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Stochastic Frontier Analysis Routines

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R/sfacross-exponential.R

R/sfacross-exponential.R
In sfaR: Stochastic Frontier Analysis Routines

Defines functions cmargexponorm_Vu cmargexponorm_Eu cexponormeff exponormAlgOpt chessexponormlike cgradexponormlike cstexponorm cexponormlike 

################################################################################
#                                                                              #
# R internal functions for the sfaR package                                    #
#                                                                              #
################################################################################

#------------------------------------------------------------------------------#
# Data: Cross sectional data & Pooled data                                     #
# Model: Standard Stochastic Frontier Analysis                                 #
# Convolution: exponential - normal                                            #
#------------------------------------------------------------------------------#

# Log-likelihood ----------
#' log-likelihood for exponential-normal distribution
#' @param parm all parameters to be estimated
#' @param nXvar number of main variables (inputs + env. var)
#' @param nuZUvar number of Zu variables
#' @param nvZVvar number of Zv variables
#' @param uHvar matrix of Zu variables
#' @param vHvar matrix of Zv variables
#' @param Yvar vector of dependent variable
#' @param Xvar matrix of main variables
#' @param wHvar vector of weights (weighted likelihood)
#' @param S integer for cost/prod estimation
#' @noRd
cexponormlike <- function(parm, nXvar, nuZUvar, nvZVvar, uHvar,
  vHvar, Yvar, Xvar, wHvar, S) {
  beta <- parm[1:(nXvar)]
  delta <- parm[(nXvar + 1):(nXvar + nuZUvar)]
  phi <- parm[(nXvar + nuZUvar + 1):(nXvar + nuZUvar + nvZVvar)]
  Wu <- as.numeric(crossprod(matrix(delta), t(uHvar)))
  Wv <- as.numeric(crossprod(matrix(phi), t(vHvar)))
  epsilon <- Yvar - as.numeric(crossprod(matrix(beta), t(Xvar)))
  ll <- (-Wu/2 + log(pnorm(-S * epsilon/sqrt(exp(Wv)) - sqrt(exp(Wv)/exp(Wu)))) +
    S * epsilon/sqrt(exp(Wu)) + exp(Wv)/(2 * exp(Wu)))
  return(ll * wHvar)
}

# starting value for the log-likelihood ----------
#' starting values for exponential-normal distribution
#' @param olsObj OLS object
#' @param epsiRes residuals from OLS
#' @param S integer for cost/prod estimation
#' @param nuZUvar number of Zu variables
#' @param nvZVvar number of Zv variables
#' @param uHvar matrix of Zu variables
#' @param vHvar matrix of Zv variables
#' @noRd
cstexponorm <- function(olsObj, epsiRes, S, nuZUvar, uHvar, nvZVvar,
  vHvar) {
  m2 <- sum(epsiRes^2)/length(epsiRes)
  m3 <- sum(epsiRes^3)/length(epsiRes)
  if (S * m3 > 0) {
    varu <- (abs((-S * m3/2)))^(2/3)
  } else {
    varu <- (-S * m3/2)^(2/3)
  }
  if (m2 < varu) {
    varv <- abs(m2 - varu)
  } else {
    varv <- m2 - varu
  }
  dep_u <- 1/2 * log((epsiRes^2 - varv)^2)
  dep_v <- 1/2 * log((epsiRes^2 - varu)^2)
  reg_hetu <- if (nuZUvar == 1) {
    lm(log(varu) ~ 1)
  } else {
    lm(dep_u ~ ., data = as.data.frame(uHvar[, 2:nuZUvar,
      drop = FALSE]))
  }
  if (any(is.na(reg_hetu$coefficients))) {
    stop("At least one of the OLS coefficients of 'uhet' is NA: ",
      paste(colnames(uHvar)[is.na(reg_hetu$coefficients)],
        collapse = ", "), ". This may be due to a singular matrix due to potential perfect multicollinearity",
      call. = FALSE)
  }
  reg_hetv <- if (nvZVvar == 1) {
    lm(log(varv) ~ 1)
  } else {
    lm(dep_v ~ ., data = as.data.frame(vHvar[, 2:nvZVvar,
      drop = FALSE]))
  }
  if (any(is.na(reg_hetv$coefficients))) {
    stop("at least one of the OLS coefficients of 'vhet' is NA: ",
      paste(colnames(vHvar)[is.na(reg_hetv$coefficients)],
        collapse = ", "), ". This may be due to a singular matrix due to potential perfect multicollinearity",
      call. = FALSE)
  }
  delta <- coefficients(reg_hetu)
  names(delta) <- paste0("Zu_", colnames(uHvar))
  phi <- coefficients(reg_hetv)
  names(phi) <- paste0("Zv_", colnames(vHvar))
  if (names(olsObj)[1] == "(Intercept)") {
    beta <- c(olsObj[1] + S * sqrt(varu), olsObj[-1])
  } else {
    beta <- olsObj
  }
  return(c(beta, delta, phi))
}

# Gradient of the likelihood function ----------
#' gradient for exponential-normal distribution
#' @param parm all parameters to be estimated
#' @param nXvar number of main variables (inputs + env. var)
#' @param nuZUvar number of Zu variables
#' @param nvZVvar number of Zv variables
#' @param uHvar matrix of Zu variables
#' @param vHvar matrix of Zv variables
#' @param Yvar vector of dependent variable
#' @param Xvar matrix of main variables
#' @param wHvar vector of weights (weighted likelihood)
#' @param S integer for cost/prod estimation
#' @noRd
cgradexponormlike <- function(parm, nXvar, nuZUvar, nvZVvar,
  uHvar, vHvar, Yvar, Xvar, wHvar, S) {
  beta <- parm[1:(nXvar)]
  delta <- parm[(nXvar + 1):(nXvar + nuZUvar)]
  phi <- parm[(nXvar + nuZUvar + 1):(nXvar + nuZUvar + nvZVvar)]
  Wu <- as.numeric(crossprod(matrix(delta), t(uHvar)))
  Wv <- as.numeric(crossprod(matrix(phi), t(vHvar)))
  epsilon <- Yvar - as.numeric(crossprod(matrix(beta), t(Xvar)))
  mustar <- -(S * (epsilon)/exp(Wv/2) + sqrt(exp(Wv)/exp(Wu)))
  pmustar <- pnorm(mustar)
  dmustar <- dnorm(mustar)
  sigx <- exp(Wu) * pmustar * sqrt(exp(Wv)/exp(Wu))
  sigx2 <- dmustar/(exp(Wv/2) * pmustar)
  pdmustar <- dmustar/pmustar
  su_sv <- sqrt(exp(Wv)/exp(Wu))
  sv_epsi <- S * (epsilon)/exp(Wv/2)
  su_epsi <- S * (epsilon)/exp(Wu/2)
  sigx3 <- 0.5 * (exp(Wv)/(exp(Wu) * su_sv)) - 0.5 * (sv_epsi)
  gradll <- cbind(sweep(Xvar, MARGIN = 1, STATS = S * (sigx2 -
    1/exp(Wu/2)), FUN = "*"), sweep(uHvar, MARGIN = 1, STATS = ((0.5 *
    (dmustar/(sigx)) - 1/(2 * exp(Wu))) * exp(Wv) - (0.5 +
    0.5 * (su_epsi))), FUN = "*"), sweep(vHvar, MARGIN = 1,
    STATS = (exp(Wv)/(2 * exp(Wu)) - (sigx3) * pdmustar),
    FUN = "*"))
  return(sweep(gradll, MARGIN = 1, STATS = wHvar, FUN = "*"))
}

# Hessian of the likelihood function ----------
#' hessian for exponential-normal distribution
#' @param parm all parameters to be estimated
#' @param nXvar number of main variables (inputs + env. var)
#' @param nuZUvar number of Zu variables
#' @param nvZVvar number of Zv variables
#' @param uHvar matrix of Zu variables
#' @param vHvar matrix of Zv variables
#' @param Yvar vector of dependent variable
#' @param Xvar matrix of main variables
#' @param wHvar vector of weights (weighted likelihood)
#' @param S integer for cost/prod estimation
#' @noRd
chessexponormlike <- function(parm, nXvar, nuZUvar, nvZVvar,
  uHvar, vHvar, Yvar, Xvar, wHvar, S) {
  beta <- parm[1:(nXvar)]
  delta <- parm[(nXvar + 1):(nXvar + nuZUvar)]
  phi <- parm[(nXvar + nuZUvar + 1):(nXvar + nuZUvar + nvZVvar)]
  Wu <- as.numeric(crossprod(matrix(delta), t(uHvar)))
  Wv <- as.numeric(crossprod(matrix(phi), t(vHvar)))
  epsilon <- Yvar - as.numeric(crossprod(matrix(beta), t(Xvar)))
  mustar <- -(S * (epsilon)/exp(Wv/2) + sqrt(exp(Wv)/exp(Wu)))
  pmustar <- pnorm(mustar)
  dmustar <- dnorm(mustar)
  sigx <- exp(Wu) * pmustar * sqrt(exp(Wv)/exp(Wu))
  sigx2 <- dmustar/(exp(Wv/2) * pmustar)
  pdmustar <- dmustar/pmustar
  su_sv <- sqrt(exp(Wv)/exp(Wu))
  sv_epsi <- S * (epsilon)/exp(Wv/2)
  su_epsi <- S * (epsilon)/exp(Wu/2)
  sigx3 <- 0.5 * (exp(Wv)/(exp(Wu) * su_sv)) - 0.5 * (sv_epsi)
  hessll <- matrix(nrow = nXvar + nuZUvar + nvZVvar, ncol = nXvar +
    nuZUvar + nvZVvar)
  hessll[1:nXvar, 1:nXvar] <- crossprod(sweep(Xvar, MARGIN = 1,
    STATS = S^2 * wHvar * ((sv_epsi + su_sv)/(exp(Wv/2)^2 *
      pmustar) - sigx2/(exp(Wv/2) * pmustar)) * dmustar,
    FUN = "*"), Xvar)
  hessll[1:nXvar, (nXvar + 1):(nXvar + nuZUvar)] <- crossprod(sweep(Xvar,
    MARGIN = 1, STATS = S * wHvar * (0.5 * (((sv_epsi + su_sv)/(sigx) -
      dmustar * exp(Wu) * su_sv/(sigx)^2) * dmustar * exp(Wv/2)) +
      0.5/exp(Wu/2)), FUN = "*"), uHvar)
  hessll[1:nXvar, (nXvar + nuZUvar + 1):(nXvar + nuZUvar +
    nvZVvar)] <- crossprod(sweep(Xvar, MARGIN = 1, STATS = -wHvar *
    (S * ((sigx3) * (sv_epsi + su_sv - pdmustar) + 0.5) *
      sigx2), FUN = "*"), vHvar)
  hessll[(nXvar + 1):(nXvar + nuZUvar), (nXvar + 1):(nXvar +
    nuZUvar)] <- crossprod(sweep(uHvar, MARGIN = 1, STATS = wHvar *
    ((0.5 * ((0.5 * ((sv_epsi + su_sv)/(exp(Wu) * pmustar)) -
      ((0.5 * (dmustar * exp(Wv)/su_sv) + exp(Wu) * pmustar) *
        su_sv - 0.5 * (exp(Wv) * pmustar/su_sv))/(sigx)^2) *
      dmustar) + (1/(2 * exp(Wu)))) * exp(Wv) + 0.25 *
      (su_epsi)), FUN = "*"), uHvar)
  hessll[(nXvar + nuZUvar + 1):(nXvar + nuZUvar + nvZVvar),
    (nXvar + nuZUvar + 1):(nXvar + nuZUvar + nvZVvar)] <- crossprod(sweep(vHvar,
    MARGIN = 1, STATS = wHvar * (exp(Wv)/(2 * exp(Wu)) -
      ((sigx3)^2 * (pdmustar + mustar) + 0.25 * (sv_epsi) +
        0.5 * ((1/exp(Wu) - 0.5 * (exp(Wv)/(exp(Wu) *
          su_sv)^2)) * exp(Wv)/su_sv)) * pdmustar), FUN = "*"),
    vHvar)
  hessll[(nXvar + 1):(nXvar + nuZUvar), (nXvar + nuZUvar +
    1):(nXvar + nuZUvar + nvZVvar)] <- crossprod(sweep(uHvar,
    MARGIN = 1, STATS = -wHvar * ((((sigx3) * (0.5 * (sv_epsi +
      su_sv) - 0.5 * (pdmustar))/(exp(Wu) * su_sv) - 0.5 *
      ((exp(Wu) * su_sv - 0.5 * (exp(Wv)/su_sv))/(exp(Wu) *
        su_sv)^2)) * pdmustar + 1/(2 * exp(Wu))) * exp(Wv)),
    FUN = "*"), vHvar)
  hessll[lower.tri(hessll)] <- t(hessll)[lower.tri(hessll)]
  # hessll <- (hessll + (hessll))/2
  return(hessll)
}

# Optimization using different algorithms ----------
#' optimizations solve for exponential-normal distribution
#' @param start starting value for optimization
#' @param olsParam OLS coefficients
#' @param dataTable dataframe contains id of observations
#' @param nXvar number of main variables (inputs + env. var)
#' @param nuZUvar number of Zu variables
#' @param nvZVvar number of Zv variables
#' @param uHvar matrix of Zu variables
#' @param vHvar matrix of Zv variables
#' @param Yvar vector of dependent variable
#' @param Xvar matrix of main variables
#' @param wHvar vector of weights (weighted likelihood)
#' @param S integer for cost/prod estimation
#' @param method algorithm for solver
#' @param printInfo logical print info during optimization
#' @param itermax maximum iteration
#' @param stepmax stepmax for ucminf
#' @param tol parameter tolerance
#' @param gradtol gradient tolerance
#' @param hessianType how hessian is computed
#' @param qac qac option for maxLik
#' @noRd
exponormAlgOpt <- function(start, olsParam, dataTable, S, nXvar,
  uHvar, nuZUvar, vHvar, nvZVvar, Yvar, Xvar, wHvar, method,
  printInfo, itermax, stepmax, tol, gradtol, hessianType, qac) {
  startVal <- if (!is.null(start))
    start else cstexponorm(olsObj = olsParam, epsiRes = dataTable[["olsResiduals"]],
    S = S, uHvar = uHvar, nuZUvar = nuZUvar, vHvar = vHvar,
    nvZVvar = nvZVvar)
  startLoglik <- sum(cexponormlike(startVal, nXvar = nXvar,
    nuZUvar = nuZUvar, nvZVvar = nvZVvar, uHvar = uHvar,
    vHvar = vHvar, Yvar = Yvar, Xvar = Xvar, wHvar = wHvar,
    S = S))
  if (method %in% c("bfgs", "bhhh", "nr", "nm", "cg", "sann")) {
    maxRoutine <- switch(method, bfgs = function(...) maxLik::maxBFGS(...),
      bhhh = function(...) maxLik::maxBHHH(...), nr = function(...) maxLik::maxNR(...),
      nm = function(...) maxLik::maxNM(...), cg = function(...) maxLik::maxCG(...),
      sann = function(...) maxLik::maxSANN(...))
    method <- "maxLikAlgo"
  }
  mleObj <- switch(method, ucminf = ucminf::ucminf(par = startVal,
    fn = function(parm) -sum(cexponormlike(parm, nXvar = nXvar,
      nuZUvar = nuZUvar, nvZVvar = nvZVvar, uHvar = uHvar,
      vHvar = vHvar, Yvar = Yvar, Xvar = Xvar, wHvar = wHvar,
      S = S)), gr = function(parm) -colSums(cgradexponormlike(parm,
      nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
      uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
      wHvar = wHvar, S = S)), hessian = 0, control = list(trace = if (printInfo) 1 else 0,
      maxeval = itermax, stepmax = stepmax, xtol = tol,
      grtol = gradtol)), maxLikAlgo = maxRoutine(fn = cexponormlike,
    grad = cgradexponormlike, hess = chessexponormlike, start = startVal,
    finalHessian = if (hessianType == 2) "bhhh" else TRUE,
    control = list(printLevel = if (printInfo) 2 else 0,
      iterlim = itermax, reltol = tol, tol = tol, qac = qac),
    nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
    uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
    wHvar = wHvar, S = S), sr1 = trustOptim::trust.optim(x = startVal,
    fn = function(parm) -sum(cexponormlike(parm, nXvar = nXvar,
      nuZUvar = nuZUvar, nvZVvar = nvZVvar, uHvar = uHvar,
      vHvar = vHvar, Yvar = Yvar, Xvar = Xvar, wHvar = wHvar,
      S = S)), gr = function(parm) -colSums(cgradexponormlike(parm,
      nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
      uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
      wHvar = wHvar, S = S)), method = "SR1", control = list(maxit = itermax,
      cgtol = gradtol, stop.trust.radius = tol, prec = tol,
      report.level = if (printInfo) 2 else 0, report.precision = 1L)),
    sparse = trustOptim::trust.optim(x = startVal, fn = function(parm) -sum(cexponormlike(parm,
      nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
      uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
      wHvar = wHvar, S = S)), gr = function(parm) -colSums(cgradexponormlike(parm,
      nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
      uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
      wHvar = wHvar, S = S)), hs = function(parm) as(-chessexponormlike(parm,
      nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
      uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
      wHvar = wHvar, S = S), "dgCMatrix"), method = "Sparse",
      control = list(maxit = itermax, cgtol = gradtol,
        stop.trust.radius = tol, prec = tol, report.level = if (printInfo) 2 else 0,
        report.precision = 1L, preconditioner = 1L)),
    mla = marqLevAlg::mla(b = startVal, fn = function(parm) -sum(cexponormlike(parm,
      nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
      uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
      wHvar = wHvar, S = S)), gr = function(parm) -colSums(cgradexponormlike(parm,
      nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
      uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
      wHvar = wHvar, S = S)), hess = function(parm) -chessexponormlike(parm,
      nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
      uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
      wHvar = wHvar, S = S), print.info = printInfo, maxiter = itermax,
      epsa = gradtol, epsb = gradtol), nlminb = nlminb(start = startVal,
      objective = function(parm) -sum(cexponormlike(parm,
        nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
        uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
        wHvar = wHvar, S = S)), gradient = function(parm) -colSums(cgradexponormlike(parm,
        nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
        uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
        wHvar = wHvar, S = S)), hessian = function(parm) -chessexponormlike(parm,
        nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
        uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
        wHvar = wHvar, S = S), control = list(iter.max = itermax,
        trace = if (printInfo) 1 else 0, eval.max = itermax,
        rel.tol = tol, x.tol = tol)))
  if (method %in% c("ucminf", "nlminb")) {
    mleObj$gradient <- colSums(cgradexponormlike(mleObj$par,
      nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
      uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
      wHvar = wHvar, S = S))
  }
  mlParam <- if (method %in% c("ucminf", "nlminb")) {
    mleObj$par
  } else {
    if (method == "maxLikAlgo") {
      mleObj$estimate
    } else {
      if (method %in% c("sr1", "sparse")) {
        mleObj$solution
      } else {
        if (method == "mla") {
          mleObj$b
        }
      }
    }
  }
  if (hessianType != 2) {
    if (method %in% c("ucminf", "nlminb"))
      mleObj$hessian <- chessexponormlike(parm = mleObj$par,
        nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
        uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
        wHvar = wHvar, S = S)
    if (method == "sr1")
      mleObj$hessian <- chessexponormlike(parm = mleObj$solution,
        nXvar = nXvar, nuZUvar = nuZUvar, nvZVvar = nvZVvar,
        uHvar = uHvar, vHvar = vHvar, Yvar = Yvar, Xvar = Xvar,
        wHvar = wHvar, S = S)
  }
  mleObj$logL_OBS <- cexponormlike(parm = mlParam, nXvar = nXvar,
    nuZUvar = nuZUvar, nvZVvar = nvZVvar, uHvar = uHvar,
    vHvar = vHvar, Yvar = Yvar, Xvar = Xvar, wHvar = wHvar,
    S = S)
  mleObj$gradL_OBS <- cgradexponormlike(parm = mlParam, nXvar = nXvar,
    nuZUvar = nuZUvar, nvZVvar = nvZVvar, uHvar = uHvar,
    vHvar = vHvar, Yvar = Yvar, Xvar = Xvar, wHvar = wHvar,
    S = S)
  return(list(startVal = startVal, startLoglik = startLoglik,
    mleObj = mleObj, mlParam = mlParam))
}

# Conditional efficiencies estimation ----------
#' efficiencies for exponential-normal distribution
#' @param object object of class sfacross
#' @param level level for confidence interval
#' @noRd
cexponormeff <- function(object, level) {
  beta <- object$mlParam[1:(object$nXvar)]
  delta <- object$mlParam[(object$nXvar + 1):(object$nXvar +
    object$nuZUvar)]
  phi <- object$mlParam[(object$nXvar + object$nuZUvar + 1):(object$nXvar +
    object$nuZUvar + object$nvZVvar)]
  Xvar <- model.matrix(object$formula, data = object$dataTable,
    rhs = 1)
  uHvar <- model.matrix(object$formula, data = object$dataTable,
    rhs = 2)
  vHvar <- model.matrix(object$formula, data = object$dataTable,
    rhs = 3)
  Wu <- as.numeric(crossprod(matrix(delta), t(uHvar)))
  Wv <- as.numeric(crossprod(matrix(phi), t(vHvar)))
  epsilon <- model.response(model.frame(object$formula, data = object$dataTable)) -
    as.numeric(crossprod(matrix(beta), t(Xvar)))
  mustar <- -object$S * epsilon - exp(Wv)/sqrt(exp(Wu))
  u <- mustar + sqrt(exp(Wv)) * dnorm(mustar/sqrt(exp(Wv)))/pnorm(mustar/sqrt(exp(Wv)))
  uLB <- mustar + qnorm(1 - (1 - (1 - level)/2) * (1 - pnorm(-mustar/sqrt(exp(Wv))))) *
    sqrt(exp(Wv))
  uUB <- mustar + qnorm(1 - (1 - level)/2 * (1 - pnorm(-mustar/sqrt(exp(Wv))))) *
    sqrt(exp(Wv))
  m <- ifelse(mustar > 0, mustar, 0)
  if (object$logDepVar == TRUE) {
    teJLMS <- exp(-u)
    teMO <- exp(-m)
    teBC <- exp(-mustar + 1/2 * exp(Wv)) * pnorm(mustar/sqrt(exp(Wv)) -
      sqrt(exp(Wv)))/pnorm(mustar/sqrt(exp(Wv)))
    teBCLB <- exp(-uUB)
    teBCUB <- exp(-uLB)
    teBC_reciprocal <- exp(mustar + 1/2 * exp(Wv)) * pnorm(mustar/sqrt(exp(Wv)) +
      sqrt(exp(Wv)))/pnorm(mustar/sqrt(exp(Wv)))
    res <- data.frame(u = u, uLB = uLB, uUB = uUB, teJLMS = teJLMS,
      m = m, teMO = teMO, teBC = teBC, teBCLB = teBCLB,
      teBCUB = teBCUB, teBC_reciprocal = teBC_reciprocal)
  } else {
    res <- data.frame(u = u, uLB = uLB, uUB = uUB, m = m)
  }
  return(res)
}

# Marginal effects on inefficiencies ----------
#' marginal impact on efficiencies for exponential-normal distribution
#' @param object object of class sfacross
#' @noRd
cmargexponorm_Eu <- function(object) {
  delta <- object$mlParam[(object$nXvar + 1):(object$nXvar +
    object$nuZUvar)]
  uHvar <- model.matrix(object$formula, data = object$dataTable,
    rhs = 2)
  Wu <- as.numeric(crossprod(matrix(delta), t(uHvar)))
  margEff <- kronecker(matrix(delta[2:object$nuZUvar] * 1/2,
    nrow = 1), matrix(exp(Wu/2), ncol = 1))
  colnames(margEff) <- paste0("Eu_", colnames(uHvar)[-1])
  return(data.frame(margEff))
}

cmargexponorm_Vu <- function(object) {
  delta <- object$mlParam[(object$nXvar + 1):(object$nXvar +
    object$nuZUvar)]
  uHvar <- model.matrix(object$formula, data = object$dataTable,
    rhs = 2)
  Wu <- as.numeric(crossprod(matrix(delta), t(uHvar)))
  margEff <- kronecker(matrix(delta[2:object$nuZUvar], nrow = 1),
    matrix(exp(Wu), ncol = 1))
  colnames(margEff) <- paste0("Vu_", colnames(uHvar)[-1])
  return(data.frame(margEff))
}

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sfaR documentation built on Oct. 29, 2024, 9:07 a.m.

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