Nothing
R/spSUR-package.R
In spsur: Spatial Seemingly Unrelated Regression Models
#' @docType package
#' @name spsur-package
#' @rdname spsur-package
#'
#' @title Spatial Seemingly Unrelated Regression Models.
#'
#' @description
#' \pkg{spsur} offers the user a collection of functions to estimate Spatial
#' Seemingly Unrelated Regression (SUR) models by maximum likelihood or
#' three-stage least squares, using spatial instrumental variables.
#' Moreover, \pkg{spsur} obtains a collection of misspecification
#' tests for omitted or wrongly specified spatial structure. The user will
#' find spatial models more popular in applied research such as the SUR-SLX,
#' SUR-SLM, SUR-SEM, SUR-SDM, SUR-SDEM SUR-SARAR and SUR-GNM
#' plus the spatially independent SUR, or SUR-SIM.
#'
#' @details
#' Some functionalities that have been included in \pkg{spsur} package are:
#'
#' @section 1. Testing for spatial effects:
#' The function \code{\link{lmtestspsur}} provides a collection of
#' Lagrange Multipliers, LM, for testing different forms of spatial
#' dependence in SUR models. They are extended versions of
#' the well-known LM tests for omitted lags of the explained variable in
#' the right hand side of the equation, LM-SLM, the LM tests for omitted
#' spatial errors, LM-SEM, the join test of omitted spatial lags and
#' spatial errors, LM-SARAR, and the robust version of the firt
#' two Lagrange Multipliers, LM*-SLM and LM*-SEM. \cr
#' These tests can be applied to models always with a SUR nature. Roughly,
#' we may distinguish two situations:
#' \itemize{
#' \item Datasets with a single equation \emph{G=1}, for different time
#' periods \emph{Tm>1} and a certain number of spatial units in the
#' cross-sectional dimension, \emph{N}. This is what we call
#' \emph{spatial panel datasets}. In this case, the SUR structure appears
#' in form of (intra) serial dependence in the errors of each spatial unit.
#' \item Datasets with a several equations \emph{G>1}, different time
#' periods \emph{Tm>1} and a certain number of spatial units, \emph{N}.
#' The SUR structure appears, as usual, because the errors
#' of the spatial units for different equations are contemporaneously
#' correlated.
#' }
#'
#'
#' @section 2. Estimation of the Spatial SUR models:
#' As indicated above, \pkg{spsur} package may work with a list of
#' different spatial specifications.
#' They are the following:
#' \itemize{
#' \item \emph{SUR-SIM}: SUR model without spatial effects
#' \deqn{ y_{tg} = X_{tg} \beta_{g} + \epsilon_{tg} }
#' \item \emph{SUR-SLX}: SUR model with spatial lags of the regresors
#' \deqn{ y_{tg} = X_{tg} \beta_{g} +
#' WX_{tg} \theta_{g} + \epsilon_{tg} }
#' \item \emph{SUR-SLM}: SUR model with spatial lags of the endogenous
#' \deqn{y_{tg} = \rho_{g} Wy_{tg} + X_{tg} \beta_{g} +
#' \epsilon_{tg} }
#' \item \emph{SUR-SEM}: SUR model with spatial errors
#' \deqn{ y_{tg} = X_{tg} \beta_{g} + u_{tg} }
#' \deqn{ u_{tg} = \lambda_{g} Wu_{tg} + \epsilon_{tg} }
#' \item \emph{SUR-SDM}: SUR model with spatial lags of the endogenous
#' variable and of the regressors or Spatial Durbin model
#' \deqn{ y_{tg} = \rho_{g} Wy_{tg} + X_{tg} \beta_{g} +
#' WX_{tg} \theta_{g} + \epsilon_{tg} }
#' \item \emph{SUR-SDEM}: SUR model with spatial errors and spatial
#' lags of the endogenous variable and of the regressors
#' \deqn{ y_{tg} = X_{tg} \beta_{g} + WX_{tg} \theta_{g} + u_{tg} }
#' \deqn{ u_{tg} = \lambda_{g} W u_{tg} + \epsilon_{tg} }
#' \item \emph{SUR-SARAR}: Spatial lag model with spatial errors
#' \deqn{ y_{tg} = \rho_{g} Wy_{tg} + X_{tg} \beta_{g} +
#' u_{tg} }
#' \deqn{ u_{tg} = \lambda_{g} W u_{tg} + \epsilon_{tg} }
#' \item \emph{SUR-GNM}: SUR model with spatial lags of the explained
#' variables, regressors and spatial errors
#' \deqn{ y_{tg} = \rho_{g} Wy_{tg} + X_{tg} \beta_{g} +
#' WX_{tg} \theta_{g} + u_{tg} }
#' \deqn{ u_{tg} = \lambda_{g} W u_{tg} + \epsilon_{tg} }
#' }
#' where \eqn{y_{tg}}, \eqn{u_{tg}} and \eqn{\epsilon_{tg}} are
#' \emph{(Nx1)} vectors; \eqn{X_{tg}} is a matrix of regressors of
#' order \emph{(NxP)}; \eqn{\rho_{g}} and \eqn{\lambda_{g}} are
#' parameters of spatial dependence and \emph{W} is the
#' \emph{(NxN)} spatial weighting matrix.
#'
#' These specifications can be estimated by maximum-likelihood
#' methods, using the function \code{\link{spsurml}}. Moroever,
#' the models that include spatial lags of the explained
#' variables in the right hand side of the equations, and the
#' errors are assumed to be spatially incorrelated (namely, the
#' SUR-SLM and the SUR-SDM), can also be estimated using
#' three-stage least-squares, \code{\link{spsur3sls}},
#' using spatial instrumental variable to correct for the problem of
#' endogeneity present in these cases.
#'
#' @section 3. Diagnostic tests:
#' Testing for inconsistencies or misspecifications in the results of an
#' estimated (SUR) model should be a primary task for the user. \pkg{spsur}
#' focuses, especifically, on two main question such as omitted
#' or wrongly specified spatial structure and the existence of structural
#' breaks or relevant restrictions
#' in the parameters of the model. In this sense, the user will find:
#'
#' \enumerate{
#' \item \emph{Marginal tests} \cr
#' The Marginal Multipliers test for omitted or wrongly specified spatial
#' structure in the equations. They are routinely part of the output of
#' the maximum-likelihood estimation, shown by \code{\link{spsurml}}.
#' In particular, the LM(\eqn{\rho}|\eqn{\lambda}) tests for omitted
#' spatial lags in a model specified with spatial errors (SUR-SEM;
#' SUR-SDEM). The LM(\eqn{\lambda}|\eqn{\rho}) tests for omitted
#' spatial error in a model specified with spatial lags
#' of the explained variable (SUR-SLM; SUR-SDM).
#'
#' \item \emph{Coefficients stability tests} \cr
#' \pkg{spsur} includes two functions designed to test for linear
#' restrictions on the \eqn{\beta} coefficients of the models and on
#' the spatial coefficients (\eqn{\rho}s and \eqn{\lambda}s terms).
#' The function for the first case is \code{\link{wald_betas}} and
#' \code{\link{wald_deltas}} that of the second case. The user has
#' ample flexibility to define different forms of linear restrictions,
#' so that it is possible, for example,
#' to test for their time constancy to identify structural breaks.
#' }
#'
#' @section 4. Marginal effects:
#' In recent years, since the publication of LeSage and Pace (2009),
#' it has become popular in
#' spatial econometrics to evaluate the multiplier effects that a change in
#' the value of a regressor, in a point in the space, has on the explained
#' variable. \pkg{spsur} includes a function, \code{\link{impacts}},
#' that computes these effects. Specifically, \code{\link{impacts}} obtains
#' the average, over the \emph{N} spatial units and \emph{Tm} time periods,
#' of such a change on the contemporaneous value of the explained variable
#' located in the same point as the modified variable. This is the
#' so-called \emph{Average Direct effect}. The \emph{Average Indirect
#' effect} measure the proportion of the impact that spills-over to other
#' locations. The sum of the two effects is the \emph{Average Total effect}.
#' \cr
#' These estimates are complemented with a measure of statistical
#' significance, following the randomization approach suggested by
#' LeSage and Pace (2009).
#'
#' @section 5. Additional functionalities:
#' A particular feature of \pkg{spsur} is that the package allows to
#' obtain simulated datasets with a SUR nature and the spatial structure
#' decided by the user. This is the purpose of the function
#' \code{\link{dgp_spsur}}. The function can be inserted into a more
#' general code to solve, for example, Monte Carlo studies related to
#' these type of models or, simply, to show some of the stylized
#' characteristics of a SUR model with certain spatial structure.
#'
#' @section Datasets:
#' \pkg{spsur} includes three different datasets: spc, NCOVR and spain.covid. These
#' sets are used to
#' illustrate the capabilities of different functions. Briefly, their
#' main characteristics are the following \cr
#' \itemize{
#' \item The \emph{spc} dataset (Spatial Phillips-Curve) is a
#' classical dataset taken from Anselin (1988, p. 203), of small
#' dimensions.
#' \item The \emph{NCOVR} dataset comprises Homicides and a list of
#' selected socio-economic variables for continental U.S. counties
#' in four decennial census years: 1960, 1970, 1980 and 1990.
#' It is freely available from
#' \url{https://geodacenter.github.io/data-and-lab/ncovr/}.
#' \emph{NCOVR} is a typical spatial panel dataset \emph{(G=1)}.
#' \item The \emph{spain.covid} dataset comprises Within and Exit mobility index
#' together with the weeklly incidence COVID-19 at Spain provinces from
#' February 21 to May 21 2020.
#' \url{https://www.mitma.gob.es/ministerio/covid-19/evolucion-movilidad-big-data}
#' }
#'
#' @references
#' \itemize{
#' \item Breusch T, Pagan A (1980). The Lagrange multiplier test
#' and its applications to model specification in econometrics.
#' \emph{Review of Economic Studies} 47: 239-254.
#'
#' \item LeSage, J., and Pace, R. K. (2009). \emph{Introduction to
#' spatial econometrics}. Chapman and Hall/CRC.
#'
#' \item Lopez, F.A., Mur, J., and Angulo, A. (2014). Spatial model
#' selection strategies in a SUR framework. The case of regional
#' productivity in EU. \emph{Annals of Regional Science},
#' 53(1), 197-220.
#' <doi:10.1007/s00168-014-0624-2>
#'
#' \item Lopez, F.A., Martinez-Ortiz, P.J., and Cegarra-Navarro, J.G.
#' (2017). Spatial spillovers in public expenditure on a municipal
#' level in Spain. \emph{Annals of Regional Science}, 58(1), 39-65.
#' <doi:10.1007/s00168-016-0780-7>
#'
#' \item Minguez, R., Lopez, F.A. and Mur, J. (2022).
#' spsur: An R Package for Dealing with Spatial
#' Seemingly Unrelated Regression Models.
#' \emph{Journal of Statistical Software},
#' 104(11), 1--43.
#' <doi:10.18637/jss.v104.i11>
#'
#' \item Mur, J., Lopez, F., and Herrera, M. (2010). Testing for spatial
#' effects in seemingly unrelated regressions. \emph{Spatial Economic
#' Analysis}, 5(4), 399-440.
#' <doi:10.1080/17421772.2010.516443>
#' }
#'
#' @author
#' \tabular{ll}{
#' Fernando Lopez \tab \email{fernando.lopez@@upct.es} \cr
#' Roman Minguez \tab \email{roman.minguez@@uclm.es} \cr
#' Jesus Mur \tab \email{jmur@@unizar.es} \cr
#' }
#'
#' @importFrom Formula Formula model.part
#' @importFrom gmodels estimable
#' @importFrom ggplot2 ggplot
#' @importFrom ggplot2 geom_pointrange
#' @importFrom ggplot2 labs
#' @importFrom gridExtra grid.arrange
#' @importFrom MASS ginv
#' @importFrom Matrix bdiag crossprod Diagonal Matrix solve t
#' @importFrom methods as
#' @importFrom minqa bobyqa
#' @importFrom numDeriv hessian
#' @importFrom rlang .data
#' @importFrom Rdpack reprompt
#' @importFrom sparseMVN rmvn.sparse
#' @importFrom spatialreg get.ZeroPolicyOption create_WX trW
#' @importFrom spatialreg can.be.simmed jacobianSetup do_ldet
#' @importFrom spatialreg impacts intImpacts lmSLX invIrW
#' @importFrom spdep knearneigh knn2nb nb2mat
#' @importFrom spdep card mat2listw listw2mat
#' @importFrom sphet spreg
#' @importFrom stats cor cov optim pchisq pnorm pt qnorm rnorm runif
#' @importFrom stats coefficients fitted lm residuals printCoefmat
#' @importFrom stats lm.fit model.frame model.matrix terms
#' @importFrom stats anova coef formula logLik AIC BIC
#' @importFrom stats na.action napredict update
NULL
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#' @docType package
#' @name spsur-package
#' @rdname spsur-package
#'
#' @title Spatial Seemingly Unrelated Regression Models.
#'
#' @description
#' \pkg{spsur} offers the user a collection of functions to estimate Spatial
#' Seemingly Unrelated Regression (SUR) models by maximum likelihood or
#' three-stage least squares, using spatial instrumental variables.
#' Moreover, \pkg{spsur} obtains a collection of misspecification
#' tests for omitted or wrongly specified spatial structure. The user will
#' find spatial models more popular in applied research such as the SUR-SLX,
#' SUR-SLM, SUR-SEM, SUR-SDM, SUR-SDEM SUR-SARAR and SUR-GNM
#' plus the spatially independent SUR, or SUR-SIM.
#'
#' @details
#' Some functionalities that have been included in \pkg{spsur} package are:
#'
#' @section 1. Testing for spatial effects:
#' The function \code{\link{lmtestspsur}} provides a collection of
#' Lagrange Multipliers, LM, for testing different forms of spatial
#' dependence in SUR models. They are extended versions of
#' the well-known LM tests for omitted lags of the explained variable in
#' the right hand side of the equation, LM-SLM, the LM tests for omitted
#' spatial errors, LM-SEM, the join test of omitted spatial lags and
#' spatial errors, LM-SARAR, and the robust version of the firt
#' two Lagrange Multipliers, LM*-SLM and LM*-SEM. \cr
#' These tests can be applied to models always with a SUR nature. Roughly,
#' we may distinguish two situations:
#' \itemize{
#' \item Datasets with a single equation \emph{G=1}, for different time
#' periods \emph{Tm>1} and a certain number of spatial units in the
#' cross-sectional dimension, \emph{N}. This is what we call
#' \emph{spatial panel datasets}. In this case, the SUR structure appears
#' in form of (intra) serial dependence in the errors of each spatial unit.
#' \item Datasets with a several equations \emph{G>1}, different time
#' periods \emph{Tm>1} and a certain number of spatial units, \emph{N}.
#' The SUR structure appears, as usual, because the errors
#' of the spatial units for different equations are contemporaneously
#' correlated.
#' }
#'
#'
#' @section 2. Estimation of the Spatial SUR models:
#' As indicated above, \pkg{spsur} package may work with a list of
#' different spatial specifications.
#' They are the following:
#' \itemize{
#' \item \emph{SUR-SIM}: SUR model without spatial effects
#' \deqn{ y_{tg} = X_{tg} \beta_{g} + \epsilon_{tg} }
#' \item \emph{SUR-SLX}: SUR model with spatial lags of the regresors
#' \deqn{ y_{tg} = X_{tg} \beta_{g} +
#' WX_{tg} \theta_{g} + \epsilon_{tg} }
#' \item \emph{SUR-SLM}: SUR model with spatial lags of the endogenous
#' \deqn{y_{tg} = \rho_{g} Wy_{tg} + X_{tg} \beta_{g} +
#' \epsilon_{tg} }
#' \item \emph{SUR-SEM}: SUR model with spatial errors
#' \deqn{ y_{tg} = X_{tg} \beta_{g} + u_{tg} }
#' \deqn{ u_{tg} = \lambda_{g} Wu_{tg} + \epsilon_{tg} }
#' \item \emph{SUR-SDM}: SUR model with spatial lags of the endogenous
#' variable and of the regressors or Spatial Durbin model
#' \deqn{ y_{tg} = \rho_{g} Wy_{tg} + X_{tg} \beta_{g} +
#' WX_{tg} \theta_{g} + \epsilon_{tg} }
#' \item \emph{SUR-SDEM}: SUR model with spatial errors and spatial
#' lags of the endogenous variable and of the regressors
#' \deqn{ y_{tg} = X_{tg} \beta_{g} + WX_{tg} \theta_{g} + u_{tg} }
#' \deqn{ u_{tg} = \lambda_{g} W u_{tg} + \epsilon_{tg} }
#' \item \emph{SUR-SARAR}: Spatial lag model with spatial errors
#' \deqn{ y_{tg} = \rho_{g} Wy_{tg} + X_{tg} \beta_{g} +
#' u_{tg} }
#' \deqn{ u_{tg} = \lambda_{g} W u_{tg} + \epsilon_{tg} }
#' \item \emph{SUR-GNM}: SUR model with spatial lags of the explained
#' variables, regressors and spatial errors
#' \deqn{ y_{tg} = \rho_{g} Wy_{tg} + X_{tg} \beta_{g} +
#' WX_{tg} \theta_{g} + u_{tg} }
#' \deqn{ u_{tg} = \lambda_{g} W u_{tg} + \epsilon_{tg} }
#' }
#' where \eqn{y_{tg}}, \eqn{u_{tg}} and \eqn{\epsilon_{tg}} are
#' \emph{(Nx1)} vectors; \eqn{X_{tg}} is a matrix of regressors of
#' order \emph{(NxP)}; \eqn{\rho_{g}} and \eqn{\lambda_{g}} are
#' parameters of spatial dependence and \emph{W} is the
#' \emph{(NxN)} spatial weighting matrix.
#'
#' These specifications can be estimated by maximum-likelihood
#' methods, using the function \code{\link{spsurml}}. Moroever,
#' the models that include spatial lags of the explained
#' variables in the right hand side of the equations, and the
#' errors are assumed to be spatially incorrelated (namely, the
#' SUR-SLM and the SUR-SDM), can also be estimated using
#' three-stage least-squares, \code{\link{spsur3sls}},
#' using spatial instrumental variable to correct for the problem of
#' endogeneity present in these cases.
#'
#' @section 3. Diagnostic tests:
#' Testing for inconsistencies or misspecifications in the results of an
#' estimated (SUR) model should be a primary task for the user. \pkg{spsur}
#' focuses, especifically, on two main question such as omitted
#' or wrongly specified spatial structure and the existence of structural
#' breaks or relevant restrictions
#' in the parameters of the model. In this sense, the user will find:
#'
#' \enumerate{
#' \item \emph{Marginal tests} \cr
#' The Marginal Multipliers test for omitted or wrongly specified spatial
#' structure in the equations. They are routinely part of the output of
#' the maximum-likelihood estimation, shown by \code{\link{spsurml}}.
#' In particular, the LM(\eqn{\rho}|\eqn{\lambda}) tests for omitted
#' spatial lags in a model specified with spatial errors (SUR-SEM;
#' SUR-SDEM). The LM(\eqn{\lambda}|\eqn{\rho}) tests for omitted
#' spatial error in a model specified with spatial lags
#' of the explained variable (SUR-SLM; SUR-SDM).
#'
#' \item \emph{Coefficients stability tests} \cr
#' \pkg{spsur} includes two functions designed to test for linear
#' restrictions on the \eqn{\beta} coefficients of the models and on
#' the spatial coefficients (\eqn{\rho}s and \eqn{\lambda}s terms).
#' The function for the first case is \code{\link{wald_betas}} and
#' \code{\link{wald_deltas}} that of the second case. The user has
#' ample flexibility to define different forms of linear restrictions,
#' so that it is possible, for example,
#' to test for their time constancy to identify structural breaks.
#' }
#'
#' @section 4. Marginal effects:
#' In recent years, since the publication of LeSage and Pace (2009),
#' it has become popular in
#' spatial econometrics to evaluate the multiplier effects that a change in
#' the value of a regressor, in a point in the space, has on the explained
#' variable. \pkg{spsur} includes a function, \code{\link{impacts}},
#' that computes these effects. Specifically, \code{\link{impacts}} obtains
#' the average, over the \emph{N} spatial units and \emph{Tm} time periods,
#' of such a change on the contemporaneous value of the explained variable
#' located in the same point as the modified variable. This is the
#' so-called \emph{Average Direct effect}. The \emph{Average Indirect
#' effect} measure the proportion of the impact that spills-over to other
#' locations. The sum of the two effects is the \emph{Average Total effect}.
#' \cr
#' These estimates are complemented with a measure of statistical
#' significance, following the randomization approach suggested by
#' LeSage and Pace (2009).
#'
#' @section 5. Additional functionalities:
#' A particular feature of \pkg{spsur} is that the package allows to
#' obtain simulated datasets with a SUR nature and the spatial structure
#' decided by the user. This is the purpose of the function
#' \code{\link{dgp_spsur}}. The function can be inserted into a more
#' general code to solve, for example, Monte Carlo studies related to
#' these type of models or, simply, to show some of the stylized
#' characteristics of a SUR model with certain spatial structure.
#'
#' @section Datasets:
#' \pkg{spsur} includes three different datasets: spc, NCOVR and spain.covid. These
#' sets are used to
#' illustrate the capabilities of different functions. Briefly, their
#' main characteristics are the following \cr
#' \itemize{
#' \item The \emph{spc} dataset (Spatial Phillips-Curve) is a
#' classical dataset taken from Anselin (1988, p. 203), of small
#' dimensions.
#' \item The \emph{NCOVR} dataset comprises Homicides and a list of
#' selected socio-economic variables for continental U.S. counties
#' in four decennial census years: 1960, 1970, 1980 and 1990.
#' It is freely available from
#' \url{https://geodacenter.github.io/data-and-lab/ncovr/}.
#' \emph{NCOVR} is a typical spatial panel dataset \emph{(G=1)}.
#' \item The \emph{spain.covid} dataset comprises Within and Exit mobility index
#' together with the weeklly incidence COVID-19 at Spain provinces from
#' February 21 to May 21 2020.
#' \url{https://www.mitma.gob.es/ministerio/covid-19/evolucion-movilidad-big-data}
#' }
#'
#' @references
#' \itemize{
#' \item Breusch T, Pagan A (1980). The Lagrange multiplier test
#' and its applications to model specification in econometrics.
#' \emph{Review of Economic Studies} 47: 239-254.
#'
#' \item LeSage, J., and Pace, R. K. (2009). \emph{Introduction to
#' spatial econometrics}. Chapman and Hall/CRC.
#'
#' \item Lopez, F.A., Mur, J., and Angulo, A. (2014). Spatial model
#' selection strategies in a SUR framework. The case of regional
#' productivity in EU. \emph{Annals of Regional Science},
#' 53(1), 197-220.
#' <doi:10.1007/s00168-014-0624-2>
#'
#' \item Lopez, F.A., Martinez-Ortiz, P.J., and Cegarra-Navarro, J.G.
#' (2017). Spatial spillovers in public expenditure on a municipal
#' level in Spain. \emph{Annals of Regional Science}, 58(1), 39-65.
#' <doi:10.1007/s00168-016-0780-7>
#'
#' \item Minguez, R., Lopez, F.A. and Mur, J. (2022).
#' spsur: An R Package for Dealing with Spatial
#' Seemingly Unrelated Regression Models.
#' \emph{Journal of Statistical Software},
#' 104(11), 1--43.
#' <doi:10.18637/jss.v104.i11>
#'
#' \item Mur, J., Lopez, F., and Herrera, M. (2010). Testing for spatial
#' effects in seemingly unrelated regressions. \emph{Spatial Economic
#' Analysis}, 5(4), 399-440.
#' <doi:10.1080/17421772.2010.516443>
#' }
#'
#' @author
#' \tabular{ll}{
#' Fernando Lopez \tab \email{fernando.lopez@@upct.es} \cr
#' Roman Minguez \tab \email{roman.minguez@@uclm.es} \cr
#' Jesus Mur \tab \email{jmur@@unizar.es} \cr
#' }
#'
#' @importFrom Formula Formula model.part
#' @importFrom gmodels estimable
#' @importFrom ggplot2 ggplot
#' @importFrom ggplot2 geom_pointrange
#' @importFrom ggplot2 labs
#' @importFrom gridExtra grid.arrange
#' @importFrom MASS ginv
#' @importFrom Matrix bdiag crossprod Diagonal Matrix solve t
#' @importFrom methods as
#' @importFrom minqa bobyqa
#' @importFrom numDeriv hessian
#' @importFrom rlang .data
#' @importFrom Rdpack reprompt
#' @importFrom sparseMVN rmvn.sparse
#' @importFrom spatialreg get.ZeroPolicyOption create_WX trW
#' @importFrom spatialreg can.be.simmed jacobianSetup do_ldet
#' @importFrom spatialreg impacts intImpacts lmSLX invIrW
#' @importFrom spdep knearneigh knn2nb nb2mat
#' @importFrom spdep card mat2listw listw2mat
#' @importFrom sphet spreg
#' @importFrom stats cor cov optim pchisq pnorm pt qnorm rnorm runif
#' @importFrom stats coefficients fitted lm residuals printCoefmat
#' @importFrom stats lm.fit model.frame model.matrix terms
#' @importFrom stats anova coef formula logLik AIC BIC
#' @importFrom stats na.action napredict update
NULL
Try the spsur package in your browser
Any scripts or data that you put into this service are public.
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