| Title: | GWR and MGWR with Spatial Autocorrelation |
|---|---|
| Description: | Functions for computing (Mixed) Geographically Weighted Regression with spatial autocorrelation, Geniaux and Martinetti (2017) <doi:10.1016/j.regsciurbeco.2017.04.001>. |
| Authors: | Ghislain Geniaux and Davide Martinetti |
| Maintainer: | Ghislain Geniaux <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0.5 |
| Built: | 2024-12-25 07:02:20 UTC |
| Source: | CRAN |
Select optimal kernel and bandwidth from a list of models, kernels and bandwidth candidates. 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.
bandwidths_mgwrsar(formula, data,coords, fixed_vars='Intercept',Models='GWR',candidates_Kernels='bisq', control=list(),control_search=list())bandwidths_mgwrsar(formula, data,coords, fixed_vars='Intercept',Models='GWR',candidates_Kernels='bisq', control=list(),control_search=list())
formula |
a formula. |
data |
a dataframe or a spatial dataframe (sp package). |
coords |
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". |
candidates_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 details below. |
if TRUE select an optimal spatial weight matrix using a moment estimator, default FALSE.
if search_W is TRUE, kernels_w is a vector of candidated kernels types, default NULL.
lower bound for bandwidth search (default, the approximate first decile of distances).
upper bound for bandwidth search (default, the approximate last decile of distances).
lower bound for discrete kernels, default 2*k+1.
ower bound for discrete kernels for finding optimal spatial weight matrix, default 2.
lower bound for bandwidth search for finding optimal spatial weight matrix (default approximate 0.005 quantile of distances).
bandwiths_MGWRSAR returns a list with:
a vector with information about model, optimal kernel and bandwidth for local regression, and optimal kernel and bandwith for spatial weight matrix W.
The sum of square residuals.
The CV criteria.
objects of class mgwrsar estimated using config_model
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.
MGWRSAR, summary_mgwrsar, plot_mgwrsar, predict_mgwrsar
library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) mytab<-bandwidths_mgwrsar(formula = 'Y_gwr~X1+X2+X3', data = mydata,coords=coords, fixed_vars=c('Intercept','X1'),Models=c('GWR','MGWR'),candidates_Kernels=c('bisq','gauss'), control=list(NN=300,adaptive=TRUE),control_search=list()) names(mytab) names(mytab[['GWR_bisq_adaptive']]) mytab[['GWR_bisq_adaptive']]$config_model mytab[['GWR_bisq_adaptive']]$CV summary(mytab[['GWR_bisq_adaptive']]$model$Betav) mybestmodel=mytab[['GWR_gauss_adaptive']]$model plot_mgwrsar(mybestmodel,type='B_coef',var='X2')library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) mytab<-bandwidths_mgwrsar(formula = 'Y_gwr~X1+X2+X3', data = mydata,coords=coords, fixed_vars=c('Intercept','X1'),Models=c('GWR','MGWR'),candidates_Kernels=c('bisq','gauss'), control=list(NN=300,adaptive=TRUE),control_search=list()) names(mytab) names(mytab[['GWR_bisq_adaptive']]) mytab[['GWR_bisq_adaptive']]$config_model mytab[['GWR_bisq_adaptive']]$CV summary(mytab[['GWR_bisq_adaptive']]$model$Betav) mybestmodel=mytab[['GWR_gauss_adaptive']]$model plot_mgwrsar(mybestmodel,type='B_coef',var='X2')
Search of a suitable set of target points. find_TP is a wrapper function that identifies a set of target points based on spatial smoothed OLS residuals.
find_TP(formula, data,coords,K,kWtp=16,Wtp=NULL,type='residuals', model_residuals=NULL,verbose=0,prev_TP=NULL,nTP=NULL)find_TP(formula, data,coords,K,kWtp=16,Wtp=NULL,type='residuals', model_residuals=NULL,verbose=0,prev_TP=NULL,nTP=NULL)
formula |
a formula |
data |
a dataframe or a spatial dataframe (SP package) |
coords |
a dataframe or a matrix with coordinates, not required if data is a spatial dataframe |
K |
the minimum number of first neighbors with lower (resp.higer) absolute value of the smoothed residuals. |
kWtp |
the number of first neighbors for computing the smoothed residuals, default 16. |
Wtp |
a precomputed matrix of weights, default NULL. |
type |
method for choosing TP, could be 'residuals', 'equidistantGrid','random', default 'residuals' |
model_residuals |
(optional) a vector of residuals. |
verbose |
verbose mode, default FALSE. |
prev_TP |
index of already used TP (version length(K)>1), default NULL. |
nTP |
numbeer of target points for random choice of target points, default NULL. |
find_TP is a wrapper function that identifies a set of target points, based on spatial smoothed residuals by default. If no vector of residuals are provided, OLS residuals are computed. The function first computes the smooth of model residuals using a Sheppard's kernel with kWtp neighbors (default 16). Then it identifies local maxima (resp. minima) that fits the requirement of having at least K neighbors with lower (resp.higer) absolute value of the smoothed residuals. As K increases the number of target points decreases.
find_TP returns an index vector of Target Points set.
library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) TP=find_TP(formula = 'Y_gwr~X1+X2+X3', data =mydata,coords=coords,K=6,type='residuals') # only 60 targets points are used length(TP) model_GWR_tp<-MGWRSAR(formula = 'Y_gwr~X1+X2+X3', data = mydata,coords=coords, fixed_vars=NULL,kernels=c('gauss'), H=0.03, Model = 'GWR', control=list(SE=TRUE,TP=TP,kWtp=12)) summary(model_GWR_tp$Betav)library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) TP=find_TP(formula = 'Y_gwr~X1+X2+X3', data =mydata,coords=coords,K=6,type='residuals') # only 60 targets points are used length(TP) model_GWR_tp<-MGWRSAR(formula = 'Y_gwr~X1+X2+X3', data = mydata,coords=coords, fixed_vars=NULL,kernels=c('gauss'), H=0.03, Model = 'GWR', control=list(SE=TRUE,TP=TP,kWtp=12)) summary(model_GWR_tp$Betav)
kernel_matW A function that returns a sparse weight matrix based computed with a specified kernel (gauss,bisq,tcub,epane,rectangle,triangle) considering coordinates provides in S and a given bandwidth. If NN<nrow(S) only NN firts neighbours are considered. If Type!='GD' then S should have additional columns and several kernels and bandwidths should be be specified by the user.
kernel_matW(H,kernels,coord_i,coord_j=NULL,NN,ncolX=1, Type='GD',adaptive=FALSE,diagnull=TRUE,rowNorm=TRUE,noisland=FALSE)kernel_matW(H,kernels,coord_i,coord_j=NULL,NN,ncolX=1, Type='GD',adaptive=FALSE,diagnull=TRUE,rowNorm=TRUE,noisland=FALSE)
H |
A vector of bandwidths |
kernels |
A vector of kernel types |
coord_i |
A matrix with variables used in kernel (reference) |
coord_j |
A matrix with variables used in kernel (neighbors), default NULL (if NULL coord_j=coord_i) |
NN |
Number of spatial Neighbours for kernels computations |
ncolX |
control parameter |
Type |
Type of Genelarized kernel product ('GD' only spatial,'GDC' spatial + a categorical variable,'GDX' spatial + a continuous variable, 'GDT' spatial + a time index, and other combinations 'GDXXC','GDTX',...) |
adaptive |
A vector of boolean to choose adaptive version for each kernel |
diagnull |
Zero on diagonal, default FALSE |
rowNorm |
A boolean, row normalization of weights, default TRUE |
noisland |
A boolean to avoid isle with no neighbours for non adaptive kernel, default FALSE |
A sparse Matrix of weights (dgCMatrix).
library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) ## Creating a spatial weight matrix (sparce dgCMatrix) of 4 nearest neighbors with 0 in diagonal W=kernel_matW(H=4,kernels='rectangle',coord_i=coords,NN=4,adaptive=TRUE,diagnull=TRUE,rowNorm=TRUE)library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) ## Creating a spatial weight matrix (sparce dgCMatrix) of 4 nearest neighbors with 0 in diagonal W=kernel_matW(H=4,kernels='rectangle',coord_i=coords,NN=4,adaptive=TRUE,diagnull=TRUE,rowNorm=TRUE)
MGWRSAR is is a wrapper function for estimating linear and local linear models with spatial autocorrelation (SAR models with spatially varying coefficients).
MGWRSAR(formula,data,coords,fixed_vars=NULL,kernels,H, Model='GWR',control=list())MGWRSAR(formula,data,coords,fixed_vars=NULL,kernels,H, Model='GWR',control=list())
formula |
a formula. |
data |
a dataframe or a spatial dataframe (sp package). |
coords |
default NULL, a dataframe or a matrix with coordinates, not required if data is a spatial dataframe. |
fixed_vars |
a vector with the names of spatiallay constant coefficient for mixed model. All other variables present in formula are supposed to be spatially varying. If empty or NULL (default), all variables in formula are supposed to be spatially varying. |
kernels |
A vector containing the kernel types. Possible types: rectangle ("rectangle"), bisquare ("bisq"), tricube ("tcub"), epanechnikov ("epane"), gaussian ("gauss")) . |
H |
vector containing the bandwidth parameters for the kernel functions. |
Model |
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". See Details for more explanation. |
control |
list of extra control arguments for MGWRSAR wrapper - see Details below |
a matrix of variables for genralized kernel product, default NULL.
a row-standardized spatial weight matrix for Spatial Aurocorrelation, default NULL.
verbose mode, default FALSE.
A vector of boolean to choose adaptive version for each kernel.
the type of kernel for computing W, default NULL.
the bandwidth value for computing W, default 0.
estimation technique for computing the models with Spatial Dependence. '2SLS' or 'B2SLS', default '2SLS'.
A vector of target points, default NULL.
Parallel computation, default FALSE
number of CPU core for parallel computation, default 1
computing LOOCV criteria (for example for selecting optimal bandwidth), default FALSE.
if TRUE, simplify the computation of CV criteria (remove or not i when using local instruments for model with lambda spatially varying), default TRUE.
when n >NmaxDist, only the maxknn first neighbours are used for distance compution, default 500.
when n >NmaxDist only the maxknn first neighbours are used for distance compution, default 5000
verbose mode, default FALSE.
MGWRSAR returns an object of class mgwrsar with at least the following components:
matrix of coefficients of dim(n,kv) x kv.
vector of coefficients of length kc.
The sum of square residuals.
The dependent variable.
The explanatory variables with constant coefficients.
The explanatory variables with varying coefficients.
The explanatory variables.
The spatial weight matrix for spatial dependence.
if gcv has been computed.
The estimated degrees of freedom.
The formula.
The dataframe used for computation.
The type of model.
The spatial coordinates of observations.
The bandwidth vector.
The names of constant coefficients.
The kernel vector.
The sum of square residuals.
The vector of residuals.
the vector of fitted values.
local standard error of parameters.
Boolean, if trace of hat matrix Tr(S) should be stored.
Maximum number of neighbors for weights computation
MGWRSAR is is a wrapper function for estimating linear and local linear model
with spatial autocorrelation that allows to estimate the following models :
(OLS)
(GWR)
(MGWR)
(MGWR-SAR(0,k,0))
(MGWR-SAR(0,0,k))
(MGWR-SAR(0,k_c,k_v))
(MGWR-SAR(1,k,0))
(MGWR-SAR(1,0,k))
(MGWR-SAR(1,k_c,k_v))
When model imply spatial autocorrelation, a row normalized spatial weight matrix must be provided. 2SLS and Best 2SLS method can be used. When model imply local regression, a bandwidth and a kernel type must be provided. Optimal bandwidth can be estimated using bandwidths_mgwrsar function. When model imply mixed local regression, the names of stationary covariates must be provided.
#' In addition to the ability of considering spatial autocorrelation in GWR/MGWR like models, MGWRSAR function introduces several useful technics for estimating local regression with space coordinates:
it uses RCCP and RCCPeigen code that speed up computation and allows parallel computing via doMC package;
it allows to drop out variables with not enough local variance in local regression, which allows to consider dummies in GWR/MGWR framework without trouble.
it allows to drop out local outliers in local regression.
it allows to consider additional variable for kernel, including time (asymetric kernel) and categorical variables (see Li and Racine 2010). Experimental version.
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.
bandwidths_mgwrsar, summary_mgwrsar, plot_mgwrsar, predict_mgwrsar, kernel_matW
library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) ## Creating a spatial weight matrix (sparce dgCMatrix) ## of 4 nearest neighbors with 0 in diagonal W=kernel_matW(H=4,kernels='rectangle',coord_i=coords,NN=4,adaptive=TRUE, diagnull=TRUE,rowNorm=TRUE) mgwrsar_0_kc_kv<-MGWRSAR(formula = 'Y_mgwrsar_0_kc_kv~X1+X2+X3', data = mydata, coords=coords, fixed_vars='X2',kernels=c('gauss'),H=20, Model = 'MGWRSAR_0_kc_kv', control=list(SE=FALSE,adaptive=TRUE,W=W)) summary_mgwrsar(mgwrsar_0_kc_kv)library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) ## Creating a spatial weight matrix (sparce dgCMatrix) ## of 4 nearest neighbors with 0 in diagonal W=kernel_matW(H=4,kernels='rectangle',coord_i=coords,NN=4,adaptive=TRUE, diagnull=TRUE,rowNorm=TRUE) mgwrsar_0_kc_kv<-MGWRSAR(formula = 'Y_mgwrsar_0_kc_kv~X1+X2+X3', data = mydata, coords=coords, fixed_vars='X2',kernels=c('gauss'),H=20, Model = 'MGWRSAR_0_kc_kv', control=list(SE=FALSE,adaptive=TRUE,W=W)) summary_mgwrsar(mgwrsar_0_kc_kv)
A bootstrap test for Betas for mgwrsar class model.
mgwrsar_bootstrap_test(x0,x1,B=100,domc=FALSE,ncore=1, type='standard',eps='H1',df='H1',focal='median',D=NULL)mgwrsar_bootstrap_test(x0,x1,B=100,domc=FALSE,ncore=1, type='standard',eps='H1',df='H1',focal='median',D=NULL)
x0 |
The H0 mgwrsar model |
x1 |
The H1 mgwrsar model |
B |
number of bootstrap repetitions, default 100 |
domc |
If TRUE, doParallel parallelization |
ncore |
number of cores |
type |
type of bootstap : 'wild','Rademacher','spatial' or 'standard' (default) |
eps |
Hypothesis under wich residuals are simulated, 'H0' or 'H1' (default) |
df |
Hypothesis under wich degree of freedom is estimated. |
focal |
see sample_stat help |
D |
A matrix of distance |
The value of the statictics test and a p ratio.
mgwrsar_bootstrap_test_all
A bootstrap test for testing nullity of all Betas for mgwrsar class model,
mgwrsar_bootstrap_test_all(model,B=100,domc=NULL)mgwrsar_bootstrap_test_all(model,B=100,domc=NULL)
model |
A mgwrsar model |
B |
number of bootstrap replications, default 100 |
domc |
If TRUE, doMC parallelization |
a matrix with statistical test values and p ratios
mgwrsar_bootstrap_test
multiscale_gwr This function adapts the multiscale Geographically Weighted Regression (GWR) methodology proposed by Fotheringam et al. in 2017, employing a backward fitting procedure within the MGWRSAR subroutines. The consecutive bandwidth optimizations are performed by minimizing the corrected Akaike criteria.
multiscale_gwr(formula,data,coords,Model = 'GWR',kernels='bisq', control=list(SE=FALSE,adaptive=TRUE,NN=800,isgcv=FALSE),init='GWR',maxiter=100, nstable=6,crit=0.000001,doMC=FALSE,ncore=1,HF=NULL,H0=NULL,model=NULL)multiscale_gwr(formula,data,coords,Model = 'GWR',kernels='bisq', control=list(SE=FALSE,adaptive=TRUE,NN=800,isgcv=FALSE),init='GWR',maxiter=100, nstable=6,crit=0.000001,doMC=FALSE,ncore=1,HF=NULL,H0=NULL,model=NULL)
formula |
A formula. |
data |
A dataframe. |
coords |
default NULL, a dataframe or a matrix with coordinates. |
Model |
The type of model: Possible values are "GWR" (default), and "MGWRSAR_1_0_kv". See Details for more explanation. |
kernels |
A vector containing the kernel types. Possible types: rectangle ("rectangle"), bisquare ("bisq"), tricube ("tcub"), epanechnikov ("epane"), gaussian("gauss")). |
control |
a list of extra control arguments, see MGWRSAR help. |
init |
starting model (lm or GWR) |
maxiter |
maximum number of iterations in the back-fitting procedure. |
nstable |
required number of consecutive unchanged optimal bandwidth (by covariate) before leaving optimisation of bandwidth size, default 3. |
crit |
value to terminate the back-fitting iterations (ratio of change in RMSE) |
doMC |
A boolean for Parallel computation, default FALSE. |
ncore |
number of CPU cores for parallel computation, default 1. |
HF |
if available, a vector containing the optimal bandwidth parameters for each covariate, default NULL. |
H0 |
A bandwidth value for the starting GWR model, default NULL. |
model |
A previous model estimated using multiscale_gwr function, default NULL. |
Return an object of class mgwrsar with at least the following components:
matrix of coefficients of dim(n,kv) x kv.
vector of coefficients of length kc.
The sum of square residuals.
The dependent variable.
The explanatory variables with constant coefficients.
The explanatory variables with varying coefficients.
The explanatory variables.
The spatial weight matrix for spatial dependence.
if gcv has been computed.
The estimated degrees of freedom.
The formula.
The dataframe used for computation.
The type of model.
The spatial coordinates of observations.
A vector of bandwidths.
The names of constant coefficients.
The kernel vector.
The sum of square residuals.
The vector of residuals.
the vector of fitted values.
local standard error of parameters.
Boolean, if trace of hat matrix Tr(S) should be stored.
Maximum number of neighbors for weights computation
tds_mgwr, bandwidths_mgwrsar, summary_mgwrsar, plot_mgwrsar, predict_mgwrsar
library(mgwrsar) mysimu<-simu_multiscale(n=1000) mydata=mysimu$mydata coords=mysimu$coords model_multiscale<-multiscale_gwr(formula=as.formula('Y~X1+X2+X3'),data=mydata, coords=coords,Model = 'GWR',kernels='bisq',control=list(SE=FALSE, adaptive=TRUE,NN=900,isgcv=FALSE),init='GWR',nstable=6,crit=0.000001) summary_mgwrsar(model_multiscale)library(mgwrsar) mysimu<-simu_multiscale(n=1000) mydata=mysimu$mydata coords=mysimu$coords model_multiscale<-multiscale_gwr(formula=as.formula('Y~X1+X2+X3'),data=mydata, coords=coords,Model = 'GWR',kernels='bisq',control=list(SE=FALSE, adaptive=TRUE,NN=900,isgcv=FALSE),init='GWR',nstable=6,crit=0.000001) summary_mgwrsar(model_multiscale)
multiscale_gwr.cv to be documented (experimental)
multiscale_gwr.cv(dataName, argDataName="data", target='Y', K=5, regFun, par_model, par_model2=NULL,regFun2=NULL, predFun, args_predNames, extra_args_pred=NULL, namesXtraArgs2Split=NULL,myseed=1)multiscale_gwr.cv(dataName, argDataName="data", target='Y', K=5, regFun, par_model, par_model2=NULL,regFun2=NULL, predFun, args_predNames, extra_args_pred=NULL, namesXtraArgs2Split=NULL,myseed=1)
dataName |
character, name of the data |
argDataName |
character, generic name to use as data name. |
target |
character, name of variable to explain |
K |
integer, number of folds for cross validation |
regFun |
character, name of the estimation function |
par_model |
named list with the arguments for the estimation function |
par_model2 |
to be documented |
regFun2 |
to be documented |
predFun |
character, name of the prediction function |
args_predNames |
named list with the arguments for the prediction function |
extra_args_pred |
named list with extra arguments for non generic prediction function |
namesXtraArgs2Split |
character, names of the objects in extra_args_pred that need to be split for cross validation. |
myseed |
seed for random number. |
mydata is a simulated data set of a mgwrsar model
Ghislain Geniaux and Davide Martinetti [email protected]
https://www.sciencedirect.com/science/article/pii/S0166046216302381
normW row normalization of dgCMatrix
normW(W)normW(W)
W |
A dgCMatrix class matrix |
A row normalized dgCMatrix
plot_effect plot_effect is a function that plots the effect of a variable X_k with spatially varying coefficient, i.e X_k * Beta_k(u_i,v_i) for comparing the magnitude of effects of between variables.
plot_effect(model,sampling=TRUE,nsample=2000,nsample_max=5000,title='')plot_effect(model,sampling=TRUE,nsample=2000,nsample_max=5000,title='')
model |
a model of mgwrsar class with some spatially varying coefficients. |
sampling |
Bolean, if nrow(model$Betav)> nsample_max a sample of size nsample is randomly selected, default TRUE. |
nsample |
integer, size of the sample if sampling is TRUE, default 2000. |
nsample_max |
integer, size max to engage sampling if sampling is TRUE, default 5000. |
title |
a title for the plot. |
library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) ## Creating a spatial weight matrix (sparce dgCMatrix) ## of 8 nearest neighbors with 0 in diagonal model_GWR0<-MGWRSAR(formula = 'Y_gwr~X1+X2+X3', data = mydata,coords=coords, fixed_vars=NULL,kernels=c('gauss'),H=0.13, Model = 'GWR',control=list(SE=TRUE)) plot_effect(model_GWR0)library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) ## Creating a spatial weight matrix (sparce dgCMatrix) ## of 8 nearest neighbors with 0 in diagonal model_GWR0<-MGWRSAR(formula = 'Y_gwr~X1+X2+X3', data = mydata,coords=coords, fixed_vars=NULL,kernels=c('gauss'),H=0.13, Model = 'GWR',control=list(SE=TRUE)) plot_effect(model_GWR0)
plot_mgwrsar plots the value of local paramaters of a mgwrsar models using a leaflet map.
plot_mgwrsar(model,type='coef',var=NULL,crs=NULL,mypalette= "RdYlGn",opacity=0.5 ,fopacity=0.5,nbins=8,radius=500,mytile='Stamen.TonerBackground',myzoom=8, myresolution=150,LayersControl=TRUE,myzoomControl=TRUE,mytile2=NULL,ScaleBar=NULL, ScaleBarOptions=list(maxWidth = 200, metric = TRUE,imperial = FALSE, updateWhenIdle = TRUE),MyLegendTitle=NULL,lopacity=0.5)plot_mgwrsar(model,type='coef',var=NULL,crs=NULL,mypalette= "RdYlGn",opacity=0.5 ,fopacity=0.5,nbins=8,radius=500,mytile='Stamen.TonerBackground',myzoom=8, myresolution=150,LayersControl=TRUE,myzoomControl=TRUE,mytile2=NULL,ScaleBar=NULL, ScaleBarOptions=list(maxWidth = 200, metric = TRUE,imperial = FALSE, updateWhenIdle = TRUE),MyLegendTitle=NULL,lopacity=0.5)
model |
a mgwsar model. |
type |
default 'coef', for plotting the value of the coefficients. Local t-Student could also be plot using 't_coef', residuals using 'residuals' and fitted using 'fitted'. |
var |
Names of variable to plot. |
crs |
A CRS projection. |
mypalette |
A leaflet palette. |
opacity |
Opacity of border color. |
fopacity |
Opacity of fill color. |
nbins |
nbins. |
radius |
radius of circle for plot of points. |
mytile |
tile 1. |
myzoom |
level of zoom for tile 1. |
myresolution |
resolution for tile 1. |
LayersControl |
layers contols. |
myzoomControl |
zoem control. |
mytile2 |
tile 2. |
ScaleBar |
ScaleBar. |
ScaleBarOptions |
options for ScaleBar. |
MyLegendTitle |
Legend title. |
lopacity |
opacity for legend. |
A Interactive Web Maps with local parameters plot and Open Street Map layer.
MGWRSAR, bandwidths_mgwrsar, summary_mgwrsar, predict_mgwrsar, kernel_matW
library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) ## Creating a spatial weight matrix (sparce dgCMatrix) ## of 4 nearest neighbors with 0 in diagonal model_GWR0<-MGWRSAR(formula = 'Y_gwr~X1+X2+X3', data = mydata,coords=coords, fixed_vars=NULL,kernels=c('gauss'),H=0.13, Model='GWR',control=list(SE=TRUE)) summary_mgwrsar(model_GWR0) plot_mgwrsar(model_GWR0,type='B_coef',var='X2') plot_mgwrsar(model_GWR0,type='t_coef',var='X2')library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) ## Creating a spatial weight matrix (sparce dgCMatrix) ## of 4 nearest neighbors with 0 in diagonal model_GWR0<-MGWRSAR(formula = 'Y_gwr~X1+X2+X3', data = mydata,coords=coords, fixed_vars=NULL,kernels=c('gauss'),H=0.13, Model='GWR',control=list(SE=TRUE)) summary_mgwrsar(model_GWR0) plot_mgwrsar(model_GWR0,type='B_coef',var='X2') plot_mgwrsar(model_GWR0,type='t_coef',var='X2')
mgwrsar Model Predictions predict_mgwrsar is a function for computing predictions of a mgwrsar models. It uses Best Linear Unbiased Predictor for mgwrsar models with spatial autocorrelation.
predict_mgwrsar(model, newdata, newdata_coords, W = NULL, type = "BPN", h_w = 100,kernel_w = "rectangle",maxobs=4000,beta_proj=FALSE, method_pred='TP', k_extra = 8)predict_mgwrsar(model, newdata, newdata_coords, W = NULL, type = "BPN", h_w = 100,kernel_w = "rectangle",maxobs=4000,beta_proj=FALSE, method_pred='TP', k_extra = 8)
model |
a model of mgwrsar class. |
newdata |
a matrix or data.frame of new data. |
newdata_coords |
a matrix of new coordinates, and eventually other variables if a General Kernel Product is used. |
W |
the spatial weight matrix for models with spatial autocorrelation. |
type |
Type for BLUP estimator, default "BPN". If NULL use predictions without spatial bias correction. |
h_w |
A bandwidth value for the spatial weight matrix |
kernel_w |
kernel type for the spatial weight matrix. Possible types: rectangle ("rectangle"), bisquare ("bisq"), tricube ("tcub"), epanechnikov ("epane"), gaussian ("gauss")) . |
maxobs |
maximum number of observations for exact calculation of solve(I- rho*W), default maxobs=4000. |
beta_proj |
A boolean, if TRUE the function then return a two elements list(Y_predicted,Beta_proj_out) |
method_pred |
If method_pred = 'TP' (default) prediction is done by recomputing a MGWRSAR model with new-data as target points, else if method_pred in ('tWtp_model','model','sheppard') a matrix for projecting estimated betas is used (see details). |
k_extra |
number of neighboors for local parameter extrapolation if sheppard kernel is used, default 8. |
if method_pred ='tWtp_model', the weighting matrix for prediction is based on the expected weights of outsample data if they were had been added to insample data to estimate the corresponding MGWRSAR (see Geniaux 2022 for further detail), if method_pred ='sheppard'a sheppard kernel with k_extra neighbours (default 8) is used and if method_pred='kernel_model' the same kernel and number of neighbors as for computing the MGWRSAR model is used.
A vector of predictions if beta_proj is FALSE or a list with a vector named Y_predicted and a matrix named Beta_proj_out.
MGWRSAR, bandwidths_mgwrsar, summary_mgwrsar, plot_mgwrsar, kernel_matW
library(mgwrsar) data(mydata) coords=as.matrix(mydata[,c("x","y")]) length_out=800 index_in=sample(1:1000,length_out) index_out=(1:1000)[-index_in] model_GWR_insample<-MGWRSAR(formula = 'Y_gwr~X1+X2+X3', data = mydata[index_in,], coords=coords[index_in,],fixed_vars=NULL,kernels=c ('gauss'),H=8, Model = 'GWR', control=list(adaptive=TRUE)) summary_mgwrsar(model_GWR_insample) newdata=mydata[index_out,] newdata_coords=coords[index_out,] newdata$Y_mgwrsar_1_0_kv=0 Y_pred=predict_mgwrsar(model_GWR_insample, newdata=newdata, newdata_coords=newdata_coords) head(Y_pred) head(mydata$Y_gwr[index_out]) sqrt(mean((mydata$Y_gwr[index_out]-Y_pred)^2)) # RMSElibrary(mgwrsar) data(mydata) coords=as.matrix(mydata[,c("x","y")]) length_out=800 index_in=sample(1:1000,length_out) index_out=(1:1000)[-index_in] model_GWR_insample<-MGWRSAR(formula = 'Y_gwr~X1+X2+X3', data = mydata[index_in,], coords=coords[index_in,],fixed_vars=NULL,kernels=c ('gauss'),H=8, Model = 'GWR', control=list(adaptive=TRUE)) summary_mgwrsar(model_GWR_insample) newdata=mydata[index_out,] newdata_coords=coords[index_out,] newdata$Y_mgwrsar_1_0_kv=0 Y_pred=predict_mgwrsar(model_GWR_insample, newdata=newdata, newdata_coords=newdata_coords) head(Y_pred) head(mydata$Y_gwr[index_out]) sqrt(mean((mydata$Y_gwr[index_out]-Y_pred)^2)) # RMSE
The simu_multiscale function is designed for simulating a spatially varying coefficient DGP (Data Generating Process) based on formulations proposed by Fotheringam et al. (2017), Gao et al. (2021), or Geniaux (2024).
simu_multiscale(n=1000,myseed=1,type='GG2024',b0_constant=FALSE)simu_multiscale(n=1000,myseed=1,type='GG2024',b0_constant=FALSE)
n |
An integer number of observations. |
myseed |
An integer seed used for the simulation. |
type |
Type of DGP used 'FT2017', 'Gao2021' or 'GG2024', default 'GG2024'. |
b0_constant |
A boolean parameter indicating whether the intercept term should be spatially varying (TRUE) or not (FALSE). |
A named list with simulated data ('mydata') and coords ('coords')
library(mgwrsar) library(ggplot2) library(gridExtra) library(grid) simu=simu_multiscale(1000) mydata=simu$mydata coords=simu$coords p1<-ggplot(mydata,aes(x,y,col=Beta1))+geom_point() +scale_color_viridis_c() p2<-ggplot(mydata,aes(x,y,col=Beta2))+geom_point() +scale_color_viridis_c() p3<-ggplot(mydata,aes(x,y,col=Beta3))+geom_point() +scale_color_viridis_c() p4<-ggplot(mydata,aes(x,y,col=Beta4))+geom_point() +scale_color_viridis_c() grid.arrange(p1,p2,p3,p4,nrow=2,ncol=2, top = textGrob("DGP Geniaux (2024)" ,gp=gpar(fontsize=20,font=3)))library(mgwrsar) library(ggplot2) library(gridExtra) library(grid) simu=simu_multiscale(1000) mydata=simu$mydata coords=simu$coords p1<-ggplot(mydata,aes(x,y,col=Beta1))+geom_point() +scale_color_viridis_c() p2<-ggplot(mydata,aes(x,y,col=Beta2))+geom_point() +scale_color_viridis_c() p3<-ggplot(mydata,aes(x,y,col=Beta3))+geom_point() +scale_color_viridis_c() p4<-ggplot(mydata,aes(x,y,col=Beta4))+geom_point() +scale_color_viridis_c() grid.arrange(p1,p2,p3,p4,nrow=2,ncol=2, top = textGrob("DGP Geniaux (2024)" ,gp=gpar(fontsize=20,font=3)))
summary_Matrix to be documented
summary_Matrix(object, ...)summary_Matrix(object, ...)
object |
to be documented |
... |
to be documented |
to be documented
Print a summary of mgwrsar models
summary_mgwrsar(model)summary_mgwrsar(model)
model |
a model of class mgwrsar |
a summary of mgwrsar models
MGWRSAR, bandwidths_mgwrsar, plot_mgwrsar, predict_mgwrsar, kernel_matW
library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) ## Creating a spatial weight matrix (sparce dgCMatrix) ## of 4 nearest neighbors with 0 in diagonal W=kernel_matW(H=4,kernels='rectangle',coord_i=coords,NN=4,adaptive=TRUE, diagnull=TRUE,rowNorm=TRUE) mgwrsar_0_kc_kv<-MGWRSAR(formula = 'Y_mgwrsar_0_kc_kv~X1+X2+X3', data = mydata, coords=coords, fixed_vars='X2',kernels=c('gauss'),H=20, Model = 'MGWRSAR_0_kc_kv', control=list(SE=FALSE,adaptive=TRUE,W=W)) summary_mgwrsar(mgwrsar_0_kc_kv)library(mgwrsar) ## loading data example data(mydata) coords=as.matrix(mydata[,c("x","y")]) ## Creating a spatial weight matrix (sparce dgCMatrix) ## of 4 nearest neighbors with 0 in diagonal W=kernel_matW(H=4,kernels='rectangle',coord_i=coords,NN=4,adaptive=TRUE, diagnull=TRUE,rowNorm=TRUE) mgwrsar_0_kc_kv<-MGWRSAR(formula = 'Y_mgwrsar_0_kc_kv~X1+X2+X3', data = mydata, coords=coords, fixed_vars='X2',kernels=c('gauss'),H=20, Model = 'MGWRSAR_0_kc_kv', control=list(SE=FALSE,adaptive=TRUE,W=W)) summary_mgwrsar(mgwrsar_0_kc_kv)