Nothing
R/summary.impacts.sphet_orig.R
In sphet: Estimation of Spatial Autoregressive Models with and without Heteroskedastic Innovations
#' #' Generate impacts for spreg lag and sarar models
#' #'
#' #'
#' #' @param object An object of class sphet
#' #' @param ... Additional arguments to be passed
#' #'
#' #'
#' #' @return Estimate of the Average Total, Average Direct, and Average Indirect Effects
#' #'
#' #' @examples
#' #' data(columbus, package="spdep")
#' #' listw <- spdep::nb2listw(col.gal.nb)
#' #' res <- spreg(CRIME~HOVAL + INC, data=columbus , listw= listw,
#' #' het = TRUE, verbose = FALSE, model = "sarar")
#' #' summary(res)
#' #' effects <- impacts(res, n_mvn = 3000)
#' #' summary(effects)
#' impacts <- function(object, ...){
#' UseMethod("impacts", object)
#' }
#' #' describedIn impacts
#' #' @param object An object of class sphet
#' #' @param ... Additional arguments to be passed
#' #'
#' #'
#' #' @return Estimate of the Average Total, Average Direct, and Average Indirect Effects
#' #'
#' #' @examples
#' #' data(columbus, package="spdep")
#' #' listw <- spdep::nb2listw(col.gal.nb)
#' #' res <- spreg(CRIME~HOVAL + INC, data=columbus , listw= listw,
#' #' het = TRUE, verbose = FALSE, model = "sarar")
#' #' summary(res)
#' #' effects <- impacts(res, n_mvn = 3000)
#' #' summary(effects)
#' impacts.sphet <- function(object, ...) {
#'
#' if(class(object$Durbin) == "formula") object$Durbin <- TRUE
#'
#' if(!is.null(object$endog)) stop("Impacts not yet implemented
#' for models with additional endogenous variables")
#'
#' if(class(object)[[2]] %in% c("ols", "error_gmm")) stop("Impacts not needed
#' for error and ols models")
#'
#'
#' if(!isTRUE(all.equal(as.numeric(Matrix::rowSums(object$listw)), rep(1,dim(object$listw)[2])))) stop("Impacts not yet implemented
#' for non row-standardized listw")
#'
#' ag <- class(object)[[2]]
#' # print(ag)
#' switch(match.arg(ag, c("lag_gmm", "sarar_gmm")),
#' sarar_gmm = impacts.sarar(object, ...),
#' lag_gmm = impacts.lag(object, ...)
#' )
#'
#' }
#' # TODO in the future implement the VC matrix of the impacts
#' # TODO check two things in the impacts: 1) calculate the impacts only for the coefficients in parameter space 2) fix the Z test
#'
#' #' Generate impacts
#' #'
#' #'
#' #' @param object An object of class sphet
#' #' @param mvn Inference based on MC simulation of mvn samples
#' #' @param n_mvn Number of samples
#' #' @param weg Eigenvalues can be provided by the user
#' #' @param inference should inference be performed
#' #' @param exact should inference be exact
#' #' @param trW either NULL or a trW from spatialreg
#' #' @param m number of traces of w - default is 30
#' #'
#' #'
#' #' @return Estimate of the Average Total, Average Direct, and Average Indirect Effects
#' #'
#' #' @examples
#' #' data(columbus, package="spdep")
#' #' listw <- spdep::nb2listw(col.gal.nb)
#' #' res <- spreg(CRIME~HOVAL + INC, data=columbus , listw= listw,
#' #' het = TRUE, verbose = FALSE, model = "sarar")
#' #' summary(res)
#' #' effects <- impacts(res, n_mvn = 3000)
#' #' summary(effects)
#' impacts.sarar <-function(object, n_mvn = 3000, weg = NULL,
#' inference = FALSE, exact = TRUE, m = 30, trW = NULL, mvn = TRUE){
#'
#' if(object$Durbin) {
#'
#' coefs <- drop(object$coefficients)
#' p2 <- length(coefs)
#' lambda <- coefs[(p2-1)]
#' beta <- coefs[1:(p2-2)]
#' rho <- coefs[p2]
#'
#'
#' dn <- grep("lag_", names(beta))
#' dc <- beta[dn]
#' beta <- beta[-dn]
#'
#' xb <- beta[which(names(beta) %in% stringr::str_remove(names(dc),"lag_") )]
#' xb <- xb[order(names(xb))]
#' xo <- beta[ -which(names(beta) %in% stringr::str_remove(names(dc),"lag_") )]
#' gamma <- dc[which( stringr::str_remove(names(dc),"lag_") %in% names(beta))]
#' gamma <- gamma[order(names(gamma))]
#' don <- dc[-which( stringr::str_remove(names(dc),"lag_") %in% names(beta))]
#'
#' icept <- grep("(Intercept)", names(xo))
#' iicept <- length(icept) > 0
#' Sigma <- object$var
#'
#' if (iicept) {
#' P <- xo[-icept]
#' Sigma <- Sigma[-c(icept,p2),-c(icept,p2)]
#' bnames <- c(names(xo[-icept]), stringr::str_remove(names(dc), "lag_"))
#' }
#' else {
#' P <- xo
#' Sigma <- Sigma[-c(p2),-c(p2)]
#' bnames <-c(names(xo), stringr::str_remove(names(dc), "lag_"))
#' }
#'
#' n <- length(object$residuals)
#'
#'
#' ATE <- c(AVTE_rn_Dur(c(P, lambda), c(0, lambda)),
#' AVTE_rn_Dur(c(xb, lambda), c(gamma, lambda)),
#' AVTE_rn_Dur(c(0, lambda), c(don, lambda)) )
#'
#'
#'
#' if(exact){
#'
#' if(is.null(weg)) weg <- eigen(object$listw)$values
#'
#'
#' ADE <- c(ADRE_rn_Dur(c(P, lambda), weg, n, m, object$listw, c(0, lambda), exact = TRUE),
#' ADRE_rn_Dur(c(xb, lambda), weg, n, m, object$listw, c(gamma, lambda), exact = TRUE),
#' ADRE_rn_Dur(c(0, lambda), weg, n, m, object$listw, c(don, lambda), exact = TRUE) )
#' }
#' else{
#'
#' if(is.null(trW)) trW <- smtrace(object$listw, m = m)
#'
#'
#' ADE <- c(ADRE_rn_Dur(c(P, lambda), weg, n, m = m, object$listw, c(0, lambda), exact = F, trW = trW),
#' ADRE_rn_Dur(c(xb, lambda), weg, n, m = m, object$listw, c(gamma, lambda), exact = F, trW = trW),
#' ADRE_rn_Dur(c(0, lambda), weg, n, m = m, object$listw, c(don, lambda), exact = F, trW = trW) )
#'
#'
#' }
#'
#' AIE <- ATE - ADE
#'
#'
#' if (inference) {
#'
#' mu <- c(P, xb, gamma, don, lambda)
#' mc_splm <- mvtnorm::rmvnorm(n_mvn, mean = mu, sigma = Sigma)
#'
#'
#' if (length(P) == 0 && length(don) == 0) ATE_inf <- rbind(apply(mc_splm[ ,c((1 : length(xb)), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c((length(xb) + 1) : ( ncol(mc_splm)-1), ncol(mc_splm))], 1, AVTE_rn_Dur_sp))
#'
#' else if(length(P) == 0 && length(don) != 0) ATE_inf <- rbind(apply(mc_splm[ ,c( (1 : length(xb)), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply(mc_splm[ , c((length(xb) + 1) : (ncol(mc_splm) - 1), ncol(mc_splm))], 1, AVTE_rn_Dur_sp),
#' apply(mc_splm[ , c(length(xb) + length(gamma) +1) : (ncol(mc_splm) - 1), ncol(mc_splm)], 1, AVTE_rn_Dur_sp))
#'
#' else if(length(P) != 0 && length(don) == 0) ATE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, AVTE_rn_Dur_fp),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( ncol(mc_splm) - 1), ncol(mc_splm))], 1, AVTE_rn_Dur_sp))
#'
#' else ATE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, AVTE_rn_Dur_fp)
#' + apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, AVTE_rn_Dur_sp),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( (length(P) + length(xb) + length(gamma))), ncol(mc_splm))], 1, AVTE_rn_Dur_sp),
#' apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c( (length(P) + length(xb) +length(gamma) +1) : (length(P) + length(xb) +length(gamma) +length(don)), ncol(mc_splm))], 1, AVTE_rn_Dur_sp))
#'
#'
#' if(exact){
#'
#'
#' if (length(P) == 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c((1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE ) +
#' apply( mc_splm[ , c((length(xb) + 1) : ( ncol(mc_splm)-1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#' else if(length(P) == 0 && length(don) != 0) ADE_inf <- rbind(apply(mc_splm[ ,c( (1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply(mc_splm[ , c((length(xb) + 1) : (ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE),
#' apply(mc_splm[ , c(length(xb) + length(gamma) +1) : (ncol(mc_splm) - 1), ncol(mc_splm)], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#' else if(length(P) != 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#' else ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE)
#' + apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( (length(P) + length(xb) + length(gamma))), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE),
#' apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply( mc_splm[ , c( (length(P) + length(xb) +length(gamma) +1) : (length(P) + length(xb) +length(gamma) +length(don)), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#'
#' }
#' else{
#'
#'
#' if (length(P) == 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c((1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW ) +
#' apply( mc_splm[ , c((length(xb) + 1) : ( ncol(mc_splm)-1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#' else if(length(P) == 0 && length(don) != 0) ADE_inf <- rbind(apply(mc_splm[ ,c( (1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply(mc_splm[ , c((length(xb) + 1) : (ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW),
#' apply(mc_splm[ , c(length(xb) + length(gamma) +1) : (ncol(mc_splm) - 1), ncol(mc_splm)], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#' else if(length(P) != 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#' else ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW)
#' + apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( (length(P) + length(xb) + length(gamma))), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW),
#' apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply( mc_splm[ , c( (length(P) + length(xb) +length(gamma) +1) : (length(P) + length(xb) +length(gamma) +length(don)), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#'
#'
#' }
#'
#' AIE_inf <- ATE_inf - ADE_inf
#'
#' res <- list(ATE, ADE, AIE, ATE_inf, ADE_inf, AIE_inf)
#' }
#' else res <- list(ATE, ADE, AIE)
#'
#'
#' }
#'
#' else{
#'
#' coefs <- drop(object$coefficients)
#' p2 <- length(coefs)
#' lambda <- coefs[(p2-1)]
#' beta <- coefs[1:(p2-2)]
#' p <- length(beta)
#' p1 <- p + 1
#' rho <- coefs[p2]
#' icept <- grep("(Intercept)", names(beta))
#' iicept <- length(icept) > 0
#' Sigma <- object$var
#' n <- length(object$residuals)
#'
#' if (iicept) {
#' P <- beta[-icept]
#' Sigma <- Sigma[-c(icept,p2),-c(icept,p2)]
#' bnames <- names(beta[-icept])
#' }
#' else {
#' P <- beta
#' Sigma <- Sigma[-c(p2),-c(p2)]
#' bnames <- names(beta)
#' }
#'
#' ATE <- AVTE_rn(c(P, lambda))
#'
#' if(exact){
#'
#' if(is.null(weg)) weg <- eigen(object$listw)$values
#' ADE <- ADRE_rn(c(P, lambda), weg, n, exact = TRUE)
#' }
#' else{
#'
#' if(is.null(trW)) trW <- smtrace(object$listw, m = m)
#'
#' ADE <- ADRE_rn(c(P, lambda), exact = FALSE, trW = trW, m = m, n = n)
#'
#' }
#' AIE <- ATE - ADE
#'
#' if (inference) {
#'
#' mu <- c(P, lambda)
#' mc_splm <- mvtnorm::rmvnorm(n_mvn, mean = mu, sigma = Sigma)
#'
#'
#' ATE_inf <- apply(mc_splm, 1, AVTE_rn)
#'
#' if(exact) ADE_inf <- apply(mc_splm, 1, ADRE_rn, weg, n, exact = TRUE)
#' else ADE_inf <- apply(mc_splm, 1, ADRE_rn, exact = FALSE, trW = trW, m = m, n = n)
#'
#' AIE_inf <- ATE_inf - ADE_inf
#'
#' res <- list(ATE, ADE, AIE, ATE_inf, ADE_inf, AIE_inf)
#' }
#' else res <- list(ATE, ADE, AIE)
#'
#' }
#'
#' attr(res, "inference") <- inference
#' class(res) <- c("impacts_sphet")
#'
#' invisible(res)
#' }
#'
#' #' Generate impacts
#' #'
#' #'
#' #' @param object An object of class sphet
#' #' @param mvn Inference based on MC simulation of mvn samples
#' #' @param n_mvn Number of samples
#' #' @param weg Eigenvalues can be provided by the user
#' #' @param inference should inference be performed
#' #' @param exact should inference be exact
#' #' @param trW either NULL or a trW from spatialreg
#' #' @param m number of traces of w - default is 30
#' #'
#' #'
#' #' @return Estimate of the Average Total, Average Direct, and Average Indirect Effects
#' #'
#' #' @examples
#' #' data(columbus, package="spdep")
#' #' listw <- spdep::nb2listw(col.gal.nb)
#' #' res <- spreg(CRIME~HOVAL + INC, data=columbus , listw= listw,
#' #' het = TRUE, verbose = FALSE, model = "sarar")
#' #' summary(res)
#' #' effects <- sphet::impacts(res, n_mvn = 3000)
#' #' summary(effects)
#' impacts.lag <-function(object, n_mvn = 3000, weg = NULL,
#' inference = FALSE, exact = TRUE, m = 30, trW = NULL, mvn = TRUE){
#'
#' if(object$Durbin){
#'
#' coefs <- drop(object$coefficients)
#' p2 <- length(coefs)
#' lambda <- coefs[p2]
#' beta <- coefs[1:(p2-1)]
#' p <- length(beta)
#' p1 <- p + 1
#'
#'
#' dn <- grep("lag_", names(beta))
#' dc <- beta[dn]
#' beta <- beta[-dn]
#'
#' xb <- beta[which(names(beta) %in% stringr::str_remove(names(dc),"lag_") )]
#' xb <- xb[order(names(xb))]
#' xo <- beta[ -which(names(beta) %in% stringr::str_remove(names(dc),"lag_") )]
#' gamma <- dc[which( stringr::str_remove(names(dc),"lag_") %in% names(beta))]
#' gamma <- gamma[order(names(gamma))]
#' don <- dc[-which( stringr::str_remove(names(dc),"lag_") %in% names(beta))]
#'
#' icept <- grep("(Intercept)", names(xo))
#' iicept <- length(icept) > 0
#' Sigma <- as.matrix(object$var)
#' #print(Sigma)
#'
#' if (iicept) {
#' P <- xo[-icept]
#' Sigma <- Sigma[-c(icept),-c(icept)]
#' bnames <- c(names(xo[-icept]), stringr::str_remove(names(dc), "lag_"), names(don))
#' }
#' else {
#' P <- xo
#' Sigma <- Sigma
#' bnames <-c(names(xo), stringr::str_remove(names(dc), "lag_"), names(don))
#' }
#'
#' n <- length(object$residuals)
#'
#'
#' ATE <- c(AVTE_rn_Dur(c(P, lambda), c(0, lambda)),
#' AVTE_rn_Dur(c(xb, lambda), c(gamma, lambda)),
#' AVTE_rn_Dur(c(0, lambda), c(don, lambda)) )
#'
#'
#'
#' if(exact){
#'
#' if(is.null(weg)) weg <- eigen(object$listw)$values
#'
#'
#' ADE <- c(ADRE_rn_Dur(c(P, lambda), weg, n, m, object$listw, c(0, lambda), exact = TRUE),
#' ADRE_rn_Dur(c(xb, lambda), weg, n, m, object$listw, c(gamma, lambda), exact = TRUE),
#' ADRE_rn_Dur(c(0, lambda), weg, n, m, object$listw, c(don, lambda), exact = TRUE) )
#' }
#' else{
#'
#' if(is.null(trW)) trW <- smtrace(object$listw, m = m)
#'
#'
#' ADE <- c(ADRE_rn_Dur(c(P, lambda), weg, n, m = m, object$listw, c(0, lambda), exact = F, trW = trW),
#' ADRE_rn_Dur(c(xb, lambda), weg, n, m = m, object$listw, c(gamma, lambda), exact = F, trW = trW),
#' ADRE_rn_Dur(c(0, lambda), weg, n, m = m, object$listw, c(don, lambda), exact = F, trW = trW) )
#'
#' }
#'
#' AIE <- ATE - ADE
#'
#'
#' if (inference) {
#'
#' mu <- c(P, xb, gamma, don, lambda)
#' mc_splm <- mvtnorm::rmvnorm(n_mvn, mean = mu, sigma = Sigma)
#'
#'
#' if (length(P) == 0 && length(don) == 0) ATE_inf <- rbind(apply(mc_splm[ ,c((1 : length(xb)), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c((length(xb) + 1) : ( ncol(mc_splm)-1), ncol(mc_splm))], 1, AVTE_rn_Dur_sp))
#'
#' else if(length(P) == 0 && length(don) != 0) ATE_inf <- rbind(apply(mc_splm[ ,c( (1 : length(xb)), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply(mc_splm[ , c((length(xb) + 1) : (ncol(mc_splm) - 1), ncol(mc_splm))], 1, AVTE_rn_Dur_sp),
#' apply(mc_splm[ , c(length(xb) + length(gamma) +1) : (ncol(mc_splm) - 1), ncol(mc_splm)], 1, AVTE_rn_Dur_sp))
#'
#' else if(length(P) != 0 && length(don) == 0) ATE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, AVTE_rn_Dur_fp),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( ncol(mc_splm) - 1), ncol(mc_splm))], 1, AVTE_rn_Dur_sp))
#'
#' else ATE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, AVTE_rn_Dur_fp)
#' + apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, AVTE_rn_Dur_sp),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( (length(P) + length(xb) + length(gamma))), ncol(mc_splm))], 1, AVTE_rn_Dur_sp),
#' apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c( (length(P) + length(xb) +length(gamma) +1) : (length(P) + length(xb) +length(gamma) +length(don)), ncol(mc_splm))], 1, AVTE_rn_Dur_sp))
#'
#'
#' # print(head(ATE_inf)[,1:5])
#'
#' if(exact){
#'
#'
#' if (length(P) == 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c((1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE ) +
#' apply( mc_splm[ , c((length(xb) + 1) : ( ncol(mc_splm)-1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#' else if(length(P) == 0 && length(don) != 0) ADE_inf <- rbind(apply(mc_splm[ ,c( (1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply(mc_splm[ , c((length(xb) + 1) : (ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE),
#' apply(mc_splm[ , c(length(xb) + length(gamma) +1) : (ncol(mc_splm) - 1), ncol(mc_splm)], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#' else if(length(P) != 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#' else ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE)
#' + apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( (length(P) + length(xb) + length(gamma))), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE),
#' apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply( mc_splm[ , c( (length(P) + length(xb) +length(gamma) +1) : (length(P) + length(xb) +length(gamma) +length(don)), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#'
#' }
#' else{
#'
#'
#' if (length(P) == 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c((1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW ) +
#' apply( mc_splm[ , c((length(xb) + 1) : ( ncol(mc_splm)-1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#' else if(length(P) == 0 && length(don) != 0) ADE_inf <- rbind(apply(mc_splm[ ,c( (1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply(mc_splm[ , c((length(xb) + 1) : (ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW),
#' apply(mc_splm[ , c(length(xb) + length(gamma) +1) : (ncol(mc_splm) - 1), ncol(mc_splm)], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#' else if(length(P) != 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#' else ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW)
#' + apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( (length(P) + length(xb) + length(gamma))), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW),
#' apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply( mc_splm[ , c( (length(P) + length(xb) +length(gamma) +1) : (length(P) + length(xb) +length(gamma) +length(don)), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#'
#'
#' }
#'
#' AIE_inf <- ATE_inf - ADE_inf
#'
#' res <- list(ATE, ADE, AIE, ATE_inf, ADE_inf, AIE_inf)
#' }
#' else res <- list(ATE, ADE, AIE)
#'
#'
#'
#'
#'
#' }
#'
#' else{
#'
#' coefs <- drop(object$coefficients)
#' p2 <- length(coefs)
#' lambda <- coefs[p2]
#' beta <- coefs[1:(p2-1)]
#' p <- length(beta)
#' p1 <- p + 1
#' icept <- grep("(Intercept)", names(beta))
#' iicept <- length(icept) > 0
#' Sigma <- as.matrix(object$var)
#'
#' if (iicept) {
#' P <- beta[-icept]
#' Sigma <- Sigma[-c(icept),-c(icept)]
#' bnames <- names(beta[-icept])
#' }
#' else {
#' P <- beta
#' Sigma <- Sigma
#' bnames <- names(beta)
#' }
#'
#' n <- length(object$residuals)
#'
#' if(exact){
#'
#' if(is.null(weg)) weg <- eigen(object$listw)$values
#'
#'
#' ATE <- AVTE_rn(c(P, lambda))
#' ADE <- ADRE_rn(c(P, lambda), weg, n, exact = TRUE)
#' AIE <- ATE - ADE
#' }
#' else{
#'
#' if(is.null(trW)) trW <- smtrace(object$listw, m = m)
#'
#'
#' ATE <- AVTE_rn(c(P, lambda))
#' ADE <- ADRE_rn(c(P, lambda), exact = FALSE, trW = trW, m = m, n = n)
#' AIE <- ATE - ADE
#'
#' }
#'
#' if (inference) {
#'
#' mu <- c(P, lambda)
#' mc_splm <- mvtnorm::rmvnorm(n_mvn, mean = mu, sigma = Sigma)
#'
#' if(exact){
#'
#' ATE_inf <- apply(mc_splm, 1, AVTE_rn)
#' ADE_inf <- apply(mc_splm, 1, ADRE_rn, weg, n, exact = TRUE)
#' AIE_inf <- ATE_inf - ADE_inf
#'
#' }
#' else{
#'
#' ATE_inf <- apply(mc_splm, 1, AVTE_rn)
#' ADE_inf <- apply(mc_splm, 1, ADRE_rn, exact = FALSE, trW = trW, m = m, n = n)
#' AIE_inf <- ATE_inf - ADE_inf
#'
#' }
#' res <- list(ATE, ADE, AIE, ATE_inf, ADE_inf, AIE_inf)
#' }
#' else res <- list(ATE, ADE, AIE)
#'
#' }
#' attr(res, "inference") <- inference
#' class(res) <- c("impacts_sphet")
#'
#' invisible(res)
#' }
#'
#' #' Summary for spreg impacts
#' #'
#' #'
#' #' @param object An object of class impacts.sphet
#' #' @param ... Additional arguments that can be passed to the function
#' #' @return Summary of the Average Total, Average Direct, and Average Indirect Effects
#' #' @method summary impacts_sphet
#' #' @examples
#' #' data(columbus, package = "spdep")
#' #' listw <- spdep::nb2listw(col.gal.nb)
#' #' res <- spreg(CRIME~HOVAL + INC, data=columbus , listw= listw,
#' #' het = TRUE, verbose = FALSE, model = "sarar")
#' #' summary(res)
#' #' effects <- impacts(res, n_mvn = 3000)
#' #' summary(effects)
#' summary.impacts_sphet <- function(object, ...){
#'
#' cat("\n ---------------------- \n")
#' cat("\n ---------------------- \n")
#' cat("\n Impacts estimates:\n")
#' cat("\n ---------------------- \n")
#' cat("\n ---------------------- \n")
#'
#' # print(cbind(ATE,apply(ATE_inf, 2, sd), (ATE - apply(ATE_inf, 2, mean) )/apply(ATE_inf, 2, sd)))
#' #print(cbind(obj[[1]], sd(obj[[4]]), obj[[1]]/sd(obj[[4]]) ))
#' eff <- cbind(object[[1]], object[[2]], object[[3]])
#' colnames(eff) <- c("ATE", "ADE", "AIE")
#' print(eff)
#'
#' if(attributes(object)$inference){
#' cat("\n ---------------------- \n")
#' cat("\n Inference for ATE:\n")
#' cat("\n ---------------------- \n")
#'
#' mean_ate <- apply(object[[4]], 1, mean)
#' # print(head(mean_ate))
#' sd_ate <- apply(object[[4]], 1, sd)
#' z_ate <- (object[[1]])/sd_ate
#' p_ate <- 2*pnorm(abs(z_ate), lower.tail = F)
#' total <- cbind(object[[1]], sd_ate, z_ate, p_ate)
#' colnames(total) <- c("ATE", "sd", "z-stat","p-val")
#' print(total)
#' cat("\n Summary stats for the simulated ATE samples:\n")
#' a <- matrix(nrow = nrow(total), ncol = 6)
#' for (i in 1:nrow(total)) a[i,] <- c(quantile(object[[4]][i,], c(0.025, 0.25, 0.5, 0.75, 0.975)), mean(object[[4]][i,]))
#' colnames(a) <- c("0.025", "Q1", "Median", "Q3", "0.975","Mean")
#' rownames(a) <- rownames(eff)
#' print(a)
#'
#' cat("\n ---------------------- \n")
#' cat("\n Inference for ADE:\n")
#' cat("\n ---------------------- \n")
#'
#' mean_ade <- apply(object[[5]], 1, mean)
#' # print(head(mean_ate))
#' sd_ade <- apply(object[[5]], 1, sd)
#' z_ade <- (object[[2]])/sd_ade
#' p_ade <- 2*pnorm(abs(z_ade), lower.tail = F)
#' direct <- cbind(object[[2]], sd_ade, z_ade, p_ade)
#' colnames(direct) <- c("ADE", "sd", "z-stat","p-val")
#' print(direct)
#' cat("\n Summary stats for the simulated ADE samples:\n")
#'
#' for (i in 1:nrow(total)) a[i,] <- c(quantile(object[[5]][i,], c(0.025, 0.25, 0.5, 0.75, 0.975)), mean(object[[5]][i,]))
#' colnames(a) <- c("0.025", "Q1", "Median", "Q3", "0.975","Mean")
#' rownames(a) <- rownames(eff)
#' print(a)
#'
#' cat("\n ---------------------- \n")
#' cat("\n Inference for AIE:\n")
#' cat("\n ---------------------- \n")
#'
#' mean_aie <- apply(object[[6]], 1, mean)
#' sd_aie <- apply(object[[6]], 1, sd)
#' z_aie <- (object[[3]])/sd_aie
#' p_aie <- 2*pnorm(abs(z_aie), lower.tail = F)
#' indirect <- cbind(object[[3]], sd_aie, z_aie, p_aie)
#' dim(indirect)
#' colnames(indirect) <- c("AIE", "sd", "z-stat","p-val")
#' print(indirect)
#' cat("\n Summary stats for the simulated AIE samples:\n")
#'
#' for (i in 1:nrow(total)) a[i,] <- c(quantile(object[[6]][i,], c(0.025, 0.25, 0.5, 0.75, 0.975)), mean(object[[6]][i,]))
#' colnames(a) <- c("0.025", "Q1", "Median", "Q3", "0.975","Mean")
#' rownames(a) <- rownames(eff)
#' print(a)
#' }
#'
#' }
#'
#'
#' AVTE_rn <- function(x){
#' x[-length(x)]/(1-x[length(x)])
#' }
#' AVTE_rn_Dur <- function(x,y){
#' x[-length(x)]/(1-x[length(x)]) + y[-length(y)]/(1-y[length(y)])
#' }
#' AVTE_rn_Dur_fp <- function(x){
#' x[-length(x)]/(1-x[length(x)])
#' }
#' AVTE_rn_Dur_sp <- function(y){
#' y[-length(y)]/(1-y[length(y)])
#' }
#'
#'
#' ADRE_rn <- function(x, egv, n, m, exact, trW){
#' if (exact) Re(x[-length(x)] *(1/n)*sum(1/(1-x[length(x)]*egv)))
#' else x[-length(x)] *(1/n) *(sum(as.numeric(sapply(x[length(x)], function(s) s^seq(1,m)), m )/n *trW) + n)
#' }
#' ADRE_rn_Dur <- function(x, egv, n, m, listw, y, exact, trW){
#' if(exact) Re(x[-length(x)] *(1/n)*sum(1/(1-x[length(x)]*egv))) +
#' (1/n)*y[-length(y)] *sum(diag(solve(Diagonal(n)- y[length(y)]* listw) %*% listw))
#' else x[-length(x)] *(1/n) *(sum(as.numeric(sapply(x[length(x)], function(s) s^seq(1,m)), m )/n *trW) + n) +
#' y[-length(y)] *(1/n) * (sum(as.numeric(sapply(y[length(y)], function(s) s^seq(1,(m-1))), m )/n *trW[-1]) )
#' }
#' ADRE_rn_Dur_fp <- function(x, egv, n, m, listw, exact, trW){
#' if(exact) Re(x[-length(x)] *(1/n)*sum(1/(1-x[length(x)]*egv)))
#' else x[-length(x)] *(1/n) *(sum(as.numeric(sapply(x[length(x)], function(s) s^seq(1,m)), m )/n *trW) + n)
#'
#' }
#' ADRE_rn_Dur_sp <- function(y, egv, n, m, listw, exact, trW){
#' if(exact) (1/n)*y[-length(y)] *sum(diag(solve(Diagonal(n)- y[length(y)]* listw) %*% listw))
#' else y[-length(y)] *(1/n) * (sum(as.numeric(sapply(y[length(y)], function(s) s^seq(1,(m-1))), m )/n *trW[-1]) )
#' }
#' smtrace <- function(listw, m){
#' listwp <- listw
#' tr <- numeric(m)
#' for (i in 1:m) {
#' tr[i] <- sum(diag(listwp))
#' listwp <- listw %*% listwp
#' }
#' return(tr)
#' }
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#' #' Generate impacts for spreg lag and sarar models
#' #'
#' #'
#' #' @param object An object of class sphet
#' #' @param ... Additional arguments to be passed
#' #'
#' #'
#' #' @return Estimate of the Average Total, Average Direct, and Average Indirect Effects
#' #'
#' #' @examples
#' #' data(columbus, package="spdep")
#' #' listw <- spdep::nb2listw(col.gal.nb)
#' #' res <- spreg(CRIME~HOVAL + INC, data=columbus , listw= listw,
#' #' het = TRUE, verbose = FALSE, model = "sarar")
#' #' summary(res)
#' #' effects <- impacts(res, n_mvn = 3000)
#' #' summary(effects)
#' impacts <- function(object, ...){
#' UseMethod("impacts", object)
#' }
#' #' describedIn impacts
#' #' @param object An object of class sphet
#' #' @param ... Additional arguments to be passed
#' #'
#' #'
#' #' @return Estimate of the Average Total, Average Direct, and Average Indirect Effects
#' #'
#' #' @examples
#' #' data(columbus, package="spdep")
#' #' listw <- spdep::nb2listw(col.gal.nb)
#' #' res <- spreg(CRIME~HOVAL + INC, data=columbus , listw= listw,
#' #' het = TRUE, verbose = FALSE, model = "sarar")
#' #' summary(res)
#' #' effects <- impacts(res, n_mvn = 3000)
#' #' summary(effects)
#' impacts.sphet <- function(object, ...) {
#'
#' if(class(object$Durbin) == "formula") object$Durbin <- TRUE
#'
#' if(!is.null(object$endog)) stop("Impacts not yet implemented
#' for models with additional endogenous variables")
#'
#' if(class(object)[[2]] %in% c("ols", "error_gmm")) stop("Impacts not needed
#' for error and ols models")
#'
#'
#' if(!isTRUE(all.equal(as.numeric(Matrix::rowSums(object$listw)), rep(1,dim(object$listw)[2])))) stop("Impacts not yet implemented
#' for non row-standardized listw")
#'
#' ag <- class(object)[[2]]
#' # print(ag)
#' switch(match.arg(ag, c("lag_gmm", "sarar_gmm")),
#' sarar_gmm = impacts.sarar(object, ...),
#' lag_gmm = impacts.lag(object, ...)
#' )
#'
#' }
#' # TODO in the future implement the VC matrix of the impacts
#' # TODO check two things in the impacts: 1) calculate the impacts only for the coefficients in parameter space 2) fix the Z test
#'
#' #' Generate impacts
#' #'
#' #'
#' #' @param object An object of class sphet
#' #' @param mvn Inference based on MC simulation of mvn samples
#' #' @param n_mvn Number of samples
#' #' @param weg Eigenvalues can be provided by the user
#' #' @param inference should inference be performed
#' #' @param exact should inference be exact
#' #' @param trW either NULL or a trW from spatialreg
#' #' @param m number of traces of w - default is 30
#' #'
#' #'
#' #' @return Estimate of the Average Total, Average Direct, and Average Indirect Effects
#' #'
#' #' @examples
#' #' data(columbus, package="spdep")
#' #' listw <- spdep::nb2listw(col.gal.nb)
#' #' res <- spreg(CRIME~HOVAL + INC, data=columbus , listw= listw,
#' #' het = TRUE, verbose = FALSE, model = "sarar")
#' #' summary(res)
#' #' effects <- impacts(res, n_mvn = 3000)
#' #' summary(effects)
#' impacts.sarar <-function(object, n_mvn = 3000, weg = NULL,
#' inference = FALSE, exact = TRUE, m = 30, trW = NULL, mvn = TRUE){
#'
#' if(object$Durbin) {
#'
#' coefs <- drop(object$coefficients)
#' p2 <- length(coefs)
#' lambda <- coefs[(p2-1)]
#' beta <- coefs[1:(p2-2)]
#' rho <- coefs[p2]
#'
#'
#' dn <- grep("lag_", names(beta))
#' dc <- beta[dn]
#' beta <- beta[-dn]
#'
#' xb <- beta[which(names(beta) %in% stringr::str_remove(names(dc),"lag_") )]
#' xb <- xb[order(names(xb))]
#' xo <- beta[ -which(names(beta) %in% stringr::str_remove(names(dc),"lag_") )]
#' gamma <- dc[which( stringr::str_remove(names(dc),"lag_") %in% names(beta))]
#' gamma <- gamma[order(names(gamma))]
#' don <- dc[-which( stringr::str_remove(names(dc),"lag_") %in% names(beta))]
#'
#' icept <- grep("(Intercept)", names(xo))
#' iicept <- length(icept) > 0
#' Sigma <- object$var
#'
#' if (iicept) {
#' P <- xo[-icept]
#' Sigma <- Sigma[-c(icept,p2),-c(icept,p2)]
#' bnames <- c(names(xo[-icept]), stringr::str_remove(names(dc), "lag_"))
#' }
#' else {
#' P <- xo
#' Sigma <- Sigma[-c(p2),-c(p2)]
#' bnames <-c(names(xo), stringr::str_remove(names(dc), "lag_"))
#' }
#'
#' n <- length(object$residuals)
#'
#'
#' ATE <- c(AVTE_rn_Dur(c(P, lambda), c(0, lambda)),
#' AVTE_rn_Dur(c(xb, lambda), c(gamma, lambda)),
#' AVTE_rn_Dur(c(0, lambda), c(don, lambda)) )
#'
#'
#'
#' if(exact){
#'
#' if(is.null(weg)) weg <- eigen(object$listw)$values
#'
#'
#' ADE <- c(ADRE_rn_Dur(c(P, lambda), weg, n, m, object$listw, c(0, lambda), exact = TRUE),
#' ADRE_rn_Dur(c(xb, lambda), weg, n, m, object$listw, c(gamma, lambda), exact = TRUE),
#' ADRE_rn_Dur(c(0, lambda), weg, n, m, object$listw, c(don, lambda), exact = TRUE) )
#' }
#' else{
#'
#' if(is.null(trW)) trW <- smtrace(object$listw, m = m)
#'
#'
#' ADE <- c(ADRE_rn_Dur(c(P, lambda), weg, n, m = m, object$listw, c(0, lambda), exact = F, trW = trW),
#' ADRE_rn_Dur(c(xb, lambda), weg, n, m = m, object$listw, c(gamma, lambda), exact = F, trW = trW),
#' ADRE_rn_Dur(c(0, lambda), weg, n, m = m, object$listw, c(don, lambda), exact = F, trW = trW) )
#'
#'
#' }
#'
#' AIE <- ATE - ADE
#'
#'
#' if (inference) {
#'
#' mu <- c(P, xb, gamma, don, lambda)
#' mc_splm <- mvtnorm::rmvnorm(n_mvn, mean = mu, sigma = Sigma)
#'
#'
#' if (length(P) == 0 && length(don) == 0) ATE_inf <- rbind(apply(mc_splm[ ,c((1 : length(xb)), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c((length(xb) + 1) : ( ncol(mc_splm)-1), ncol(mc_splm))], 1, AVTE_rn_Dur_sp))
#'
#' else if(length(P) == 0 && length(don) != 0) ATE_inf <- rbind(apply(mc_splm[ ,c( (1 : length(xb)), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply(mc_splm[ , c((length(xb) + 1) : (ncol(mc_splm) - 1), ncol(mc_splm))], 1, AVTE_rn_Dur_sp),
#' apply(mc_splm[ , c(length(xb) + length(gamma) +1) : (ncol(mc_splm) - 1), ncol(mc_splm)], 1, AVTE_rn_Dur_sp))
#'
#' else if(length(P) != 0 && length(don) == 0) ATE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, AVTE_rn_Dur_fp),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( ncol(mc_splm) - 1), ncol(mc_splm))], 1, AVTE_rn_Dur_sp))
#'
#' else ATE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, AVTE_rn_Dur_fp)
#' + apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, AVTE_rn_Dur_sp),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( (length(P) + length(xb) + length(gamma))), ncol(mc_splm))], 1, AVTE_rn_Dur_sp),
#' apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c( (length(P) + length(xb) +length(gamma) +1) : (length(P) + length(xb) +length(gamma) +length(don)), ncol(mc_splm))], 1, AVTE_rn_Dur_sp))
#'
#'
#' if(exact){
#'
#'
#' if (length(P) == 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c((1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE ) +
#' apply( mc_splm[ , c((length(xb) + 1) : ( ncol(mc_splm)-1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#' else if(length(P) == 0 && length(don) != 0) ADE_inf <- rbind(apply(mc_splm[ ,c( (1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply(mc_splm[ , c((length(xb) + 1) : (ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE),
#' apply(mc_splm[ , c(length(xb) + length(gamma) +1) : (ncol(mc_splm) - 1), ncol(mc_splm)], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#' else if(length(P) != 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#' else ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE)
#' + apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( (length(P) + length(xb) + length(gamma))), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE),
#' apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply( mc_splm[ , c( (length(P) + length(xb) +length(gamma) +1) : (length(P) + length(xb) +length(gamma) +length(don)), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#'
#' }
#' else{
#'
#'
#' if (length(P) == 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c((1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW ) +
#' apply( mc_splm[ , c((length(xb) + 1) : ( ncol(mc_splm)-1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#' else if(length(P) == 0 && length(don) != 0) ADE_inf <- rbind(apply(mc_splm[ ,c( (1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply(mc_splm[ , c((length(xb) + 1) : (ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW),
#' apply(mc_splm[ , c(length(xb) + length(gamma) +1) : (ncol(mc_splm) - 1), ncol(mc_splm)], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#' else if(length(P) != 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#' else ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW)
#' + apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( (length(P) + length(xb) + length(gamma))), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW),
#' apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply( mc_splm[ , c( (length(P) + length(xb) +length(gamma) +1) : (length(P) + length(xb) +length(gamma) +length(don)), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#'
#'
#' }
#'
#' AIE_inf <- ATE_inf - ADE_inf
#'
#' res <- list(ATE, ADE, AIE, ATE_inf, ADE_inf, AIE_inf)
#' }
#' else res <- list(ATE, ADE, AIE)
#'
#'
#' }
#'
#' else{
#'
#' coefs <- drop(object$coefficients)
#' p2 <- length(coefs)
#' lambda <- coefs[(p2-1)]
#' beta <- coefs[1:(p2-2)]
#' p <- length(beta)
#' p1 <- p + 1
#' rho <- coefs[p2]
#' icept <- grep("(Intercept)", names(beta))
#' iicept <- length(icept) > 0
#' Sigma <- object$var
#' n <- length(object$residuals)
#'
#' if (iicept) {
#' P <- beta[-icept]
#' Sigma <- Sigma[-c(icept,p2),-c(icept,p2)]
#' bnames <- names(beta[-icept])
#' }
#' else {
#' P <- beta
#' Sigma <- Sigma[-c(p2),-c(p2)]
#' bnames <- names(beta)
#' }
#'
#' ATE <- AVTE_rn(c(P, lambda))
#'
#' if(exact){
#'
#' if(is.null(weg)) weg <- eigen(object$listw)$values
#' ADE <- ADRE_rn(c(P, lambda), weg, n, exact = TRUE)
#' }
#' else{
#'
#' if(is.null(trW)) trW <- smtrace(object$listw, m = m)
#'
#' ADE <- ADRE_rn(c(P, lambda), exact = FALSE, trW = trW, m = m, n = n)
#'
#' }
#' AIE <- ATE - ADE
#'
#' if (inference) {
#'
#' mu <- c(P, lambda)
#' mc_splm <- mvtnorm::rmvnorm(n_mvn, mean = mu, sigma = Sigma)
#'
#'
#' ATE_inf <- apply(mc_splm, 1, AVTE_rn)
#'
#' if(exact) ADE_inf <- apply(mc_splm, 1, ADRE_rn, weg, n, exact = TRUE)
#' else ADE_inf <- apply(mc_splm, 1, ADRE_rn, exact = FALSE, trW = trW, m = m, n = n)
#'
#' AIE_inf <- ATE_inf - ADE_inf
#'
#' res <- list(ATE, ADE, AIE, ATE_inf, ADE_inf, AIE_inf)
#' }
#' else res <- list(ATE, ADE, AIE)
#'
#' }
#'
#' attr(res, "inference") <- inference
#' class(res) <- c("impacts_sphet")
#'
#' invisible(res)
#' }
#'
#' #' Generate impacts
#' #'
#' #'
#' #' @param object An object of class sphet
#' #' @param mvn Inference based on MC simulation of mvn samples
#' #' @param n_mvn Number of samples
#' #' @param weg Eigenvalues can be provided by the user
#' #' @param inference should inference be performed
#' #' @param exact should inference be exact
#' #' @param trW either NULL or a trW from spatialreg
#' #' @param m number of traces of w - default is 30
#' #'
#' #'
#' #' @return Estimate of the Average Total, Average Direct, and Average Indirect Effects
#' #'
#' #' @examples
#' #' data(columbus, package="spdep")
#' #' listw <- spdep::nb2listw(col.gal.nb)
#' #' res <- spreg(CRIME~HOVAL + INC, data=columbus , listw= listw,
#' #' het = TRUE, verbose = FALSE, model = "sarar")
#' #' summary(res)
#' #' effects <- sphet::impacts(res, n_mvn = 3000)
#' #' summary(effects)
#' impacts.lag <-function(object, n_mvn = 3000, weg = NULL,
#' inference = FALSE, exact = TRUE, m = 30, trW = NULL, mvn = TRUE){
#'
#' if(object$Durbin){
#'
#' coefs <- drop(object$coefficients)
#' p2 <- length(coefs)
#' lambda <- coefs[p2]
#' beta <- coefs[1:(p2-1)]
#' p <- length(beta)
#' p1 <- p + 1
#'
#'
#' dn <- grep("lag_", names(beta))
#' dc <- beta[dn]
#' beta <- beta[-dn]
#'
#' xb <- beta[which(names(beta) %in% stringr::str_remove(names(dc),"lag_") )]
#' xb <- xb[order(names(xb))]
#' xo <- beta[ -which(names(beta) %in% stringr::str_remove(names(dc),"lag_") )]
#' gamma <- dc[which( stringr::str_remove(names(dc),"lag_") %in% names(beta))]
#' gamma <- gamma[order(names(gamma))]
#' don <- dc[-which( stringr::str_remove(names(dc),"lag_") %in% names(beta))]
#'
#' icept <- grep("(Intercept)", names(xo))
#' iicept <- length(icept) > 0
#' Sigma <- as.matrix(object$var)
#' #print(Sigma)
#'
#' if (iicept) {
#' P <- xo[-icept]
#' Sigma <- Sigma[-c(icept),-c(icept)]
#' bnames <- c(names(xo[-icept]), stringr::str_remove(names(dc), "lag_"), names(don))
#' }
#' else {
#' P <- xo
#' Sigma <- Sigma
#' bnames <-c(names(xo), stringr::str_remove(names(dc), "lag_"), names(don))
#' }
#'
#' n <- length(object$residuals)
#'
#'
#' ATE <- c(AVTE_rn_Dur(c(P, lambda), c(0, lambda)),
#' AVTE_rn_Dur(c(xb, lambda), c(gamma, lambda)),
#' AVTE_rn_Dur(c(0, lambda), c(don, lambda)) )
#'
#'
#'
#' if(exact){
#'
#' if(is.null(weg)) weg <- eigen(object$listw)$values
#'
#'
#' ADE <- c(ADRE_rn_Dur(c(P, lambda), weg, n, m, object$listw, c(0, lambda), exact = TRUE),
#' ADRE_rn_Dur(c(xb, lambda), weg, n, m, object$listw, c(gamma, lambda), exact = TRUE),
#' ADRE_rn_Dur(c(0, lambda), weg, n, m, object$listw, c(don, lambda), exact = TRUE) )
#' }
#' else{
#'
#' if(is.null(trW)) trW <- smtrace(object$listw, m = m)
#'
#'
#' ADE <- c(ADRE_rn_Dur(c(P, lambda), weg, n, m = m, object$listw, c(0, lambda), exact = F, trW = trW),
#' ADRE_rn_Dur(c(xb, lambda), weg, n, m = m, object$listw, c(gamma, lambda), exact = F, trW = trW),
#' ADRE_rn_Dur(c(0, lambda), weg, n, m = m, object$listw, c(don, lambda), exact = F, trW = trW) )
#'
#' }
#'
#' AIE <- ATE - ADE
#'
#'
#' if (inference) {
#'
#' mu <- c(P, xb, gamma, don, lambda)
#' mc_splm <- mvtnorm::rmvnorm(n_mvn, mean = mu, sigma = Sigma)
#'
#'
#' if (length(P) == 0 && length(don) == 0) ATE_inf <- rbind(apply(mc_splm[ ,c((1 : length(xb)), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c((length(xb) + 1) : ( ncol(mc_splm)-1), ncol(mc_splm))], 1, AVTE_rn_Dur_sp))
#'
#' else if(length(P) == 0 && length(don) != 0) ATE_inf <- rbind(apply(mc_splm[ ,c( (1 : length(xb)), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply(mc_splm[ , c((length(xb) + 1) : (ncol(mc_splm) - 1), ncol(mc_splm))], 1, AVTE_rn_Dur_sp),
#' apply(mc_splm[ , c(length(xb) + length(gamma) +1) : (ncol(mc_splm) - 1), ncol(mc_splm)], 1, AVTE_rn_Dur_sp))
#'
#' else if(length(P) != 0 && length(don) == 0) ATE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, AVTE_rn_Dur_fp),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( ncol(mc_splm) - 1), ncol(mc_splm))], 1, AVTE_rn_Dur_sp))
#'
#' else ATE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, AVTE_rn_Dur_fp)
#' + apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, AVTE_rn_Dur_sp),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( (length(P) + length(xb) + length(gamma))), ncol(mc_splm))], 1, AVTE_rn_Dur_sp),
#' apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, AVTE_rn_Dur_fp) +
#' apply( mc_splm[ , c( (length(P) + length(xb) +length(gamma) +1) : (length(P) + length(xb) +length(gamma) +length(don)), ncol(mc_splm))], 1, AVTE_rn_Dur_sp))
#'
#'
#' # print(head(ATE_inf)[,1:5])
#'
#' if(exact){
#'
#'
#' if (length(P) == 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c((1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE ) +
#' apply( mc_splm[ , c((length(xb) + 1) : ( ncol(mc_splm)-1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#' else if(length(P) == 0 && length(don) != 0) ADE_inf <- rbind(apply(mc_splm[ ,c( (1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply(mc_splm[ , c((length(xb) + 1) : (ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE),
#' apply(mc_splm[ , c(length(xb) + length(gamma) +1) : (ncol(mc_splm) - 1), ncol(mc_splm)], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#' else if(length(P) != 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#' else ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE)
#' + apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( (length(P) + length(xb) + length(gamma))), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE),
#' apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= TRUE) +
#' apply( mc_splm[ , c( (length(P) + length(xb) +length(gamma) +1) : (length(P) + length(xb) +length(gamma) +length(don)), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= TRUE))
#'
#'
#' }
#' else{
#'
#'
#' if (length(P) == 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c((1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW ) +
#' apply( mc_splm[ , c((length(xb) + 1) : ( ncol(mc_splm)-1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#' else if(length(P) == 0 && length(don) != 0) ADE_inf <- rbind(apply(mc_splm[ ,c( (1 : length(xb)), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply(mc_splm[ , c((length(xb) + 1) : (ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW),
#' apply(mc_splm[ , c(length(xb) + length(gamma) +1) : (ncol(mc_splm) - 1), ncol(mc_splm)], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#' else if(length(P) != 0 && length(don) == 0) ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( ncol(mc_splm) - 1), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#' else ADE_inf <- rbind(apply(mc_splm[ ,c(1:length(P), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW)
#' + apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW),
#' apply( mc_splm[ ,c( ((length(P) + 1) : (length(P) + length(xb))), ncol(mc_splm))], 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply( mc_splm[ , c((length(P) + length(xb) + 1) : ( (length(P) + length(xb) + length(gamma))), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW),
#' apply(cbind(0, mc_splm[ ,c(ncol(mc_splm))]), 1, ADRE_rn_Dur_fp, weg, n, m, object$listw, exact= F, trW) +
#' apply( mc_splm[ , c( (length(P) + length(xb) +length(gamma) +1) : (length(P) + length(xb) +length(gamma) +length(don)), ncol(mc_splm))], 1, ADRE_rn_Dur_sp, weg, n, m, object$listw, exact= F, trW))
#'
#'
#'
#' }
#'
#' AIE_inf <- ATE_inf - ADE_inf
#'
#' res <- list(ATE, ADE, AIE, ATE_inf, ADE_inf, AIE_inf)
#' }
#' else res <- list(ATE, ADE, AIE)
#'
#'
#'
#'
#'
#' }
#'
#' else{
#'
#' coefs <- drop(object$coefficients)
#' p2 <- length(coefs)
#' lambda <- coefs[p2]
#' beta <- coefs[1:(p2-1)]
#' p <- length(beta)
#' p1 <- p + 1
#' icept <- grep("(Intercept)", names(beta))
#' iicept <- length(icept) > 0
#' Sigma <- as.matrix(object$var)
#'
#' if (iicept) {
#' P <- beta[-icept]
#' Sigma <- Sigma[-c(icept),-c(icept)]
#' bnames <- names(beta[-icept])
#' }
#' else {
#' P <- beta
#' Sigma <- Sigma
#' bnames <- names(beta)
#' }
#'
#' n <- length(object$residuals)
#'
#' if(exact){
#'
#' if(is.null(weg)) weg <- eigen(object$listw)$values
#'
#'
#' ATE <- AVTE_rn(c(P, lambda))
#' ADE <- ADRE_rn(c(P, lambda), weg, n, exact = TRUE)
#' AIE <- ATE - ADE
#' }
#' else{
#'
#' if(is.null(trW)) trW <- smtrace(object$listw, m = m)
#'
#'
#' ATE <- AVTE_rn(c(P, lambda))
#' ADE <- ADRE_rn(c(P, lambda), exact = FALSE, trW = trW, m = m, n = n)
#' AIE <- ATE - ADE
#'
#' }
#'
#' if (inference) {
#'
#' mu <- c(P, lambda)
#' mc_splm <- mvtnorm::rmvnorm(n_mvn, mean = mu, sigma = Sigma)
#'
#' if(exact){
#'
#' ATE_inf <- apply(mc_splm, 1, AVTE_rn)
#' ADE_inf <- apply(mc_splm, 1, ADRE_rn, weg, n, exact = TRUE)
#' AIE_inf <- ATE_inf - ADE_inf
#'
#' }
#' else{
#'
#' ATE_inf <- apply(mc_splm, 1, AVTE_rn)
#' ADE_inf <- apply(mc_splm, 1, ADRE_rn, exact = FALSE, trW = trW, m = m, n = n)
#' AIE_inf <- ATE_inf - ADE_inf
#'
#' }
#' res <- list(ATE, ADE, AIE, ATE_inf, ADE_inf, AIE_inf)
#' }
#' else res <- list(ATE, ADE, AIE)
#'
#' }
#' attr(res, "inference") <- inference
#' class(res) <- c("impacts_sphet")
#'
#' invisible(res)
#' }
#'
#' #' Summary for spreg impacts
#' #'
#' #'
#' #' @param object An object of class impacts.sphet
#' #' @param ... Additional arguments that can be passed to the function
#' #' @return Summary of the Average Total, Average Direct, and Average Indirect Effects
#' #' @method summary impacts_sphet
#' #' @examples
#' #' data(columbus, package = "spdep")
#' #' listw <- spdep::nb2listw(col.gal.nb)
#' #' res <- spreg(CRIME~HOVAL + INC, data=columbus , listw= listw,
#' #' het = TRUE, verbose = FALSE, model = "sarar")
#' #' summary(res)
#' #' effects <- impacts(res, n_mvn = 3000)
#' #' summary(effects)
#' summary.impacts_sphet <- function(object, ...){
#'
#' cat("\n ---------------------- \n")
#' cat("\n ---------------------- \n")
#' cat("\n Impacts estimates:\n")
#' cat("\n ---------------------- \n")
#' cat("\n ---------------------- \n")
#'
#' # print(cbind(ATE,apply(ATE_inf, 2, sd), (ATE - apply(ATE_inf, 2, mean) )/apply(ATE_inf, 2, sd)))
#' #print(cbind(obj[[1]], sd(obj[[4]]), obj[[1]]/sd(obj[[4]]) ))
#' eff <- cbind(object[[1]], object[[2]], object[[3]])
#' colnames(eff) <- c("ATE", "ADE", "AIE")
#' print(eff)
#'
#' if(attributes(object)$inference){
#' cat("\n ---------------------- \n")
#' cat("\n Inference for ATE:\n")
#' cat("\n ---------------------- \n")
#'
#' mean_ate <- apply(object[[4]], 1, mean)
#' # print(head(mean_ate))
#' sd_ate <- apply(object[[4]], 1, sd)
#' z_ate <- (object[[1]])/sd_ate
#' p_ate <- 2*pnorm(abs(z_ate), lower.tail = F)
#' total <- cbind(object[[1]], sd_ate, z_ate, p_ate)
#' colnames(total) <- c("ATE", "sd", "z-stat","p-val")
#' print(total)
#' cat("\n Summary stats for the simulated ATE samples:\n")
#' a <- matrix(nrow = nrow(total), ncol = 6)
#' for (i in 1:nrow(total)) a[i,] <- c(quantile(object[[4]][i,], c(0.025, 0.25, 0.5, 0.75, 0.975)), mean(object[[4]][i,]))
#' colnames(a) <- c("0.025", "Q1", "Median", "Q3", "0.975","Mean")
#' rownames(a) <- rownames(eff)
#' print(a)
#'
#' cat("\n ---------------------- \n")
#' cat("\n Inference for ADE:\n")
#' cat("\n ---------------------- \n")
#'
#' mean_ade <- apply(object[[5]], 1, mean)
#' # print(head(mean_ate))
#' sd_ade <- apply(object[[5]], 1, sd)
#' z_ade <- (object[[2]])/sd_ade
#' p_ade <- 2*pnorm(abs(z_ade), lower.tail = F)
#' direct <- cbind(object[[2]], sd_ade, z_ade, p_ade)
#' colnames(direct) <- c("ADE", "sd", "z-stat","p-val")
#' print(direct)
#' cat("\n Summary stats for the simulated ADE samples:\n")
#'
#' for (i in 1:nrow(total)) a[i,] <- c(quantile(object[[5]][i,], c(0.025, 0.25, 0.5, 0.75, 0.975)), mean(object[[5]][i,]))
#' colnames(a) <- c("0.025", "Q1", "Median", "Q3", "0.975","Mean")
#' rownames(a) <- rownames(eff)
#' print(a)
#'
#' cat("\n ---------------------- \n")
#' cat("\n Inference for AIE:\n")
#' cat("\n ---------------------- \n")
#'
#' mean_aie <- apply(object[[6]], 1, mean)
#' sd_aie <- apply(object[[6]], 1, sd)
#' z_aie <- (object[[3]])/sd_aie
#' p_aie <- 2*pnorm(abs(z_aie), lower.tail = F)
#' indirect <- cbind(object[[3]], sd_aie, z_aie, p_aie)
#' dim(indirect)
#' colnames(indirect) <- c("AIE", "sd", "z-stat","p-val")
#' print(indirect)
#' cat("\n Summary stats for the simulated AIE samples:\n")
#'
#' for (i in 1:nrow(total)) a[i,] <- c(quantile(object[[6]][i,], c(0.025, 0.25, 0.5, 0.75, 0.975)), mean(object[[6]][i,]))
#' colnames(a) <- c("0.025", "Q1", "Median", "Q3", "0.975","Mean")
#' rownames(a) <- rownames(eff)
#' print(a)
#' }
#'
#' }
#'
#'
#' AVTE_rn <- function(x){
#' x[-length(x)]/(1-x[length(x)])
#' }
#' AVTE_rn_Dur <- function(x,y){
#' x[-length(x)]/(1-x[length(x)]) + y[-length(y)]/(1-y[length(y)])
#' }
#' AVTE_rn_Dur_fp <- function(x){
#' x[-length(x)]/(1-x[length(x)])
#' }
#' AVTE_rn_Dur_sp <- function(y){
#' y[-length(y)]/(1-y[length(y)])
#' }
#'
#'
#' ADRE_rn <- function(x, egv, n, m, exact, trW){
#' if (exact) Re(x[-length(x)] *(1/n)*sum(1/(1-x[length(x)]*egv)))
#' else x[-length(x)] *(1/n) *(sum(as.numeric(sapply(x[length(x)], function(s) s^seq(1,m)), m )/n *trW) + n)
#' }
#' ADRE_rn_Dur <- function(x, egv, n, m, listw, y, exact, trW){
#' if(exact) Re(x[-length(x)] *(1/n)*sum(1/(1-x[length(x)]*egv))) +
#' (1/n)*y[-length(y)] *sum(diag(solve(Diagonal(n)- y[length(y)]* listw) %*% listw))
#' else x[-length(x)] *(1/n) *(sum(as.numeric(sapply(x[length(x)], function(s) s^seq(1,m)), m )/n *trW) + n) +
#' y[-length(y)] *(1/n) * (sum(as.numeric(sapply(y[length(y)], function(s) s^seq(1,(m-1))), m )/n *trW[-1]) )
#' }
#' ADRE_rn_Dur_fp <- function(x, egv, n, m, listw, exact, trW){
#' if(exact) Re(x[-length(x)] *(1/n)*sum(1/(1-x[length(x)]*egv)))
#' else x[-length(x)] *(1/n) *(sum(as.numeric(sapply(x[length(x)], function(s) s^seq(1,m)), m )/n *trW) + n)
#'
#' }
#' ADRE_rn_Dur_sp <- function(y, egv, n, m, listw, exact, trW){
#' if(exact) (1/n)*y[-length(y)] *sum(diag(solve(Diagonal(n)- y[length(y)]* listw) %*% listw))
#' else y[-length(y)] *(1/n) * (sum(as.numeric(sapply(y[length(y)], function(s) s^seq(1,(m-1))), m )/n *trW[-1]) )
#' }
#' smtrace <- function(listw, m){
#' listwp <- listw
#' tr <- numeric(m)
#' for (i in 1:m) {
#' tr[i] <- sum(diag(listwp))
#' listwp <- listw %*% listwp
#' }
#' return(tr)
#' }
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