INST_C to be documented

Description

INST_C to be documented

Usage

INST_C(XX, WW, withlambda, llambda)

Arguments

Value

to be documented

Estimation of linear and local linear model with spatial autocorrelation model (mgwrsar).

Description

MGWRSAR is is a wrapper function for estimating linear and local linear models with spatial autocorrelation (SAR models with spatially varying coefficients).

Usage

MGWRSAR(formula, data, coords, fixed_vars = NULL, kernels, H,
Model = "GWR", control = list())

Arguments

Details

Z

A matrix of variables for genralized kernel product, default NULL.

W

A row-standardized spatial weight matrix for Spatial Aurocorrelation, default NULL.

type

Verbose mode, default FALSE.

adaptive

A vector of boolean to choose adaptive version for each kernel.

kernel_w

The type of kernel for computing W, default NULL.

h_w

The bandwidth value for computing W, default 0.

Method

Estimation method for computing the models with Spatial Dependence. '2SLS' or 'B2SLS', default '2SLS'.

TP

Avector of target points, default NULL.

doMC

Parallel computation, default FALSE. If TRUE and control_tds$doMC is also TRUE, then control$doMC is set to FALSE.

ncore

Number of CPU core for parallel computation, default 1

isgcv

If TRUE, compute a LOOCV criteria, default FALSE.

isfgcv

If TRUE, simplify the computation of CV criteria (remove or not i when using local instruments for model with lambda spatially varying), default TRUE.

maxknn

When n >NmaxDist, only the maxknn first neighbours are used for distance compution, default 500.

NmaxDist

When n >NmaxDist only the maxknn first neighbours are used for distance compution, default 5000

verbose

Verbose mode, default FALSE.

Value

MGWRSAR returns an object of class mgwrsar with at least the following components:

Betav

matrix of coefficients of dim(n,kv) x kv.

Betac

vector of coefficients of length kc.

Model

The sum of square residuals.

Y

The dependent variable.

XC

The explanatory variables with constant coefficients.

XV

The explanatory variables with varying coefficients.

X

The explanatory variables.

W

The spatial weight matrix for spatial dependence.

isgcv

if gcv has been computed.

edf

The estimated degrees of freedom.

formula

The formula.

data

The dataframe used for computation.

Method

The type of model.

coords

The spatial coordinates of observations.

H

The bandwidth vector.

fixed_vars

The names of constant coefficients.

kernels

The kernel vector.

SSR

The sum of square residuals.

residuals

The vector of residuals.

fit

the vector of fitted values.

sev

local standard error of parameters.

get_ts

Boolean, if trace of hat matrix Tr(S) should be stored.

NN

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 : y=\beta_c X_c+\,\epsilon_i (OLS)

y=\beta_v(u_i,v_i) X_v+\,\epsilon_i (GWR)

y=\beta_c X_c+\beta_v(u_i,v_i) X_v+\,\epsilon_i (MGWR)

y=\lambda Wy+\beta_c X_c+\,\epsilon_i (MGWR-SAR(0,k,0))

y=\lambda Wy+\beta_v(u_i,v_i)X_v+\,\epsilon_i (MGWR-SAR(0,0,k))

y=\lambda Wy+\beta_c X_c+\beta_v(u_i,v_i)X_v+\,\epsilon_i (MGWR-SAR(0,k_c,k_v))

y=\lambda(u_i,v_i) Wy+\beta_c X_c+\,\epsilon_i (MGWR-SAR(1,k,0))

y=\lambda(u_i,v_i)Wy+\beta_v(u_i,v_i)X_v+\,\epsilon_i (MGWR-SAR(1,0,k))

y=\lambda(u_i,v_i)Wy+\beta_cX_c+\beta_v(u_i,v_i)X_v+\,\epsilon_i (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.

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

bandwidths_mgwrsar, summary, plot, predict, kernel_matW

Examples

 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',coords=coords,NN=4,adaptive=TRUE,
 diagnull=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_0_kc_kv)

PhWY_C to be documented

Description

PhWY_C to be documented

Usage

PhWY_C(YY, XX, WW, Wi)

Arguments

Value

to be documented

Proj_C to be documented

Description

Proj_C to be documented

Usage

Proj_C(HH, XX)

Arguments

Value

to be documented

QRcpp2_C to be documented

Description

QRcpp2_C to be documented

Usage

QRcpp2_C(AA, bb, cc)

Arguments

Value

to be documented

Sl_C to be documented

Description

Sl_C to be documented

Usage

Sl_C(llambda, WW, iinv, aapprox)

Arguments

Value

to be documented

atds_gwr Top-Down Scaling approach of GWR

Description

This function performs a Geographically Weighted Regression (GWR) using a top-down scaling approach, adjusting GWR coefficients with a progressively decreasing bandwidth as long as the AICc criterion improves.

Usage

atds_gwr(formula,data,coords,kernels='triangle',fixed_vars=NULL,
control_tds=list(nns=30),control=list(adaptive=TRUE,verbose=FALSE))

Arguments

See Also

tds_mgwr, gwr_multiscale, MGWRSAR, bandwidths_mgwrsar, summary_mgwrsar.

coef for mgwrsar model

Description

coef for mgwrsar model

Usage

## S4 method for signature 'mgwrsar'
coef(object, ...)

Arguments

Value

A named list with a matrix of varying coefficients and a vector or non varying coefficients.

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.

Description

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.

Usage

find_TP(formula, data,coords,kt,ks=16,Wtp=NULL,type='residuals',
model_residuals=NULL,verbose=0,prev_TP=NULL,nTP=NULL)

Arguments

Details

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 Shepard's kernel with ks neighbors (default 16). Then it identifies local maxima (resp. minima) that fits the requirement of having at least kt neighbors with lower (resp.higer) absolute value of the smoothed residuals. As kt increases the number of target points decreases.

Value

find_TP returns an index vector of Target Points set.

Examples

 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,kt=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,ks=12))
 summary(model_GWR_tp@Betav)
 

fitted for mgwrsar model

Description

fitted for mgwrsar model

Usage

## S4 method for signature 'mgwrsar'
fitted(object, ...)

Arguments

Value

A vector of fitted values.

golden_search_bandwidth to be documented

Description

golden_search_bandwidth to be documented

Usage

golden_search_bandwidth(formula,H2=NULL,data, coords, fixed_vars,
kernels, Model, control,lower.bound, upper.bound,tolerance=0.000001)

Arguments

Value

a list(minimum=res,objective=objective,model=model).

int_prems to be documented

Description

int_prems to be documented

Usage

int_prems(X)

Arguments

Value

to be documented

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.

Description

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.

Usage

kernel_matW(H,kernels,coords,NN,TP=NULL,Type='GD',adaptive=FALSE,
diagnull=TRUE,alpha=1,theta=1,dists=NULL,indexG=NULL,extrapol=FALSE,QP=NULL,K=0)

Arguments

Value

A sparse Matrix of weights (dgCMatrix).

Examples

 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',coords=coords,NN=4,adaptive=TRUE,diagnull=TRUE)

Class of mgwrsar Model.

Description

Class of mgwrsar Model.

Slots

Betav

matrix, the estimated varying coefficients, dim(n,kv).

Betac

numeric, the estimated constant coefficients, length kc.

Model

character, The type of model.

fixed_vars

character, a vector with name of constant covarariate.

Y

numeric, the dependent variable.

XC

matrix, the explanatory variables with constant coefficients.

XV

matrix, the explanatory variables with varying coefficients.

X

matrix, the explanatory variables.

W

SparseMatrix, the spatial weight matrix for spatial dependence.

isgcv

logical, if gcv has been computed.

edf

numeric, the estimated degrees of freedom.

formula

formula

data

dataframe, The dataframe used for computation.

Method

character, the estimation technique for computing the models with Spatial Dependence. '2SLS' or 'B2SLS', default '2SLS'.

coords

matrix, the spatial coordinates of observations.

H

numeric, the bandwidth vector.

H2

numeric, the time bandwidth vector.

kernels

character, the type of kernel.

adaptive

logical, adaptive kernel.

Type

character, the type of General Kernel Product.

TP

numeric, index of target points.

SSRtp

numeric, the sum of square residuals for TP.

SSR

numeric, the sum of square residuals.

residuals

numeric, the vector of residuals.

fit

numeric, the vector of fitted values.

pred

numeric, the vector of predicted values.

sev

matrix, local standard error of varying coefficients.

se

numeric, standard error of constant coefficients.

tS

numeric, Trace(S).

Shat,

hat matrix

R_k,

list of hat matrix by var

h_w

numeric, the bandwidth value for computing W, default 0.

kernel_w

the type of kernel for computing W, default NULL.

RMSE

numeric, Root Mean Square Error for Target Points.

RMSEtp

numeric, Root Mean Square Error for all Points.

CV

numeric, Leave One Out CV.

AIC

numeric, Akaike Criteria.

AICc

numeric, Corrected Akaike Criteria.

AICctp

numeric, Corrected Akaike Criteria for TP

BIC

numeric, Bayesian Information Criteria.

R2

numeric, R2.

R2_adj

numeric, adjusted R2.

get_ts

logical, if trace of hat matrix Tr(S) should be stored.

NN

numeric, the maximum number of neighbors for weights computation

doMC

logical, parallel computation.

ncore

numeric, number of cores.

mycall

a call, the call of the model.

ctime

numeric, the computing times in seconds.

HRMSE

matrix, RMSE log.

HBETA

list, estimated BETA at each iteration.

loglik

numeric, value of loglik.

G

list, list of neighboring index and distances (knn object from nabor package).

V

numeric, neighbors sequence for TDS.

Vt

numeric, neighbors sequence for TDS.

Z

numeric, time for GDT kernel type

TS

numeric, Diagonal of Hat Matrix

alpha

numeric, ratio for GDT kernels

theta

numeric, ratio for GDT kernels

A bootstrap test for Betas for mgwrsar class model.

Description

A bootstrap test for Betas for mgwrsar class model.

Usage

mgwrsar_bootstrap_test(x0,x1,B=100,doMC=FALSE,ncore=1,type='standard'
,eps='H1',df='H1',focal='median',D=NULL)

Arguments

Value

The value of the statictics test and a p ratio.

See Also

mgwrsar_bootstrap_test_all

A bootstrap test for testing nullity of all Betas for mgwrsar class model,

Description

A bootstrap test for testing nullity of all Betas for mgwrsar class model,

Usage

mgwrsar_bootstrap_test_all(model,B=100,doMC=FALSE,ncore=1,
type='standard')

Arguments

Value

a matrix with statistical test values and p ratios

See Also

mgwrsar_bootstrap_test

modc is a set of models to correct approximation of hat matrix trace

Description

modc is a set of models to correct approximation of hat matrix trace

Author(s)

Ghislain Geniaux and Davide Martinetti ghislain.geniaux@inra.fr

References

doi:10.1016/j.regsciurbeco.2017.04.001

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.

Description

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.

Usage

multiscale_gwr(formula,data,coords,kernels='bisq',init='GWR',
maxiter=20,nstable=6,tolerance=0.000001,doMC=FALSE,ncore=1,HF=NULL,
H0=NULL,H2=NULL,Model=NULL,model=NULL,get_AICg=FALSE,verbose=FALSE,
control=list(SE=FALSE,adaptive=TRUE,NN=800,isgcv=FALSE,family=gaussian()))

Arguments

Value

Return an object of class mgwrsar

mydata is a simulated data set of a mgwrsar model

Description

mydata is a simulated data set of a mgwrsar model

Format

A data frames with 1000 rows 22 variables and a matrix of coordinates with two columns

Author(s)

Ghislain Geniaux and Davide Martinetti ghislain.geniaux@inrae.fr

References

doi:10.1016/j.regsciurbeco.2017.04.001

mydataf is a Simple Feature object with real estate data in south of France.

Description

mydataf is a Simple Feature object with real estate data in south of France.

Format

A sf object with 1403 rows, 5 columns

Author(s)

Ghislain Geniaux ghislain.geniaux@inrea.fr

References

https://www.data.gouv.fr/fr/datasets/demandes-de-valeurs-foncieres/

normW row normalization of dgCMatrix

Description

normW row normalization of dgCMatrix

Usage

normW(W)

Arguments

Value

A row normalized dgCMatrix

Plot method for mgwrsar model

Description

Plot method for mgwrsar model

Usage

## S4 method for signature 'mgwrsar,missing'
plot(
  x,
  y,
  type = "coef",
  var = NULL,
  crs = NULL,
  mypalette = "RdYlGn",
  opacity = 0.5,
  fopacity = 0.5,
  nbins = 8,
  radius = 500,
  mytile = "Stadia.StamenTonerBackground",
  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
)

Arguments

Value

A Interactive Web Maps with local parameters plot and Open Street Map layer.

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.

Description

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.

Usage

plot_effect(model,sampling=TRUE,nsample=2000,nsample_max=5000,title='')

Arguments

Examples

 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)

predict method for mgwrsar model

Description

predict method for mgwrsar model

Usage

## S4 method for signature 'mgwrsar'
predict(
  object,
  newdata,
  newdata_coords,
  W = NULL,
  type = "BPN",
  h_w = 100,
  kernel_w = "rectangle",
  maxobs = 4000,
  beta_proj = FALSE,
  method_pred = "TP",
  k_extra = 8,
  ...
)

Arguments

Details

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 ='shepard'a shepard 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.

Value

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.

A vector of predictions.

residuals for mgwrsar model

Description

residuals for mgwrsar model

Usage

## S4 method for signature 'mgwrsar'
residuals(object, ...)

Arguments

Value

A vector of residuals.

Estimation of linear and local linear model with spatial autocorrelation model (mgwrsar).

Description

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).

Usage

simu_multiscale(n=1000,myseed=1,type='GG2024',constant=NULL,
nuls=NULL,config_beta='default',config_snr=0.7,config_eps='normal',
ratiotime=1)

Arguments

Value

A named list with simulated data ('mydata') and coords ('coords')

Examples

 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 for mgwrsar model

Description

summary for mgwrsar model

Usage

## S4 method for signature 'mgwrsar'
summary(object, ...)

Arguments

Value

A summary object.

summary_Matrix to be documented

Description

summary_Matrix to be documented

Usage

summary_Matrix(object, ...)

Arguments

Value

to be documented

Top-Down Scaling approach of multiscale GWR

Description

This function performs a multiscale Geographically Weighted Regression (GWR) using a top-down scaling approach, adjusting GWR coefficients with a progressively decreasing bandwidth as long as the AICc criterion improves.

Usage

tds_mgwr(formula,data,coords,Model='tds_mgwr',kernels='triangle',
fixed_vars=NULL,H2=NULL,control_tds=list(nns=30,get_AIC=FALSE),
control=list(adaptive=TRUE))

Arguments

Details

nns

Length of the sequence of decreasing bandwidth. Should be between 20 and 100, default 30

get_AIC

Boolean, if the Global AICc using Yu et al 2019 should be computed. Required if the second stage 'atds_mgwr' has to be estimated. default FALSE

init_model

Starting model, 'GWR' or 'OLS', 'default OLS'.

model_stage1

If model='tds_mgwr', model_stage1 can be used as a starting model (either a GWR model or a preious tds_mgwr model). For model='atds_mgwr, the user can specified an tds_mgwr model already computed with get_AIC=TRUE. default NULL.

doMC

Parallel computation, default FALSE.

ncore

number of CPU core for parallel computation, default 1

tol

Tolerance for stopping criteria, default 0.0001

nrounds

Number of nrounds for 'atds_mgwr' model. Default 3.

verbose

verbose mode, default FALSE.

V

A vector of decreasing bandwidths given by the user, default NULL

first_nn

The value of the highest bandwidth for the sequence of decreasing bandwidth, default NULL.

minv

The value of the smallest bandwidth for the sequence of decreasing bandwidth, default number of covariates + 2 .

H

A vector of bandwidth, default NULL

Z

A matrix of variables for genralized kernel product, default NULL.

W

A row-standardized spatial weight matrix for Spatial Aurocorrelation, default NULL.

type

Verbose mode, default FALSE.

adaptive

A vector of boolean to choose adaptive version for each kernel.

kernel_w

The type of kernel for computing W, default NULL.

h_w

The bandwidth value for computing W, default 0.

Method

Estimation method for computing the models with Spatial Dependence. '2SLS' or 'B2SLS', default '2SLS'.

TP

Avector of target points, default NULL.

doMC

Parallel computation, default FALSE. If TRUE and control_tds$doMC is also TRUE, then control$doMC is set to FALSE.

ncore

Number of CPU core for parallel computation, default 1

isgcv

If TRUE, compute a LOOCV criteria, default FALSE.

isfgcv

If TRUE, simplify the computation of CV criteria (remove or not i when using local instruments for model with lambda spatially varying), default TRUE.

maxknn

When n >NmaxDist, only the maxknn first neighbours are used for distance compution, default 500.

NmaxDist

When n >NmaxDist only the maxknn first neighbours are used for distance compution, default 5000

verbose

Verbose mode, default FALSE.

See Also

gwr_multiscale, MGWRSAR, bandwidths_mgwrsar, summary_mgwrsar.