Package 'spboost' reference manual

Title:	Gradient Boosting for Nonlinear Spatial Autoregressive Models
Description:	Flexible nonlinear extension of spatial autoregressive (SAR), spatial error (SEM), and spatial autoregressive with autoregressive disturbances (SARAR) models with multiple regression engines (generalized additive models ('mgcv'), gradient boosting ('mboost'), multivariate adaptive regression splines ('earth'), and 'xgboost') and two families of spatial-parameter estimators: maximum likelihood and the determinant-free Closed-Form Estimator of Smirnov (2020) <doi:10.1111/gean.12268>. See Geniaux G. (2026). "Flexible nonlinear spatial autoregressive models: a gradient boosting approach with closed-form estimation." Presented at Spatial Econometrics World Congress (SEA/SEW 2026, Paris), unpublished.
Authors:	Ghislain Geniaux [aut, cre]
Maintainer:	Ghislain Geniaux <[email protected]>
License:	GPL (>= 2)
Version:	0.7.0
Built:	2026-06-09 11:37:35 UTC
Source:	https://github.com/cran/spboost

ApproxiW

Description

Approximate $(I - \lambda W)^{-1}$ with a truncated Neumann series.

Usage

ApproxiW(W, lambda, order = NULL, tol = 1e-06, max_order = 50L)
ApproxiW(W, lambda, order = NULL, tol = 1e-06, max_order = 50L)

Arguments

W

Sparse or dense square matrix.

lambda

Scalar spatial parameter.

order

Optional truncation order. If 'NULL', an adaptive order is chosen from 'tol' and a row-sum bound of '|lambda W|'.

tol

Target truncation tolerance when 'order = NULL'.

max_order

Maximum order allowed when using the adaptive rule.

Value

A matrix approximating $(I - \lambda W)^{-1}$ .

Examples

W <- Matrix::Matrix(c(0, 1, 1, 0), nrow = 2, sparse = TRUE)
ApproxiW(W, lambda = 0.2, order = 3)
W <- Matrix::Matrix(c(0, 1, 1, 0), nrow = 2, sparse = TRUE)
ApproxiW(W, lambda = 0.2, order = 3)

BLA_SAR_ML BLA_SAR_ML allows the estimation of SAR models using the gradient boosting method with linear base learner for estimating the coefficients Beta while the estimation of the spatial parameter is based on a concentrated likelihood function. This function makes it possible to estimate a SAR model while automatically selecting the explanatory variables.

Description

BLA_SAR_ML BLA_SAR_ML allows the estimation of SAR models using the gradient boosting method with linear base learner for estimating the coefficients Beta while the estimation of the spatial parameter is based on a concentrated likelihood function. This function makes it possible to estimate a SAR model while automatically selecting the explanatory variables.

Usage

BLA_SAR_ML(formula,data,W,center=TRUE,RHO=NULL,WW=NULL,
control=boost_control(),verbose=0)
BLA_SAR_ML(formula,data,W,center=TRUE,RHO=NULL,WW=NULL,
control=boost_control(),verbose=0)

Arguments

formula

a regular lm formula

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Aurocorrelation.

center

a boolean, if covariate should be centered or not.

RHO

a vector of rho values, default NULL

WW

a list of row-standardized spatial weight matrices for Spatial Autocorrelation, default NULL

control

boost_control() see mboost help.

verbose

if verbose>0 verbose mode, default verbose=0.

Details

the determinant of (I -rho W) is computed using code from Matrix packages with a sparse matrix decomposition approach (option 'LU' of function lagsarlm from spatialreg).

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho value and RMSE.

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = FALSE, myseed = 8
)
fit <- BLA_SAR_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2)
)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = FALSE, myseed = 8
)
fit <- BLA_SAR_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2)
)
fit$rho
summary(fit)

BLA_SARAR_ML BLA_SARAR_ML allows the estimation of SARAR models using the gradient boosting method with linear base learner for estimating the coefficients Beta while the estimation of the spatial parameter is based on a concentrated likelihood function. This function makes it possible to estimate a SARAR model while automatically selecting the explanatory variables.

Description

BLA_SARAR_ML BLA_SARAR_ML allows the estimation of SARAR models using the gradient boosting method with linear base learner for estimating the coefficients Beta while the estimation of the spatial parameter is based on a concentrated likelihood function. This function makes it possible to estimate a SARAR model while automatically selecting the explanatory variables.

Usage

BLA_SARAR_ML(formula,data,W,W2,center=TRUE,mstop0=NULL,mstop_init=500,nu=0.3,ncores=2,
rho0=c(0,0.6),lambda0=c(0,0.6),verbose=0)
BLA_SARAR_ML(formula,data,W,W2,center=TRUE,mstop0=NULL,mstop_init=500,nu=0.3,ncores=2,
rho0=c(0,0.6),lambda0=c(0,0.6),verbose=0)

Arguments

formula

a regular lm formula

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Aurocorrelation of endogenous.

W2

a row-standardized spatial weight matrix for Spatial Aurocorrelation of errors.

center

logical indicating of the predictor variables are centered before fitting, Default TRUE.

mstop0

an integer giving the number of boosting iterations

mstop_init

an integer giving the number of initial boosting iterations. If mstop = 0, the offset model is returned. Used only if mstop0 is NULL.

nu

a double (between 0 and 1) defining the step size or shrinkage parameter.

ncores

number of cores for parallel computing of cross validation of mstop, default ncores=7

rho0

a set of rho values (between -1 and 1) for estimating initial mstop0. Used only if mstop0 is NULL. Default c(0,0.6).

lambda0

a set of lambda values (between -1 and 1) for estimating initial mstop0. Used only if mstop0 is NULL. Default c(0,0.6).

verbose

if verbose>0 verbose mode, default verbose=0.

Details

the determinant of (I -rho W) is computed using code from Matrix packages with a sparse matrix decomposition approach (option 'LU' of function lagsarlm from spatialreg).

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho value and RMSE.

Examples

sim <- dgp(
  n = 500, rho = 0.2, lambda = 0.2, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SARAR", nonlin = FALSE, myseed = 10
)
fit <- BLA_SARAR_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W, W2 = sim$W2,
  mstop0 = 5, nu = 0.2
)
c(rho = fit$rho, lambda = fit$lambda)
summary(fit)
sim <- dgp(
  n = 500, rho = 0.2, lambda = 0.2, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SARAR", nonlin = FALSE, myseed = 10
)
fit <- BLA_SARAR_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W, W2 = sim$W2,
  mstop0 = 5, nu = 0.2
)
c(rho = fit$rho, lambda = fit$lambda)
summary(fit)

BLA_SEM_ML BLA_SEM_ML allows the estimation of SEM models using the gradient boosting method with linear base learner for estimating the coefficients Beta while the estimation of the spatial parameter is based on a concentrated likelihood function. This function makes it possible to estimate a SEM model while automatically selecting the explanatory variables.

Description

BLA_SEM_ML BLA_SEM_ML allows the estimation of SEM models using the gradient boosting method with linear base learner for estimating the coefficients Beta while the estimation of the spatial parameter is based on a concentrated likelihood function. This function makes it possible to estimate a SEM model while automatically selecting the explanatory variables.

Usage

BLA_SEM_ML(formula,data,W,center=TRUE,mstop0=NULL,mstop_init=500,nu=0.3,ncores=2,
rho0=c(0),verbose=0)
BLA_SEM_ML(formula,data,W,center=TRUE,mstop0=NULL,mstop_init=500,nu=0.3,ncores=2,
rho0=c(0),verbose=0)

Arguments

formula

a regular lm formula

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Aurocorrelation.

center

logical indicating of the predictor variables are centered before fitting, Default TRUE.

mstop0

an integer giving the number of boosting iterations

mstop_init

an integer giving the number of initial boosting iterations. If mstop = 0, the offset model is returned. Used only if mstop0 is NULL.

nu

a double (between 0 and 1) defining the step size or shrinkage parameter.

ncores

number of cores for parallel computing of cross validation of mstop, default ncores=2

rho0

a set of rho values (between -1 and 1) for estimating initial mstop0. Used only if mstop0 is NULL. Default c(0,0.8).

verbose

if verbose>0 verbose mode, default verbose=0.

Details

the determinant of (I -rho W) is computed using code from Matrix packages with a sparse matrix decomposition approach (option 'LU' of function lagsarlm from spatialreg).

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho value and RMSE.

Examples

sim <- dgp(
  n = 500, rho = 0, lambda = 0.3, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SEM", nonlin = FALSE, myseed = 9
)
fit <- BLA_SEM_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  mstop0 = 5, nu = 0.2
)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0, lambda = 0.3, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SEM", nonlin = FALSE, myseed = 9
)
fit <- BLA_SEM_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  mstop0 = 5, nu = 0.2
)
fit$rho
summary(fit)

BSPA_SAR_CFE BSPA_SAR_CFE allows the estimation of additive non linear SAR models using gradient boosting for the non linear part while the spatial parameter is estimated with the determinant-free Closed-Form Estimator of Smirnov (2020, doi:10.1111/gean.12268). This function makes it possible to estimate an additive non linear SAR model while automatically selecting the explanatory variables.

Description

BSPA_SAR_CFE BSPA_SAR_CFE allows the estimation of additive non linear SAR models using gradient boosting for the non linear part while the spatial parameter is estimated with the determinant-free Closed-Form Estimator of Smirnov (2020, doi:10.1111/gean.12268). This function makes it possible to estimate an additive non linear SAR model while automatically selecting the explanatory variables.

Usage

BSPA_SAR_CFE(formula,data,W,control=boost_control(),doMC=FALSE,ncores=3,
fallback=c('auto','none'),rho_bounds=c(-0.99,0.99),tol=1e-10)
BSPA_SAR_CFE(formula,data,W,control=boost_control(),doMC=FALSE,ncores=3,
fallback=c('auto','none'),rho_bounds=c(-0.99,0.99),tol=1e-10)

Arguments

formula

a gamboost formula (see mboost help)

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Aurocorrelation.

control

boost_control() see mboost help.

doMC

deprecated, ignored. CFE pre-fits are now sequential.

ncores

deprecated, ignored. CFE pre-fits are now sequential.

fallback

fallback strategy when exact CFE root is not real or unstable. "auto" uses ratio/IV approximations, "none" returns an error object.

rho_bounds

lower and upper bounds used to clip the estimated spatial parameter.

tol

numerical tolerance used for near-singular denominators/discriminant.

Details

the determinant of (I -rho W) is computed using code from Matrix packages with a sparse matrix decomposition approach (option 'LU' of function lagsarlm from spatialreg).

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho value and RMSE.

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 3
)
fit <- BSPA_SAR_CFE(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2)
)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 3
)
fit <- BSPA_SAR_CFE(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2)
)
fit$rho
summary(fit)

BSPA_SAR_ML BSPA_SAR_ML allows the estimation of additive non linear SAR models using gradient boosting for the non linear part while the spatial parameter is estimated with a concentrated likelihood function. This function makes it possible to estimate an additive non linear SAR model while automatically selecting the explanatory variables.

Description

BSPA_SAR_ML BSPA_SAR_ML allows the estimation of additive non linear SAR models using gradient boosting for the non linear part while the spatial parameter is estimated with a concentrated likelihood function. This function makes it possible to estimate an additive non linear SAR model while automatically selecting the explanatory variables.

Usage

BSPA_SAR_ML(formula,data,W,RHO=NULL,WW=NULL,control=boost_control(),verbose=0)
BSPA_SAR_ML(formula,data,W,RHO=NULL,WW=NULL,control=boost_control(),verbose=0)

Arguments

formula

a gamboost formula (see mboost help)

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Aurocorrelation

RHO

a vector of rho values

WW

a list of row-standardized spatial weight matrix for Spatial Aurocorrelation, default NULL

control

boost_control() see mboost help.

verbose

verbose mode, default verbose=0.

Details

the determinant of (I -rho W) is computed using code from Matrix packages with a sparse matrix decomposition approach (option 'LU' of function lagsarlm from spatialreg).

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho value and RMSE.

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 11
)
fit <- BSPA_SAR_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2)
)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 11
)
fit <- BSPA_SAR_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2)
)
fit$rho
summary(fit)

BSPA_SARAR_CFE CFE-style alternating estimator for SARAR models with a gamboost core.

Description

BSPA_SARAR_CFE CFE-style alternating estimator for SARAR models with a gamboost core.

Usage

BSPA_SARAR_CFE(formula,data,W,W2=NULL,control=boost_control(),
                      iter_max=6L,tol_iter=1e-4,
                      damping=0.5,
                      fallback=c('auto','none'),
                      rho_bounds=c(-0.99,0.99),
                      lambda_bounds=c(-0.99,0.99),
                      lambda_switch=0.80,
                      tol=1e-10,verbose=0,
                      debug=FALSE,debug_fit_each_iter=FALSE,debug_print=TRUE)
BSPA_SARAR_CFE(formula,data,W,W2=NULL,control=boost_control(),
                      iter_max=6L,tol_iter=1e-4,
                      damping=0.5,
                      fallback=c('auto','none'),
                      rho_bounds=c(-0.99,0.99),
                      lambda_bounds=c(-0.99,0.99),
                      lambda_switch=0.80,
                      tol=1e-10,verbose=0,
                      debug=FALSE,debug_fit_each_iter=FALSE,debug_print=TRUE)

Arguments

formula

a gamboost formula (see mboost help)

data

a dataframe.

W

a row-standardized spatial weight matrix for spatial lag on Y.

W2

a row-standardized spatial weight matrix for spatial lag on errors. If 'NULL', 'W' is used.

control

boost_control() see mboost help.

iter_max

maximum number of alternating CFE updates.

tol_iter

stopping tolerance on successive $(\rho,\lambda)$ updates.

damping

damping factor applied to alternating updates.

fallback

fallback strategy when exact CFE root is not real or unstable. "auto" uses ratio/projection approximations, "none" returns an error object.

rho_bounds

lower and upper bounds used to clip $\rho$ .

lambda_bounds

lower and upper bounds used to clip $\lambda$ .

lambda_switch

threshold used by the robust lambda update rule.

tol

numerical tolerance used for near-singular denominators/discriminant.

verbose

verbosity level (0/1).

debug

logical; if TRUE, stores per-iteration diagnostics in $trace_iter.

debug_fit_each_iter

logical; if TRUE, runs an auxiliary SARAR fit-at-current-(rho,lambda) each iteration to report RMSE on Y scale (costly).

debug_print

logical; if TRUE and debug=TRUE, prints one-line diagnostics each iteration.

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with $\rho$ , $\lambda$ , RMSE and alternating-fit metadata.

Examples

sim <- dgp(
  n = 500, rho = 0.2, lambda = 0.2, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SARAR", nonlin = TRUE, myseed = 16
)
fit <- BSPA_SARAR_CFE(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W, W2 = sim$W2,
  control = mboost::boost_control(mstop = 5, nu = 0.2),
  iter_max = 2
)
c(rho = fit$rho, lambda = fit$lambda)
summary(fit)
sim <- dgp(
  n = 500, rho = 0.2, lambda = 0.2, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SARAR", nonlin = TRUE, myseed = 16
)
fit <- BSPA_SARAR_CFE(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W, W2 = sim$W2,
  control = mboost::boost_control(mstop = 5, nu = 0.2),
  iter_max = 2
)
c(rho = fit$rho, lambda = fit$lambda)
summary(fit)

BSPA_SARAR_ML

Description

BSPA_SARAR_ML allows the estimation of SARAR models using the gradient boosting method for estimating the non linear part while the estimation of the spatial parameter is based on a concentrated likelihood function. This implementation estimates directly the transformed equation

$(I-\lambda W_2)(I-\rho W)Y = g(X) + \varepsilon$

using a standard Gaussian gamboost fit on the transformed response.

Usage

BSPA_SARAR_ML(formula,data,W,W2,control=boost_control(),verbose=0,multi_start=FALSE)
BSPA_SARAR_ML(formula,data,W,W2,control=boost_control(),verbose=0,multi_start=FALSE)

Arguments

formula

a regular lm formula

data

a dataframe.

W

a row-standardized spatial weight matrix for spatial autocorrelation of the endogenous variable.

W2

a row-standardized spatial weight matrix for spatial autocorrelation of errors.

control

boost_control() see mboost help.

verbose

if verbose>0 verbose mode, default verbose=0.

multi_start

logical. If FALSE and W2 = W, the estimator constrains rho = lambda. Otherwise, if FALSE, it runs a single unconstrained optimization from (0,0). If TRUE, it runs an unconstrained optimization over (rho, lambda) from multiple starting points and keeps the best optimum.

Details

The determinants of $(I-\rho W)$ and $(I-\lambda W_2)$ are computed using sparse LU decompositions. To avoid the non-separable custom-loss issue in SARAR boosting, the estimator works on the transformed response $(I-\lambda W_2)(I-\rho W)Y$ and estimates a transformed regression function $g(X)$ with standard Gaussian boosting.

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho, lambda, fitted values and RMSE on the original Y scale.

Examples

sim <- dgp(
  n = 500, rho = 0.2, lambda = 0.2, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SARAR", nonlin = TRUE, myseed = 15
)
fit <- BSPA_SARAR_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W, W2 = sim$W2,
  control = mboost::boost_control(mstop = 5, nu = 0.2)
)
c(rho = fit$rho, lambda = fit$lambda)
summary(fit)
sim <- dgp(
  n = 500, rho = 0.2, lambda = 0.2, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SARAR", nonlin = TRUE, myseed = 15
)
fit <- BSPA_SARAR_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W, W2 = sim$W2,
  control = mboost::boost_control(mstop = 5, nu = 0.2)
)
c(rho = fit$rho, lambda = fit$lambda)
summary(fit)

BSPA_SEM_CFE BSPA_SEM_CFE keeps the historical SEM CFE interface while using the same one-shot BRUT/filtered workflow as GAM_SEM_CFE: a non-spatial BRUT CFE estimate is computed first, then the filtered CFE backend is used when the BRUT rho estimate is high.

Description

BSPA_SEM_CFE BSPA_SEM_CFE keeps the historical SEM CFE interface while using the same one-shot BRUT/filtered workflow as GAM_SEM_CFE: a non-spatial BRUT CFE estimate is computed first, then the filtered CFE backend is used when the BRUT rho estimate is high.

Usage

BSPA_SEM_CFE(formula,data,W,control=boost_control(),doMC=TRUE,
fallback=c('auto','none'),rho_bounds=c(-0.99,0.99),tol=1e-10,
cfe_aux_cv=FALSE,cfe_cv_nfold=5L,cfe_cv_ncore=1L,cfe_cv_seed=NULL)
BSPA_SEM_CFE(formula,data,W,control=boost_control(),doMC=TRUE,
fallback=c('auto','none'),rho_bounds=c(-0.99,0.99),tol=1e-10,
cfe_aux_cv=FALSE,cfe_cv_nfold=5L,cfe_cv_ncore=1L,cfe_cv_seed=NULL)

Arguments

formula

a gamboost formula (see mboost help)

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Aurocorrelation.

control

boost_control() see mboost help.

doMC

boolean for parallelization in the filtered fallback stage.

fallback

fallback strategy when exact CFE root is not real or unstable. "auto" uses projection fallback, "none" returns an error object.

rho_bounds

lower and upper bounds used to clip the estimated spatial parameter.

tol

numerical tolerance used for near-singular denominators/discriminant.

cfe_aux_cv

logical; if TRUE, tune the two auxiliary CFE regressions by internal CV.

cfe_cv_nfold

number of folds for auxiliary CFE CV.

cfe_cv_ncore

number of workers for auxiliary CFE CV.

cfe_cv_seed

optional seed for auxiliary CFE CV.

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho value and RMSE.

Examples

sim <- dgp(
  n = 500, rho = 0, lambda = 0.3, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SEM", nonlin = TRUE, myseed = 13
)
fit <- BSPA_SEM_CFE(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2)
)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0, lambda = 0.3, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SEM", nonlin = TRUE, myseed = 13
)
fit <- BSPA_SEM_CFE(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2)
)
fit$rho
summary(fit)

BSPA_SEM_CFE_BRUT Experimental SEM CFE variant using raw residuals for the CFE update.

Description

BSPA_SEM_CFE_BRUT Experimental SEM CFE variant using raw residuals for the CFE update.

Usage

BSPA_SEM_CFE_BRUT(formula,data,W,control=boost_control(),
                         rho_bounds=c(-0.99,0.99),lambda_switch=0.80,
                         tol=1e-10,max_iter=3L,tol_lambda=1e-4,verbose=0)
BSPA_SEM_CFE_BRUT(formula,data,W,control=boost_control(),
                         rho_bounds=c(-0.99,0.99),lambda_switch=0.80,
                         tol=1e-10,max_iter=3L,tol_lambda=1e-4,verbose=0)

Arguments

formula

a gamboost formula.

data

a dataframe.

W

a row-standardized spatial weight matrix.

control

boost_control() object (mboost).

rho_bounds

admissible bounds for lambda.

lambda_switch

threshold above which the filtered CFE update is used.

tol

numerical tolerance.

max_iter

maximum number of adaptive CFE iterations.

tol_lambda

convergence tolerance on $\lambda$ .

verbose

verbosity level (0/1).

Value

An object of class mboost augmented with SEM spatial outputs.

Examples

sim <- dgp(
  n = 500, rho = 0, lambda = 0.3, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SEM", nonlin = TRUE, myseed = 14
)
fit <- BSPA_SEM_CFE_BRUT(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2),
  max_iter = 1
)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0, lambda = 0.3, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SEM", nonlin = TRUE, myseed = 14
)
fit <- BSPA_SEM_CFE_BRUT(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2),
  max_iter = 1
)
fit$rho
summary(fit)

BSPA_SEM_CFE_iter Iterative CFE estimator for additive nonlinear SEM with joint updates of spatial parameter and boosting fit.

Description

BSPA_SEM_CFE_iter Iterative CFE estimator for additive nonlinear SEM with joint updates of spatial parameter and boosting fit.

Usage

BSPA_SEM_CFE_iter(formula,data,W,control=boost_control(),
                         iter_max=1L,tol_lambda=1e-4,
                         doMC=FALSE,cfe_aux_cv=FALSE,
                         cfe_cv_nfold=5L,cfe_cv_ncore=1L,cfe_cv_seed=NULL,
                         fallback=c('auto','none'),
                         rho_bounds=c(-0.99,0.99),tol=1e-10,verbose=0)
BSPA_SEM_CFE_iter(formula,data,W,control=boost_control(),
                         iter_max=1L,tol_lambda=1e-4,
                         doMC=FALSE,cfe_aux_cv=FALSE,
                         cfe_cv_nfold=5L,cfe_cv_ncore=1L,cfe_cv_seed=NULL,
                         fallback=c('auto','none'),
                         rho_bounds=c(-0.99,0.99),tol=1e-10,verbose=0)

Arguments

formula

a gamboost formula.

data

a data.frame.

W

a row-standardized spatial weight matrix.

control

boost_control() object used in each boosting step.

iter_max

maximum number of fixed-point iterations for ( $\lambda$ , $f$ ).

tol_lambda

convergence tolerance on successive $\lambda$ .

doMC

logical; if TRUE and 'cfe_aux_cv=FALSE', auxiliary CFE fits can run in parallel.

cfe_aux_cv

logical; if TRUE, tune 'mstop' by standard k-fold CV in each auxiliary CFE regression.

cfe_cv_nfold

number of CV folds for auxiliary CFE regressions.

cfe_cv_ncore

number of workers for auxiliary CFE CV ('mboost::cvrisk').

cfe_cv_seed

optional seed for auxiliary CFE CV.

fallback

fallback strategy when the quadratic CFE step has no real root.

rho_bounds

lower/upper admissible bounds for $\lambda$ .

tol

numerical tolerance used for near-singular cases.

verbose

verbosity level (0/1).

Value

An object of class mboost augmented with SEM spatial outputs.

BSPA_SEM_ML BSPA_SEM_ML allows the estimation of additive non linear SAR models using the gradient boosting method for estimating the non linear part while the estimation of the spatial parameter is based on a concentrated likelihood function. This function makes it possible to estimate an additive non linear SAR model while automatically selecting the explanatory variables.

Description

BSPA_SEM_ML BSPA_SEM_ML allows the estimation of additive non linear SAR models using the gradient boosting method for estimating the non linear part while the estimation of the spatial parameter is based on a concentrated likelihood function. This function makes it possible to estimate an additive non linear SAR model while automatically selecting the explanatory variables.

Usage

BSPA_SEM_ML(formula,data,W,control=boost_control(),verbose=0)
BSPA_SEM_ML(formula,data,W,control=boost_control(),verbose=0)

Arguments

formula

a gambboost formula (see mboost help)

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Aurocorrelation.

control

boost_control() see mboost help.

verbose

verbose mode, default verbose=0.

Details

the determinant of (I -rho W) is computed using code from Matrix packages with a sparse matrix decomposition approach (option 'LU' of function lagsarlm from spatialreg).

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho value and RMSE.

Examples

sim <- dgp(
  n = 500, rho = 0, lambda = 0.3, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SEM", nonlin = TRUE, myseed = 12
)
fit <- BSPA_SEM_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2)
)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0, lambda = 0.3, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SEM", nonlin = TRUE, myseed = 12
)
fit <- BSPA_SEM_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2)
)
fit$rho
summary(fit)

datatest is a simulated data for spatial autoregressive non linear model

Description

datatest is a simulated data for spatial autoregressive non linear model

Author(s)

Ghislain Geniaux [email protected]

dgp a function to simulate non-linear spatial autoregressive SAR SEM and SARAR model.

Description

dgp a function to simulate non-linear spatial autoregressive SAR SEM and SARAR model.

Usage

dgp(n,rho,betas=NULL,sigma2,model='SAR',lambda=NULL,
nonlin=FALSE,X_het=FALSE,X_sp=FALSE,X3_sp=FALSE,f_sp=FALSE,f_corsp=FALSE,
X_cor=FALSE,zeta=1,K1=4,K2=6,maxobs=10000,myseed=1,
SNR=NULL,snr_method=c('exact','hutch'),snr_m=64L,snr_seed=NULL)
dgp(n,rho,betas=NULL,sigma2,model='SAR',lambda=NULL,
nonlin=FALSE,X_het=FALSE,X_sp=FALSE,X3_sp=FALSE,f_sp=FALSE,f_corsp=FALSE,
X_cor=FALSE,zeta=1,K1=4,K2=6,maxobs=10000,myseed=1,
SNR=NULL,snr_method=c('exact','hutch'),snr_m=64L,snr_seed=NULL)

Arguments

n

to be documented

rho

to be documented

betas

numeric vector of length 'p+1' where 'p' is the number of true covariates in the DGP (currently 'p=3'). The first element is the intercept ('beta0'), followed by coefficients for 'X1, X2, X3'. If 'NULL', defaults to 'c(0,0,0,0)'.

sigma2

to be documented

model

to be documented

lambda

to be documented

nonlin

to be documented

X_het

to be documented

X_sp

to be documented

X3_sp

logical. If TRUE, inject spatial autocorrelation into X3 using the same fixed coefficient (0.7) used for X_sp.

f_sp

to be documented

f_corsp

logical/numeric flag. If TRUE (or 1), build X4, X5, X6 from normalized Euclidean distances to fixed points (0.2,0.2), (0.8,0.2), (0.5,0.8), instead of random draws.

X_cor

to be documented

zeta

scalar multiplier applied to the spatial heterogeneity term 'HS' in the disturbance when 'X_het=TRUE', i.e. 'eps <- eps + zeta*HS'.

K1

number of neighbors (SAR, SEM)

K2

number of neighbors (SARAR)

maxobs

max observation for solve default 10000

myseed

seed number

SNR

target signal-to-noise ratio in ]0,1[ for SAR/SEM. If provided, sigma2 is calibrated analytically for each simulated dataset.

snr_method

method for tau_B in SNR calibration: 'exact' or 'hutch'

snr_m

number of Rademacher vectors for Hutchinson trace estimator

snr_seed

optional seed used only for SNR calibration with hutch

Value

to be documented

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 1
)
names(sim)
head(sim$data)
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 1
)
names(sim)
head(sim$data)

fitted_decomp_spboost Decompose fitted values of a spboost model by variable.

Description

Names are simplified to variable-level labels when possible (e.g. bbs(X1, ...) or s(X1) become X1). Contributions are returned on the linear predictor scale of the fitted model. When newdata = NULL, the fitted column uses model$fitted when available.

Usage

fitted_decomp_spboost(
  model, newdata = NULL, include_offset = TRUE, include_total = TRUE,
  aggregate = TRUE, include_wy_resu = FALSE
)
fitted_decomp_spboost(
  model, newdata = NULL, include_offset = TRUE, include_total = TRUE,
  aggregate = TRUE, include_wy_resu = FALSE
)

Arguments

model

an object returned by spbgam (mboost, gam/glm/lm or xgboost based classes).

newdata

optional data.frame for out-of-sample decomposition. If NULL, in-sample fitted decomposition is returned.

include_offset

logical, include the intercept in output (Intercept column).

include_total

logical, include the summed fitted value (Intercept + sum(contributions)).

aggregate

logical, if several base learners have the same name, aggregate them by summing their contributions.

include_wy_resu

logical, include Wy and resU contribution columns when present.

Value

A data.frame with one column per variable contribution, and optional Intercept and fitted.

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 7
)
fit <- spbgam(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  DGP = "SAR", method = "BSPA_SAR_CFE",
  control = list(control_gamboost = mboost::boost_control(mstop = 5, nu = 0.2))
)
fit$rho
summary(fit)
head(fitted_decomp_spboost(fit))
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 7
)
fit <- spbgam(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  DGP = "SAR", method = "BSPA_SAR_CFE",
  control = list(control_gamboost = mboost::boost_control(mstop = 5, nu = 0.2))
)
fit$rho
summary(fit)
head(fitted_decomp_spboost(fit))

GAM_SAR_CFE GAM_SAR_CFE allows the estimation of additive non linear SAR models using generalized additive models for the non linear part while the spatial parameter is estimated with the determinant-free Closed-Form Estimator of Smirnov (2020, doi:10.1111/gean.12268). This function makes it possible to estimate an additive non linear SAR model while automatically selecting the explanatory variables.

Description

GAM_SAR_CFE GAM_SAR_CFE allows the estimation of additive non linear SAR models using generalized additive models for the non linear part while the spatial parameter is estimated with the determinant-free Closed-Form Estimator of Smirnov (2020, doi:10.1111/gean.12268). This function makes it possible to estimate an additive non linear SAR model while automatically selecting the explanatory variables.

Usage

GAM_SAR_CFE(formula,data,W,doMC=FALSE,ncores=3,
engine=c('auto','gam','bam'),bam_threshold=12000L,bam_discrete=TRUE,bam_nthreads=NULL,
fallback=c('auto','none'),rho_bounds=c(-0.99,0.99),tol=1e-10)
GAM_SAR_CFE(formula,data,W,doMC=FALSE,ncores=3,
engine=c('auto','gam','bam'),bam_threshold=12000L,bam_discrete=TRUE,bam_nthreads=NULL,
fallback=c('auto','none'),rho_bounds=c(-0.99,0.99),tol=1e-10)

Arguments

formula

a gambboost formula (see mboost help)

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Aurocorrelation.

doMC

deprecated, ignored. CFE pre-fits are now sequential.

ncores

maximum number of threads used by bam defaults; capped at 3.

engine

fitting backend for the non-spatial regressions: "gam", "bam" or "auto".

bam_threshold

threshold on sample size used when engine="auto".

bam_discrete

logical passed to mgcv::bam(discrete=...).

bam_nthreads

number of threads used by bam; platform-aware defaults apply.

fallback

fallback strategy when exact CFE root is not real or unstable. "auto" uses ratio/IV approximations, "none" returns an error object.

rho_bounds

lower and upper bounds used to clip the estimated spatial parameter.

tol

numerical tolerance used for near-singular denominators/discriminant.

Details

the determinant of (I -rho W) is computed using code from Matrix packages with a sparse matrix decomposition approach (option 'LU' of function lagsarlm from spatialreg).

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho value and RMSE.

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 4
)
fit <- GAM_SAR_CFE(Y ~ X1 + X2 + X3, data = sim$data, W = sim$W)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 4
)
fit <- GAM_SAR_CFE(Y ~ X1 + X2 + X3, data = sim$data, W = sim$W)
fit$rho
summary(fit)

GAM_SAR_ML GAM_SAR_ML allows the estimation of additive non linear SAR models using GAM/IPRLS with thin plate regression spline (mgcv package) for non linear part while the estimation of the spatial parameter is based on a concentrated likelihood function.

Description

GAM_SAR_ML GAM_SAR_ML allows the estimation of additive non linear SAR models using GAM/IPRLS with thin plate regression spline (mgcv package) for non linear part while the estimation of the spatial parameter is based on a concentrated likelihood function.

Usage

GAM_SAR_ML(formula,data,W,verbose=0)
GAM_SAR_ML(formula,data,W,verbose=0)

Arguments

formula

a gam formula

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Autocorrelation.

verbose

if verbose>0 verbose mode, default verbose=0.

Value

An object of class "gam" (see mgcv package), augmented with rho value and RMSE.

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 19
)
fit <- GAM_SAR_ML(Y ~ X1 + X2 + X3, data = sim$data, W = sim$W)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 19
)
fit <- GAM_SAR_ML(Y ~ X1 + X2 + X3, data = sim$data, W = sim$W)
fit$rho
summary(fit)

GAM_SEM_CFE GAM_SEM_CFE allows the estimation of additive non linear SEM models using generalized additive models for the non linear part while the spatial parameter is estimated with the determinant-free Closed-Form Estimator of Smirnov (2020, doi:10.1111/gean.12268). This function makes it possible to estimate an additive non linear SEM model while automatically selecting the explanatory variables.

Description

GAM_SEM_CFE GAM_SEM_CFE allows the estimation of additive non linear SEM models using generalized additive models for the non linear part while the spatial parameter is estimated with the determinant-free Closed-Form Estimator of Smirnov (2020, doi:10.1111/gean.12268). This function makes it possible to estimate an additive non linear SEM model while automatically selecting the explanatory variables.

Usage

GAM_SEM_CFE(formula,data,W,doMC=FALSE,ncores=3,
engine=c('auto','gam','bam'),bam_threshold=12000L,bam_discrete=TRUE,bam_nthreads=NULL,
fallback=c('auto','none'),rho_bounds=c(-0.99,0.99),tol=1e-10)
GAM_SEM_CFE(formula,data,W,doMC=FALSE,ncores=3,
engine=c('auto','gam','bam'),bam_threshold=12000L,bam_discrete=TRUE,bam_nthreads=NULL,
fallback=c('auto','none'),rho_bounds=c(-0.99,0.99),tol=1e-10)

Arguments

formula

a gambboost formula (see mboost help)

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Aurocorrelation.

doMC

deprecated, ignored. CFE pre-fits are now sequential.

ncores

maximum number of threads used by bam defaults; capped at 3.

engine

fitting backend for the non-spatial regressions: "gam", "bam" or "auto".

bam_threshold

threshold on sample size used when engine="auto".

bam_discrete

logical passed to mgcv::bam(discrete=...).

bam_nthreads

number of threads used by bam; platform-aware defaults apply.

fallback

fallback strategy when exact CFE root is not real or unstable. "auto" uses the weighted projection approximation, "none" returns an error object.

rho_bounds

lower and upper bounds used to clip the estimated spatial parameter.

tol

numerical tolerance used for near-singular denominators/discriminant.

Details

the determinant of (I -rho W) is computed using code from Matrix packages with a sparse matrix decomposition approach (option 'LU' of function erroesarlm from spatialreg).

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho value and RMSE.

LM_SAR_ML LM_SAR_ML allows the estimation of linear SAR model

Description

LM_SAR_ML LM_SAR_ML allows the estimation of linear SAR model

Usage

LM_SAR_ML(formula,data,W,RHO=NULL,WW=NULL,verbose=0)
LM_SAR_ML(formula,data,W,RHO=NULL,WW=NULL,verbose=0)

Arguments

formula

a regular lm formula

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Aurocorrelation

RHO

a set of rho values (between -1 and 1)

WW

a named list of candidate row-standardized spatial weight matrix for Spatial Aurocorrelation.

verbose

if verbose>0 verbose mode, default verbose=0.

Details

the determinant of (I -rho W) is computed using code from Matrix packages with a sparse matrix decomposition approach (option 'LU' of function lagsarlm from spatialreg).

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho value and RMSE.

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = FALSE, myseed = 21
)
fit <- LM_SAR_ML(Y ~ X1 + X2 + X3, data = sim$data, W = sim$W)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = FALSE, myseed = 21
)
fit <- LM_SAR_ML(Y ~ X1 + X2 + X3, data = sim$data, W = sim$W)
fit$rho
summary(fit)

MARS_SAR_CFE MARS_SAR_CFE estimates additive nonlinear SAR models using a MARS backend ('earth::earth') for the nonlinear component and the determinant-free Closed-Form Estimator of Smirnov (2020, doi:10.1111/gean.12268) for the spatial autoregressive parameter.

Description

MARS_SAR_CFE MARS_SAR_CFE estimates additive nonlinear SAR models using a MARS backend ('earth::earth') for the nonlinear component and the determinant-free Closed-Form Estimator of Smirnov (2020, doi:10.1111/gean.12268) for the spatial autoregressive parameter.

Usage

MARS_SAR_CFE(formula,data,W,control=boost_control(),control_earth=list(),
doMC=FALSE,ncores=3,fallback=c('auto','none'),rho_bounds=c(-0.99,0.99),tol=1e-10)
MARS_SAR_CFE(formula,data,W,control=boost_control(),control_earth=list(),
doMC=FALSE,ncores=3,fallback=c('auto','none'),rho_bounds=c(-0.99,0.99),tol=1e-10)

Arguments

formula

a model formula. mboost-style terms are converted to an earth-compatible formula.

data

a dataframe.

W

a row-standardized spatial weight matrix for spatial autocorrelation.

control

boost_control() object (used for compatibility and optional defaults for control_earth).

control_earth

list of control parameters passed to earth::earth (e.g. degree, nprune, nk, penalty, thresh, trace). Optional CV tuning of nprune is available with use_cv_nprune=TRUE and controls cv_nfold, cv_ncore, cv_mode, cv_nprune_grid (or cv_nprune_min/max/length).

doMC

deprecated, ignored. CFE pre-fits are now sequential.

ncores

deprecated, ignored. CFE pre-fits are now sequential.

fallback

fallback strategy when exact CFE root is not real or unstable. "auto" uses ratio/IV approximations, "none" returns an error object.

rho_bounds

lower and upper bounds used to clip the estimated spatial parameter.

tol

numerical tolerance used for near-singular denominators/discriminant.

Value

An object of class earth, augmented with spboost fields including rho, rmse, fitted values and residuals.

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 22
)
fit <- MARS_SAR_CFE(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2),
  control_earth = list(degree = 1, nk = 10, nprune = 5)
)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 22
)
fit <- MARS_SAR_CFE(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2),
  control_earth = list(degree = 1, nk = 10, nprune = 5)
)
fit$rho
summary(fit)

MARS_SAR_ML MARS_SAR_ML estimates additive nonlinear SAR models using a MARS backend ('earth::earth') for the nonlinear component and concentrated likelihood for the spatial autoregressive parameter.

Description

MARS_SAR_ML MARS_SAR_ML estimates additive nonlinear SAR models using a MARS backend ('earth::earth') for the nonlinear component and concentrated likelihood for the spatial autoregressive parameter.

Usage

MARS_SAR_ML(formula,data,W,RHO=NULL,WW=NULL,control=boost_control(),
control_earth=list(),verbose=0,fallback=c("auto","none"))
MARS_SAR_ML(formula,data,W,RHO=NULL,WW=NULL,control=boost_control(),
control_earth=list(),verbose=0,fallback=c("auto","none"))

Arguments

formula

a model formula. mboost-style terms are converted to an earth-compatible formula.

data

a dataframe.

W

a row-standardized spatial weight matrix for spatial autocorrelation.

RHO

a vector of fixed rho values (used when WW is provided).

WW

a list of row-standardized spatial weight matrices, default NULL.

control

boost_control() object (used for compatibility and optional defaults for control_earth).

control_earth

verbose

verbose mode, default 0.

fallback

fallback strategy when exact ML optimization is unstable.

Value

An object of class earth, augmented with spboost fields including rho, rmse, fitted values and residuals.

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 23
)
fit <- MARS_SAR_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2),
  control_earth = list(degree = 1, nk = 10, nprune = 5)
)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 23
)
fit <- MARS_SAR_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2),
  control_earth = list(degree = 1, nk = 10, nprune = 5)
)
fit$rho
summary(fit)

MARS_SEM_CFE MARS_SEM_CFE estimates nonlinear SEM models using a MARS backend ('earth::earth') and the CFE approach for the spatial error parameter.

Description

MARS_SEM_CFE MARS_SEM_CFE estimates nonlinear SEM models using a MARS backend ('earth::earth') and the CFE approach for the spatial error parameter.

Usage

MARS_SEM_CFE(formula,data,W,control=boost_control(),control_earth=list(),
doMC=FALSE,ncores=3,fallback=c('auto','none'),rho_bounds=c(-0.99,0.99),tol=1e-10)
MARS_SEM_CFE(formula,data,W,control=boost_control(),control_earth=list(),
doMC=FALSE,ncores=3,fallback=c('auto','none'),rho_bounds=c(-0.99,0.99),tol=1e-10)

Arguments

formula

a model formula. mboost-style terms are converted to an earth-compatible formula.

data

a dataframe.

W

a row-standardized spatial weight matrix for spatial autocorrelation.

control

boost_control() object (used for compatibility and optional defaults for control_earth).

control_earth

doMC

deprecated, ignored. CFE pre-fits are now sequential.

ncores

deprecated, ignored. CFE pre-fits are now sequential.

fallback

fallback strategy when exact CFE root is not real or unstable. "auto" uses projection fallback, "none" returns an error object.

rho_bounds

lower and upper bounds used to clip the estimated spatial parameter.

tol

numerical tolerance used for near-singular denominators/discriminant.

Value

An object of class earth, augmented with spboost fields including rho, rmse, fitted values and residuals.

Examples

sim <- dgp(
  n = 500, rho = 0, lambda = 0.3, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SEM", nonlin = TRUE, myseed = 24
)
fit <- MARS_SEM_CFE(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2),
  control_earth = list(degree = 1, nk = 10, nprune = 5)
)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0, lambda = 0.3, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SEM", nonlin = TRUE, myseed = 24
)
fit <- MARS_SEM_CFE(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2),
  control_earth = list(degree = 1, nk = 10, nprune = 5)
)
fit$rho
summary(fit)

MARS_SEM_ML MARS_SEM_ML estimates nonlinear SEM models using a MARS backend ('earth::earth') and concentrated likelihood optimization for the spatial error parameter.

Description

MARS_SEM_ML MARS_SEM_ML estimates nonlinear SEM models using a MARS backend ('earth::earth') and concentrated likelihood optimization for the spatial error parameter.

Usage

MARS_SEM_ML(formula,data,W,control=boost_control(),control_earth=list(),verbose=0)
MARS_SEM_ML(formula,data,W,control=boost_control(),control_earth=list(),verbose=0)

Arguments

formula

a model formula. mboost-style terms are converted to an earth-compatible formula.

data

a dataframe.

W

a row-standardized spatial weight matrix for spatial autocorrelation.

control

boost_control() object (used for compatibility and optional defaults for control_earth).

control_earth

verbose

verbose mode, default 0.

Value

An object of class earth, augmented with spboost fields including rho, rmse, fitted values and residuals.

Examples

sim <- dgp(
  n = 500, rho = 0, lambda = 0.3, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SEM", nonlin = TRUE, myseed = 25
)
fit <- MARS_SEM_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2),
  control_earth = list(degree = 1, nk = 10, nprune = 5)
)
fit$rho
summary(fit)
sim <- dgp(
  n = 500, rho = 0, lambda = 0.3, betas = c(0, 0.5, 1, -1),
  sigma2 = 1, model = "SEM", nonlin = TRUE, myseed = 25
)
fit <- MARS_SEM_ML(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  control = mboost::boost_control(mstop = 5, nu = 0.2),
  control_earth = list(degree = 1, nk = 10, nprune = 5)
)
fit$rho
summary(fit)

predict.spboost A prediction function for object of class GAM_SAR_FIVA, GAM_SAR_ML, BSPA_SAR_ML, MARS_SAR_ML, BLA_SAR_2SLS, BLA_SAR_ML, BLA_SAR_2SLS, XGBOOST_LINEAR_SAR_ML, XGBOOST_SAR_ML, XGBOOST_LINEAR_SAR_CFE, XGBOOST_SAR_CFE. and glmboost_sar.

Description

predict.spboost A prediction function for object of class GAM_SAR_FIVA, GAM_SAR_ML, BSPA_SAR_ML, MARS_SAR_ML, BLA_SAR_2SLS, BLA_SAR_ML, BLA_SAR_2SLS, XGBOOST_LINEAR_SAR_ML, XGBOOST_SAR_ML, XGBOOST_LINEAR_SAR_CFE, XGBOOST_SAR_CFE. and glmboost_sar.

Usage

predict_spboost(model,newdata,data,W,W2=NULL,type = "BPN",maxobs=25000,chunksize=4000)
predict_spboost(model,newdata,data,W,W2=NULL,type = "BPN",maxobs=25000,chunksize=4000)

Arguments

model

a model of class spboost

newdata

a dataframe with out-sample data.

data

a dataframe with in-sample data.

W

a row-normalized weight matrix for the full sample (in-sample + out-sample) using same spatial weighting scheme as that used for model estimation.

W2

optional second row-normalized matrix (SARAR only). If NULL, 'W2=W'.

type

for BLUP estimator, default "BPN". If NULL use predictions without spatial bias correction.

maxobs

integer, beyond maxobs an approximation of solve(I -rho*W) is used (ApproxiW functions).

chunksize

predict.mboost are done by chunk of size equal to chunksize to avoid memory problem.

Value

A vector of prediction.

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 6
)
train_id <- 1:400
test_id <- 401:500
W_train <- sim$W[train_id, train_id, drop = FALSE]
row_sum_train <- Matrix::rowSums(W_train)
W_train <- Matrix::Diagonal(
  x = ifelse(row_sum_train > 0, 1 / row_sum_train, 0)
) %*% W_train
fit <- spbgam(
  Y ~ X1 + X2 + X3, data = sim$data[train_id, ], W = W_train,
  DGP = "SAR", method = "BSPA_SAR_CFE",
  control = list(control_gamboost = mboost::boost_control(mstop = 5, nu = 0.2))
)
fit$rho
summary(fit)
predict_spboost(
  fit,
  newdata = sim$data[test_id, ],
  data = sim$data[train_id, ],
  W = sim$W
)
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 6
)
train_id <- 1:400
test_id <- 401:500
W_train <- sim$W[train_id, train_id, drop = FALSE]
row_sum_train <- Matrix::rowSums(W_train)
W_train <- Matrix::Diagonal(
  x = ifelse(row_sum_train > 0, 1 / row_sum_train, 0)
) %*% W_train
fit <- spbgam(
  Y ~ X1 + X2 + X3, data = sim$data[train_id, ], W = W_train,
  DGP = "SAR", method = "BSPA_SAR_CFE",
  control = list(control_gamboost = mboost::boost_control(mstop = 5, nu = 0.2))
)
fit$rho
summary(fit)
predict_spboost(
  fit,
  newdata = sim$data[test_id, ],
  data = sim$data[train_id, ],
  W = sim$W
)

Predict Method For 'spboost' Objects

Description

Predict Method For 'spboost' Objects

Usage

## S3 method for class 'spboost'
predict(
  object, newdata = NULL, data = NULL, W = NULL, W2 = NULL,
  type = "BPN", maxobs = 25000, chunksize = 4000, ...
)
## S3 method for class 'spboost'
predict(
  object, newdata = NULL, data = NULL, W = NULL, W2 = NULL,
  type = "BPN", maxobs = 25000, chunksize = 4000, ...
)

Arguments

object

a fitted object returned by 'spbgam' (class 'spboost').

newdata

optional data frame for prediction.

data

optional in-sample data (required with 'W' for BLUP-style out-of-sample prediction).

W

optional full-sample row-normalized matrix (required with 'data' for BLUP-style out-of-sample prediction).

W2

optional second full-sample row-normalized matrix (SARAR only). If missing, defaults to 'W'.

type

prediction type for spatial correction, default '"BPN"'.

maxobs

integer, beyond maxobs an approximation of solve(I -rho*W) is used (ApproxiW functions).

chunksize

predict.mboost are done by chunk of size equal to chunksize to avoid memory problem.

...

additional arguments passed to the underlying estimator 'predict()'.

Value

A numeric vector of predictions.

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 5
)
train_id <- 1:400
test_id <- 401:500
W_train <- sim$W[train_id, train_id, drop = FALSE]
row_sum_train <- Matrix::rowSums(W_train)
W_train <- Matrix::Diagonal(
  x = ifelse(row_sum_train > 0, 1 / row_sum_train, 0)
) %*% W_train
fit <- spbgam(
  Y ~ X1 + X2 + X3, data = sim$data[train_id, ], W = W_train,
  DGP = "SAR", method = "BSPA_SAR_CFE",
  control = list(control_gamboost = mboost::boost_control(mstop = 5, nu = 0.2))
)
fit$rho
summary(fit)
pred_new<-predict(
  fit,
  newdata = sim$data[test_id, ],
  data = sim$data[train_id, ],
  W = sim$W
)
head(pred_new)
head(sim$data[test_id,'Y'])
# diff RMSE train - test
fit$rmse
rmse_test<-sqrt(mean((pred_new-sim$data[test_id, 'Y'])^2))
rmse_test
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 5
)
train_id <- 1:400
test_id <- 401:500
W_train <- sim$W[train_id, train_id, drop = FALSE]
row_sum_train <- Matrix::rowSums(W_train)
W_train <- Matrix::Diagonal(
  x = ifelse(row_sum_train > 0, 1 / row_sum_train, 0)
) %*% W_train
fit <- spbgam(
  Y ~ X1 + X2 + X3, data = sim$data[train_id, ], W = W_train,
  DGP = "SAR", method = "BSPA_SAR_CFE",
  control = list(control_gamboost = mboost::boost_control(mstop = 5, nu = 0.2))
)
fit$rho
summary(fit)
pred_new<-predict(
  fit,
  newdata = sim$data[test_id, ],
  data = sim$data[train_id, ],
  W = sim$W
)
head(pred_new)
head(sim$data[test_id,'Y'])
# diff RMSE train - test
fit$rmse
rmse_test<-sqrt(mean((pred_new-sim$data[test_id, 'Y'])^2))
rmse_test

SNR_SAR

Description

Compute the theoretical signal-to-noise ratio for a SAR model.

Usage

SNR_SAR(xb, W, rho, sigma_carre,
        method = c("hutch", "exact"),
        m = 64L, seed = NULL,
        tau_B = NULL)
SNR_SAR(xb, W, rho, sigma_carre,
        method = c("hutch", "exact"),
        m = 64L, seed = NULL,
        tau_B = NULL)

Arguments

xb

deterministic linear predictor (signal part before spatial filtering).

W

row-standardized spatial weights matrix.

rho

spatial autoregressive parameter.

sigma_carre

noise variance.

method

method used to compute tau_B: "exact" or "hutch".

m

number of Rademacher vectors for Hutchinson estimator.

seed

optional random seed used only when method="hutch".

tau_B

optional precomputed tr(B^T B) with B=(I-rho W)^{-1}.

Value

A scalar SNR value in [0,1].

Examples

W <- Matrix::Matrix(c(0, 1, 1, 0), nrow = 2, sparse = TRUE)
SNR_SAR(xb = c(1, -1), W = W, rho = 0.2, sigma_carre = 1)
W <- Matrix::Matrix(c(0, 1, 1, 0), nrow = 2, sparse = TRUE)
SNR_SAR(xb = c(1, -1), W = W, rho = 0.2, sigma_carre = 1)

SNR_SEM

Description

Compute the theoretical signal-to-noise ratio for a SEM model.

Usage

SNR_SEM(xb, W, rho, sigma_carre,
        method = c("hutch", "exact"),
        m = 64L, seed = NULL,
        tau_B = NULL)
SNR_SEM(xb, W, rho, sigma_carre,
        method = c("hutch", "exact"),
        m = 64L, seed = NULL,
        tau_B = NULL)

Arguments

xb

deterministic linear predictor (signal part).

W

row-standardized spatial weights matrix.

rho

spatial error parameter.

sigma_carre

noise variance.

method

method used to compute tau_B: "exact" or "hutch".

m

number of Rademacher vectors for Hutchinson estimator.

seed

optional random seed used only when method="hutch".

tau_B

optional precomputed tr(B^T B) with B=(I-rho W)^{-1}.

Value

A scalar SNR value in [0,1].

Examples

W <- Matrix::Matrix(c(0, 1, 1, 0), nrow = 2, sparse = TRUE)
SNR_SEM(xb = c(1, -1), W = W, rho = 0.2, sigma_carre = 1)
W <- Matrix::Matrix(c(0, 1, 1, 0), nrow = 2, sparse = TRUE)
SNR_SEM(xb = c(1, -1), W = W, rho = 0.2, sigma_carre = 1)

spbgam spbgam allows the estimation of gaussian additive non linear SAR/SEM models using gradient boosting or generalized additive models for estimating the non linear part of the model while the estimation of the spatial parameter is based on a concentrated likelihood function (ML) or the determinant-free Closed-Form Estimator of Smirnov (2020, doi:10.1111/gean.12268). This function makes it possible to estimate an additive non linear SAR or SEM model while automatically selecting the explanatory variables. If the functional forms are already known, GAM (`mgcv`) can be used directly for the nonlinear component. When variable selection or data-driven smoothness is needed, gradient boosting (`mboost`) is preferred.

Description

spbgam spbgam allows the estimation of gaussian additive non linear SAR/SEM models using gradient boosting or generalized additive models for estimating the non linear part of the model while the estimation of the spatial parameter is based on a concentrated likelihood function (ML) or the determinant-free Closed-Form Estimator of Smirnov (2020, doi:10.1111/gean.12268). This function makes it possible to estimate an additive non linear SAR or SEM model while automatically selecting the explanatory variables. If the functional forms are already known, GAM (mgcv) can be used directly for the nonlinear component. When variable selection or data-driven smoothness is needed, gradient boosting (mboost) is preferred.

Usage

spbgam(formula,data,W,W2=NULL,DGP='SAR',method='gamboost_ML',control=list(),
             debug=NULL,debug_fit_each_iter=NULL,debug_print=NULL)
spbgam(formula,data,W,W2=NULL,DGP='SAR',method='gamboost_ML',control=list(),
             debug=NULL,debug_fit_each_iter=NULL,debug_print=NULL)

Arguments

formula

a gamboost formula (see mboost help) or a gam formula (see mgcv help)

data

a dataframe.

W

a row-standardized spatial sparse weight matrix for Spatial Autocorrelation.

W2

a row-standardized spatial sparse weight matrix for Spatial Autocorrelation.

DGP

the name of the spatial autoregressive model that can be SAR or SEM, default='SAR'.

method

a method for estimation. The available choices are 'BSPA_SAR_ML', 'BSPA_SAR_CFE', 'BLA_SAR_ML', 'MARS_SAR_ML', 'MARS_SAR_CFE', 'GAM_SAR_ML', 'GAM_SAR_CFE', 'XGBOOST_SAR_ML', 'LM_SAR_ML', 'BSPA_SEM_ML', 'BSPA_SEM_CFE', 'BSPA_SEM_CFE_iter', 'MARS_SEM_ML', 'MARS_SEM_CFE', 'BSPA_SARAR_ML', 'BSPA_SARAR_CFE', 'BLA_SARAR_ML'. The suffix ML indicates the use of maximum likelihood for estimating the spatial autoregressive terms, while the suffix CFE refers to the Closed Form Estimator approach of Smirnov (2020, doi:10.1111/gean.12268). The prefix 'BSPA' refers to gradient boosting (mboost package) with splines for the nonlinear part, 'GAM' to the gam function from mgcv, 'MARS' to multivariate adaptive regression splines (earth package), and 'XGBOOST' to xgboost.

control

a list of control parameters, see details.

debug

Logical debug flag for selected iterative estimators.

debug_fit_each_iter

Logical; when supported, compute auxiliary fit diagnostics at each iteration.

debug_print

Logical; when supported, print iterative debug details.

Details

The syntax of the spline functions in formula should be coherent with the chosen method (see mboost and mgcv packages for the syntax). When ML is used, the determinant of (I - rho W) is computed using code from Matrix packages with a sparse matrix decomposition approach (option 'LU' of function lagsarlm from spatialreg). If 'gamboost' is used, the user can adapt the hyper parameters using control=list(control_gamboost=boost_control()), see mboost package. If 'MARS' is used, set control_earth=list(...) with earth::earth controls (e.g. degree, nprune, nk, penalty, thresh, trace). Optional internal CV tuning of nprune is available via control_earth$use_cv_nprune=TRUE with cv_nfold, cv_ncore, cv_mode ("random", "spatial_block", "spatial_hex" or "predefined"), and cv_nprune_grid. For method = "BSPA_SAR_CFE" or "BSPA_SAR_ML", control can include mstop_criterion = "CV" to select mstop by cross-validation. For SEM methods, mstop_criterion = "CV" tunes mstop using the SEM-filtered loss. Use cv_mode for fold construction strategy and cv_plot = TRUE to draw spatial CV folds.

Value

An object of class spboost, which, depending on the method and underlying package used, inherits from the mboost, xgboost or mgcv class, augmented with spatial parameter estimates, residuals, fitted values and RMSE.

Examples

sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 2
)
fit <- spbgam(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  DGP = "SAR", method = "BSPA_SAR_CFE",
  control = list(control_gamboost = mboost::boost_control(mstop = 5, nu = 0.2))
)
fit$rho
fit$rmse
summary(fit)
sim <- dgp(
  n = 500, rho = 0.3, betas = c(0, 0.5, 1, -1), sigma2 = 1,
  model = "SAR", nonlin = TRUE, myseed = 2
)
fit <- spbgam(
  Y ~ X1 + X2 + X3, data = sim$data, W = sim$W,
  DGP = "SAR", method = "BSPA_SAR_CFE",
  control = list(control_gamboost = mboost::boost_control(mstop = 5, nu = 0.2))
)
fit$rho
fit$rmse
summary(fit)

Summary method for 'spboost' objects

Description

Summary method for 'spboost' objects

Usage

## S3 method for class 'spboost'
summary(object, ...)
## S3 method for class 'spboost'
summary(object, ...)

Arguments

object

A fitted object returned by 'spbgam'.

...

Additional arguments passed to the underlying summary method.

Value

An object of class 'summary.spboost'.

XGBOOST_SAR_CFE XGBOOST_SAR_CFE allows the estimation of SAR models using the gradient boosting method with linear base learner or btree while the estimation of the spatial parameter is based on the determinant-free Closed-Form Estimator of Smirnov (2020, doi:10.1111/gean.12268). This function makes it possible to estimate a SAR linear or non linear model while automatically selecting the explanatory variables.

Description

XGBOOST_SAR_CFE XGBOOST_SAR_CFE allows the estimation of SAR models using the gradient boosting method with linear base learner or btree while the estimation of the spatial parameter is based on the determinant-free Closed-Form Estimator of Smirnov (2020, doi:10.1111/gean.12268). This function makes it possible to estimate a SAR linear or non linear model while automatically selecting the explanatory variables.

Usage

XGBOOST_SAR_CFE(formula,data,W,mstop0=NULL,mstop_init=500,
myparams=list(booster="gblinear",eta=0.3,gamma = 1, max_depth = 4,
min_child_weight = 5,subsample = 0.9,colsample_bytree = 0.9,
nthread=7,nfold=5,folds = NULL,early_stopping_rounds=3,
verbose = 0),verbose=0)
XGBOOST_SAR_CFE(formula,data,W,mstop0=NULL,mstop_init=500,
myparams=list(booster="gblinear",eta=0.3,gamma = 1, max_depth = 4,
min_child_weight = 5,subsample = 0.9,colsample_bytree = 0.9,
nthread=7,nfold=5,folds = NULL,early_stopping_rounds=3,
verbose = 0),verbose=0)

Arguments

formula

a regular lm formula

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Aurocorrelation.

mstop0

an integer giving the number of iterations

mstop_init

max number of iterations for cross validation of mstop0. mstop_init is used only if mstop0 is NULL, default 500.

myparams

the list of parameters: * booster which booster to use, can be gbtree or gblinear. Default: gbtree. * eta control the learning rate: scale the contribution of each tree by a factor of 0 < eta < 1 when it is added to the current approximation. Used to prevent overfitting by making the boosting process more conservative. Lower value for eta implies larger value for nrounds: low eta value means model more robust to overfitting but slower to compute. Default: 0.3 * gamma minimum loss reduction required to make a further partition on a leaf node of the tree. the larger, the more conservative the algorithm will be. * max_depth maximum depth of a tree. Default: 6 * min_child_weight minimum sum of instance weight (hessian) needed in a child. If the tree partition step results in a leaf node with the sum of instance weight less than min_child_weight, then the building process will give up further partitioning. In linear regression mode, this simply corresponds to minimum number of instances needed to be in each node. The larger, the more conservative the algorithm will be. Default: 1 * subsample subsample ratio of the training instance. Setting it to 0.5 means that xgboost randomly collected half of the data instances to grow trees and this will prevent overfitting. It makes computation shorter (because less data to analyse). It is advised to use this parameter with eta and increase nrounds. Default: 1 * colsample_bytree colsample_bytree subsample ratio of columns when constructing each tree. Default: 1 * nthread number of parallel threads * nfold during cross-validation the original dataset is randomly partitioned into nfold equal size subsamples. Default: 5 * folds list provides a possibility to use a list of pre-defined CV folds (each element must be a vector of test fold's indices). When folds are supplied, the nfold and stratified parameters are ignored. * early_stopping_rounds if NULL, the early stopping function is not triggered. If set to an integer k, training with a validation set will stop if the performance doesn't improve for k rounds. * verbose if verbose>0 Give verbose output for xgboost and xgb.cv function.

verbose

if verbose>0 verbose mode, default verbose=0.

Details

the determinant of (I -rho W) is computed using code from Matrix packages with a sparse matrix decomposition approach (option 'LU' of function lagsarlm from spatialreg).

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho value and RMSE.

XGBOOST_SAR_ML XGBOOST_SAR_ML allows the estimation of SAR models using the gradient boosting method with linear base learner or btree while the estimation of the spatial parameter is based on a concentrated likelihood function. This function makes it possible to estimate a SAR linear or non linear model while automatically selecting the explanatory variables.

Description

XGBOOST_SAR_ML XGBOOST_SAR_ML allows the estimation of SAR models using the gradient boosting method with linear base learner or btree while the estimation of the spatial parameter is based on a concentrated likelihood function. This function makes it possible to estimate a SAR linear or non linear model while automatically selecting the explanatory variables.

Usage

XGBOOST_SAR_ML(formula,data,W,mstop0=NULL,mstop_init=500,
myparams=list(booster="gblinear", eta=0.3,gamma = 1, max_depth = 4,
min_child_weight = 5,subsample = 0.9,colsample_bytree = 0.9,
nthread=7,nfold=5,folds = NULL,early_stopping_rounds=3,verbose = 0),
rho0=c(0,0.2,0.8,0.8),verbose=0)
XGBOOST_SAR_ML(formula,data,W,mstop0=NULL,mstop_init=500,
myparams=list(booster="gblinear", eta=0.3,gamma = 1, max_depth = 4,
min_child_weight = 5,subsample = 0.9,colsample_bytree = 0.9,
nthread=7,nfold=5,folds = NULL,early_stopping_rounds=3,verbose = 0),
rho0=c(0,0.2,0.8,0.8),verbose=0)

Arguments

formula

a regular lm formula

data

a dataframe.

W

a row-standardized spatial weight matrix for Spatial Aurocorrelation.

mstop0

an integer giving the number of iterations

mstop_init

max number of iterations for cross validation of mstop0. mstop_init is used only if mstop0 is NULL, default 500.

myparams

rho0

a set of rho values (between -1 and 1) for estimating initial mstop0. Used only if mstop0 is NULL. Default c(0,0.8).

verbose

if verbose>0 verbose mode, default verbose=0.

Details

the determinant of (I -rho W) is computed using code from Matrix packages with a sparse matrix decomposition approach (option 'LU' of function lagsarlm from spatialreg).

Value

An object of class mboost with print, AIC, plot and predict methods being available, augmented with rho value and RMSE.

Package 'spboost'

Help Index

ApproxiW

Description

Usage

Arguments

Value

Examples

Description

Usage

Arguments

Details

Value

Examples

Description

Usage

Arguments

Details

Value

Examples

Description

Usage

Arguments

Details

Value

Examples

Description

Usage

Arguments

Details

Value

Examples

Description

Usage

Arguments

Details

Value

Examples

BSPA_SARAR_CFE CFE-style alternating estimator for SARAR models with a gamboost core.

Description

Usage

Arguments

Value

Examples

BSPA_SARAR_ML

Description

Usage

Arguments

Details

Value

Examples

BSPA_SEM_CFE BSPA_SEM_CFE keeps the historical SEM CFE interface while using the same one-shot BRUT/filtered workflow as GAM_SEM_CFE: a non-spatial BRUT CFE estimate is computed first, then the filtered CFE backend is used when the BRUT rho estimate is high.

Description

Usage

Arguments

Value

Examples

BSPA_SEM_CFE_BRUT Experimental SEM CFE variant using raw residuals for the CFE update.

Description

Usage

Arguments

Value

Examples

BSPA_SEM_CFE_iter Iterative CFE estimator for additive nonlinear SEM with joint updates of spatial parameter and boosting fit.

Description

Usage

Arguments

Value

Description

Usage

Arguments

Details

Value

Examples

datatest is a simulated data for spatial autoregressive non linear model

Description

Author(s)

dgp a function to simulate non-linear spatial autoregressive SAR SEM and SARAR model.

Description

Usage