kv","MGWRSAR_1_0_kv", "MGWRSAR_0_kc_kv", "MGWRSAR_1_kc_kv", "MGWRSAR_1_kc_0".

Kernels

a vector with the names of kernel type.

control

list of extra control arguments for MGWRSAR wrapper - see MGWRSAR help.

control_search

list of extra control arguments for bandwidth/kernel search - see section below. @details

• search_Wif TRUE select an optimal spatial weight matrix using a moment estimator, default FALSE.

• kernels_wif search_W is TRUE, kernels_w is a vector of candidated kernels types, default NULL.

• lower_clower bound for bandwidth search (default, the approximate first decile of distances).

• upper_cupper bound for bandwidth search (default, the approximate last decile of distances).

• lower_dlower bound for discrete kernels, default 2*k+1.

• lower_dWower bound for discrete kernels for finding optimal spatial weight matrix, default 2.

• lower_cWlower bound for bandwidth search for finding optimal spatial weight matrix (default approximate 0.005 quantile of distances).

Value

bandwiths_MGWRSAR returns a list with:

config_model

a vector with information about model, optimal kernel and bandwidth for local regression, and optimal kernel and bandwith for spatial weight matrix W.

SSR

The sum of square residuals.

CV

The CV criteria.

model

objects of class mgwrsar estimated using config_model

Details

Given a lm formula and a dataframe with coordinates, for each model in Models for wich a bandwidth is required, this function optimizes the choice of a bandwidth value for each of the chosen models and kernel types using a leave one out cross validation criteria. A cross validated criteria is also used for selecting the best kernel type for a given model.

References

Geniaux, G. and Martinetti, D. (2017). A new method for dealing simultaneously with spatial autocorrelation and spatial heterogeneity in regression models. Regional Science and Urban Economics. (https://doi.org/10.1016/j.regsciurbeco.2017.04.001)

McMillen, D. and Soppelsa, M. E. (2015). A conditionally parametric probit model of microdata land use in chicago. Journal of Regional Science, 55(3):391-415.

Loader, C. (1999). Local regression and likelihood, volume 47. Springer New York.

Franke, R. and Nielson, G. (1980). Smooth interpolation of large sets of scattered data. International journal for numerical methods in engineering, 15(11):1691-1704.

See Also

MGWRSAR, summary_mgwrsar, plot_mgwrsar, predict_mgwrsar, kernelW_C

Examples

# NOT RUN {
library(mgwrsar)
data(mydata)
coord=as.matrix(mydata[,c("x_lat","y_lon")])
W=KNN(coord,8)
######################
#### Finding bandwith by hand
#####################

### kernel only space
model_GWR<-MGWRSAR(formula = 'Y_gwr~X1+X2+X3', data = mydata,coord=coord,
fixed_vars=NULL,kernels=c('bisq_knn'),H=50,
Model = 'GWR', control=list(isgcv=FALSE,minv=1))
cat('SSR =')
summary_mgwrsar(model_GWR)

myCV<-function(H){model_GWR<-MGWRSAR(formula = 'Y_gwr~X1+X2+X3', data = mydata,
coord=coord, fixed_vars=NULL,kernels=c('gauss_adapt'),H,
 Model = 'GWR',control=list(isgcv=TRUE))
model_GWR$SSR
}

res=optimize(myCV,upper=500,lower=10)
res

## model with optimal bandwith with adaptative gaussian kernel

model_GWR<-MGWRSAR(formula = 'Y_gwr~X1+X2+X3', data = mydata,coord=coord,
fixed_vars=NULL,kernels=c ('gauss_adapt'),H=ceiling(res$minimum),
Model = 'GWR',control=list(isgcv=FALSE))
summary_mgwrsar(model_GWR)

######################
#### finding the bandwidths using bandwidths_mgwrsar
#####################


mytab<-bandwidths_mgwrsar(formula = 'Y_gwr~X1+X2+X3', data = mydata,coord=coord,
fixed_vars='Intercept',Models=c('GWR','MGWR'),Kernels=c('bisq_knn','gauss_adapt','gauss'),
control=list(),control_search=list (lower_d=8,lower_c=0.03,upper_c=0.65))

names(mytab)
names(mytab[['GWR']])

mytab[['GWR']]$config_model
mytab[['GWR']]$CV
summary(mytab[['GWR']]$model$Betav)


mytab[['GWR_2']]$config_model
mytab[['GWR_2']]$CV
summary(mytab[['GWR_2']]$model$Betav)

mytab[['GWR_3']]$config_model
mytab[['GWR_3']]$CV
summary(mytab[['GWR_3']]$model$Betav)

mytab[['MGWR']]$config_model
mytab[['MGWR']]$CV
mytab[['MGWR']]$model$Betac
summary(mytab[['MGWR']]$model$Betav)

mytab[['MGWR_2']]$config_model
mytab[['MGWR_2']]$CV
mytab[['MGWR_2']]$model$Betac
summary(mytab[['MGWR_2']]$model$Betav)

mytab[['MGWR_3']]$config_model
mytab[['MGWR_3']]$CV
mytab[['MGWR_3']]$model$Betac
summary(mytab[['MGWR_3']]$model$Betav)

mytab2<-bandwidths_mgwrsar(formula = 'Y_gwr~X1+X2+X3', data = mydata,coord=coord,
 fixed_vars='Intercept',Models=c('MGWRSAR_0_kc_kv'),Kernels=c('gauss_adapt'),
 control=list(),control_search=list(search_W=TRUE,kernels_w=c('bisq','gauss_adapt')))

mytab2[['MGWRSAR_0_kc_kv']]$config_model
mytab2[['MGWRSAR_0_kc_kv']]$CV
mytab2[['MGWRSAR_0_kc_kv']]$model$Betac
summary(mytab2[['MGWRSAR_0_kc_kv']]$model$Betav)

# }