# Gradient Boosting for Nonlinear Spatial Autoregressive Models

## Documentation for package ‘spboost’ version 0.7.0

- DESCRIPTION file.
- User guides, package vignettes and other documentation.

## Help Pages

ApproxiW | ApproxiW
BLA_SARAR_ML | 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.
BLA_SAR_ML | 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.
BLA_SEM_ML | 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.
BSPA_SARAR_CFE | BSPA_SARAR_CFE CFE-style alternating estimator for SARAR models with a gamboost core.
BSPA_SARAR_ML | BSPA_SARAR_ML
BSPA_SAR_CFE | 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.
BSPA_SAR_ML | 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.
BSPA_SEM_CFE | 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.
BSPA_SEM_CFE_BRUT | BSPA_SEM_CFE_BRUT Experimental SEM CFE variant using raw residuals for the CFE update.
BSPA_SEM_CFE_iter | BSPA_SEM_CFE_iter Iterative CFE estimator for additive nonlinear SEM with joint updates of spatial parameter and boosting fit.
BSPA_SEM_ML | 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.
datatest | datatest is a simulated data for spatial autoregressive non linear model
dgp | dgp a function to simulate non-linear spatial autoregressive SAR SEM and SARAR model.
fitted_decomp_spboost | fitted_decomp_spboost Decompose fitted values of a spboost model by variable.
GAM_SAR_CFE | 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.
GAM_SAR_ML | 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.
GAM_SEM_CFE | 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.
LM_SAR_ML | LM_SAR_ML LM_SAR_ML allows the estimation of linear SAR model
MARS_SAR_CFE | 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.
MARS_SAR_ML | 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.
MARS_SEM_CFE | 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.
MARS_SEM_ML | 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.
predict.spboost | Predict Method For 'spboost' Objects
predict_spboost | 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.
SNR_SAR | SNR_SAR
SNR_SEM | SNR_SEM
spbgam | 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.
summary.spboost | Summary method for 'spboost' objects
XGBOOST_SAR_CFE | 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.
XGBOOST_SAR_ML | 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.