R/E_DHx_HmDm_HT.f.R
In jonibio/TapeR: Flexible Tree Taper Curves Based on Semiparametric Mixed Models
Defines functions
E_DHx_HmDm_HT.f
Documented in
E_DHx_HmDm_HT.f
#' @title Estimate diameter and approximate confidence and prediction intervals
#' @description Calibrates a taper curve based on at least one diameter
#' measurement and returns the expected diameters and approximate variances
#' @param Hx Numeric vector of stem heights (m) along which to return the
#' expected diameter.
#' @param Hm Numeric vector of stem heights (m) along which diameter
#' measurements were taken for calibration. Can be of length 1. Must be of same
#' length as \code{Dm}.
#' @param Dm Numeric vector of diameter measurements (cm) taken for calibration.
#' Can be of length 1. Must be of same length as \code{Hm}.
#' @param mHt Scalar. Tree height (m).
#' @param sHt Scalar. Standard deviation of stem height. Can be 0 if height was
#' measured without error.
#' @param par.lme List of taper model parameters obtained by
#' \code{\link{TapeR_FIT_LME.f}}.
#' @param R0 indicator whether taper curve should interpolate measurements
#' @param ... not currently used
#' @details calibrates the tree specific taper curve and calculates approximate
#' confidence intervals, which can be useful for plotting. Uncertainty resulting
#' from tariff height estimates if tree height was not measured is incorporated.
#' Using \code{R0} the taper curve can be forced through the measured diameters
#' (if \code{R0=TRUE}).
#' @return a list holding six elements:
#' \itemize{
#' \item{DHx: }{Numeric vector of diameters (cm) (expected value) along the
#' heights given by \code{Hx}.}
#' \item{Hx: }{Numeric vector of heights (m) along which to return the expected
#' diameter.}
#' \item{MSE_Mean: }{Mean squared error for the expected value of the diameter.}
#' \item{CI_Mean: }{Confidence interval. Matrix of the 95\% conf. int. for the
#' expected value of the diameter (cm). First column: lower limit, second
#' column: mean, third column: upper limit.}
#' \item{MSE_Pred: }{Mean squared error for the prediction of the diameter.}
#' \item{CI_Mean: }{Prediction interval. Matrix of the 95\% conf. int. for the
#' prediction of the diameter (cm). First column: lower limit, second column:
#' mean, third column: upper limit.}
#' \item{R0: }{Taper curve forced through measurements (if TRUE) or not (if FALSE).}
#' }
#' @author Edgar Kublin
#' @references Kublin, E., Breidenbach, J., Kaendler, G. (2013) A flexible stem
#' taper and volume prediction method based on mixed-effects B-spline
#' regression, Eur J For Res, 132:983-997.
#' @seealso \code{\link{TapeR_FIT_LME.f}}
#' @export
#'
#' @examples
#' #example data
#' data(DxHx.df)
#' taper curve parameters based on all measured trees
#' data(SK.par.lme)
#'
#' #select data of first tree
#' Idi <- (DxHx.df[,"Id"] == unique(DxHx.df$Id)[1])
#' (tree1 <- DxHx.df[Idi,])
#'
#' ## Predict the taper curve based on the diameter measurement in 2 m
#' ## height and known height
#' tc.tree1 <- E_DHx_HmDm_HT.f(Hx=1:tree1$Ht[1],
#' Hm=tree1$Hx[3],
#' Dm=tree1$Dx[3],
#' mHt = tree1$Ht[1],
#' sHt = 0,
#' par.lme = SK.par.lme)
#' #plot the predicted taper curve
#' plot(tc.tree1$Hx, tc.tree1$DHx, type="l", las=1)
#' #lower CI
#' lines(tc.tree1$Hx, tc.tree1$CI_Mean[,1], lty=2)
#' #upper CI
#' lines(tc.tree1$Hx, tc.tree1$CI_Mean[,3], lty=2)
#' #lower prediction interval
#' lines(tc.tree1$Hx, tc.tree1$CI_Pred[,1], lty=3)
#' #upper prediction interval
#' lines(tc.tree1$Hx, tc.tree1$CI_Pred[,3], lty=3)
#' #add measured diameter used for calibration
#' points(tree1$Hx[3], tree1$Dx[3], pch=3, col=2)
#' #add the observations
#' points(tree1$Hx, tree1$Dx)
#'
#' ## feature of forcing taper curve through measured diameters
#' i <- c(3, 5)
#' tc.tree1 <- E_DHx_HmDm_HT.f(Hx=1:tree1$Ht[1],
#' Hm=tree1$Hx[i],
#' Dm=tree1$Dx[i],
#' mHt = tree1$Ht[1],
#' sHt = 0,
#' par.lme = SK.par.lme,
#' R0=FALSE)
#' tc.tree2 <- E_DHx_HmDm_HT.f(Hx=1:tree1$Ht[1],
#' Hm=tree1$Hx[i],
#' Dm=tree1$Dx[i],
#' mHt = tree1$Ht[1],
#' sHt = 0,
#' par.lme = SK.par.lme,
#' R0=TRUE)
#' #plot the predicted taper curve
#' plot(tc.tree1$Hx, tc.tree1$DHx, type="l", las=1)
#' #added taper curve through measurement
#' points(x=tc.tree2$Hx, y=tc.tree2$DHx, type="l", lty=2)
#' #add measured diameter used for calibration
#' points(tree1$Hx[i], tree1$Dx[i], pch=3, col=2)
#' #add the observations
#' points(tree1$Hx, tree1$Dx)
E_DHx_HmDm_HT.f <-
function( Hx, Hm, Dm, mHt, sHt = 0, par.lme, R0=FALSE, ...){
if(sHt > 0){
# SK.par.lme = par.lme
mw_HtT = mHt
sd_HtT = sHt
nx = c(30,20)
Ht_u = mw_HtT - 2*sd_HtT
Ht_m = mw_HtT
Ht_o = mw_HtT + 2*sd_HtT
# ------------------------------------------------------------------------
# CI_SK_u
# ------------------------------------------------------------------------
# SK_u :..................................................................
hx = seq(0,1,length.out = sum(nx))
SK_u = SK_EBLUP_LME.f(xm = Hm/Ht_u, ym = Dm, xp = hx, par.lme, R0) # Kalibrierung/LME
u.ssp = smooth.spline(x = hx*Ht_u, y = SK_u$yp, df=10)
u.ssp$fit$coef[length(u.ssp$fit$coef)] = 0 # u.ssp(Ht_u)=0
# CI_u(SK_m) :............................................................
SK_m = SK_EBLUP_LME.f(xm = Hm/Ht_m, ym = Dm, xp = hx, par.lme, R0)
m.ssp = smooth.spline(x = hx*Ht_m, y = SK_m$CI_Pred[,1] , df=10)
m.ssp$fit$coef[length(u.ssp$fit$coef)] = 0 # m.ssp(Ht_m)=0
# CI_SK_u (Approximation):................................................
# nx = c(30,20)
hx = c(seq(0,0.3*Ht_u,length.out = nx[1]),seq(0.6*Ht_u,Ht_u,length.out = nx[2]))
qu = predict(u.ssp,x = hx, deriv = 0)$y; qu = apply(cbind(0,qu),1,max)
qm = predict(m.ssp,x = hx, deriv = 0)$y; qm = apply(cbind(0,qm),1,max)
qmin = apply(cbind(qu,qm),1,min); qmin = apply(cbind(qmin,0),1,max)
qD_u.ssp = smooth.spline(x = hx, y = qmin, df=10); qD_u.ssp$fit$coef[length(qD_u.ssp$fit$coef)] = 0
# ----------------------------------------------------------------------------------------
# CI_SK_o
# ----------------------------------------------------------------------------------------
hx = seq(0,1,length.out = sum(nx))
SK_o = SK_EBLUP_LME.f(xm = Hm/Ht_o, ym = Dm, xp = hx, par.lme, R0)
o.ssp = smooth.spline(x = hx*Ht_o, y = SK_o$yp, df=10); o.ssp$fit$coef[length(u.ssp$fit$coef)] = 0 # u.ssp(Ht_u)=0
# ----------------------------------------------------------------------------------------
SK_m = SK_EBLUP_LME.f(xm = Hm/Ht_m, ym = Dm, xp = hx, par.lme, R0)
m.ssp = smooth.spline(x = hx*Ht_m, y = SK_m$CI_Pred[,3] , df=10)
# CI_SK_o (Approximation):................................................................
# nx=c(30,20)
hx = c(seq(0,0.3*Ht_o,length.out = nx[1]),seq(min(Ht_u,0.6*Ht_o),Ht_o,length.out=nx[2]))
qm = predict(m.ssp,x = hx, deriv = 0)$y; qm = apply(cbind(0,qm),1,max)
qo = predict(o.ssp,x = hx, deriv = 0)$y; qo = apply(cbind(0,qo),1,max)
qmax = apply(cbind(qm,qo),1,max)
qD_o.ssp = smooth.spline(x = hx, y = qmax, df=10); qD_o.ssp$fit$coef[length(qD_o.ssp$fit$coef)] = 0
# ----------------------------------------------------------------------------------------
HHx = Hx[order(Hx)]
qD_u = qD_o = list(x=0,y=0)
hx = HHx/Ht_m; hx = apply(cbind(hx,1),1,min)
SK_m = SK_EBLUP_LME.f(xm = Hm/Ht_m, ym = Dm, xp = hx, par.lme, R0)
DHx = SK_m$yp
MSE_Mean = SK_m$MSE_Mean
MSE_Pred = SK_m$MSE_Pred
HHx = Hx[order(Hx)]; HHx = apply(cbind(Ht_u,HHx),1,min)
qD_u[["x"]] = HHx
qD_u[["y"]] = predict(qD_u.ssp,x = HHx)$y
HHx = Hx[order(Hx)]; HHx = apply(cbind(Ht_o,HHx),1,min)
qD_o[["x"]] = HHx
qD_o[["y"]] = predict(qD_o.ssp,x = HHx)$y
CI_Mean = cbind(qD_u[["y"]],DHx,qD_o[["y"]])
sig2_eps = par.lme$sig2_eps
dfRes = par.lme$dfRes
c_alpha = qt(p=0.025, df=dfRes, ncp=0, lower.tail = F, log.p = FALSE)
CI_Pred = CI_Mean
# qD_u = CI_Mean[,2] - c_alpha*sqrt(MSE_Mean)
# sqrt(MSE_Mean) = (CI_Mean[,2]-qD_u)/c_alpha
dci = sqrt(((DHx - qD_u[["y"]])/c_alpha)^2 + sig2_eps)
CI_Pred[,1] = DHx - c_alpha*dci
CI_Pred[,1] = apply(cbind(CI_Pred[,1],0),1,max)
# ii = (Ht_u<=Hx); CI_Pred[ii,1] = 0
dci = sqrt(((qD_o[["y"]] - DHx)/c_alpha)^2 + sig2_eps)
CI_Pred[,3] = DHx + c_alpha*dci
CI_Pred[,3] = apply(cbind(CI_Pred[,3],0),1,max)
# ii = (Ht_o<=Hx); CI_Pred[ii,3]=0
if(F){
plot(Hx,CI_Mean[,3],type="n")
matlines(Hx,CI_Mean, col = "blue", lwd=2, lty=1)
matlines(Hx,CI_Pred,col = "red", lwd=2, lty=1)
cbind(CI_Pred[,1],CI_Mean[,1])
cbind(CI_Mean[,3],CI_Pred[,3])
}
}else{ # mHt=DxHx.df[Idi,"Ht"][1]gemessen
xm = Hm/mHt
ym = Dm
hx = Hx[order(Hx)]/mHt
hx = apply(cbind(1,hx),1,min)
# ----------------------------------------------------------------------------------------
SK_m = SK_EBLUP_LME.f(xm = Hm/mHt, ym = Dm, xp = hx, par.lme, R0) # Kalibrierung/LME
# ----------------------------------------------------------------------------------------
DHx = SK_m$yp
MSE_Mean = SK_m$MSE_Mean
MSE_Pred = SK_m$MSE_Pred
dfRes = par.lme$dfRes
c_alpha = qt(p=0.025, df=dfRes, ncp=0, lower.tail = F, log.p = FALSE)
CI_Mean = cbind(DHx - c_alpha*sqrt(MSE_Mean),DHx,DHx + c_alpha*sqrt(MSE_Mean))
CI_Pred = cbind(DHx - c_alpha*sqrt(MSE_Pred),DHx,DHx + c_alpha*sqrt(MSE_Pred))
}
return(list(DHx = DHx, Hx = Hx[order(Hx)],
MSE_Mean = MSE_Mean, CI_Mean = CI_Mean,
MSE_Pred = MSE_Pred, CI_Pred = CI_Pred,
R0=R0))
}
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Defines functions E_DHx_HmDm_HT.f
Documented in E_DHx_HmDm_HT.f
#' @title Estimate diameter and approximate confidence and prediction intervals
#' @description Calibrates a taper curve based on at least one diameter
#' measurement and returns the expected diameters and approximate variances
#' @param Hx Numeric vector of stem heights (m) along which to return the
#' expected diameter.
#' @param Hm Numeric vector of stem heights (m) along which diameter
#' measurements were taken for calibration. Can be of length 1. Must be of same
#' length as \code{Dm}.
#' @param Dm Numeric vector of diameter measurements (cm) taken for calibration.
#' Can be of length 1. Must be of same length as \code{Hm}.
#' @param mHt Scalar. Tree height (m).
#' @param sHt Scalar. Standard deviation of stem height. Can be 0 if height was
#' measured without error.
#' @param par.lme List of taper model parameters obtained by
#' \code{\link{TapeR_FIT_LME.f}}.
#' @param R0 indicator whether taper curve should interpolate measurements
#' @param ... not currently used
#' @details calibrates the tree specific taper curve and calculates approximate
#' confidence intervals, which can be useful for plotting. Uncertainty resulting
#' from tariff height estimates if tree height was not measured is incorporated.
#' Using \code{R0} the taper curve can be forced through the measured diameters
#' (if \code{R0=TRUE}).
#' @return a list holding six elements:
#' \itemize{
#' \item{DHx: }{Numeric vector of diameters (cm) (expected value) along the
#' heights given by \code{Hx}.}
#' \item{Hx: }{Numeric vector of heights (m) along which to return the expected
#' diameter.}
#' \item{MSE_Mean: }{Mean squared error for the expected value of the diameter.}
#' \item{CI_Mean: }{Confidence interval. Matrix of the 95\% conf. int. for the
#' expected value of the diameter (cm). First column: lower limit, second
#' column: mean, third column: upper limit.}
#' \item{MSE_Pred: }{Mean squared error for the prediction of the diameter.}
#' \item{CI_Mean: }{Prediction interval. Matrix of the 95\% conf. int. for the
#' prediction of the diameter (cm). First column: lower limit, second column:
#' mean, third column: upper limit.}
#' \item{R0: }{Taper curve forced through measurements (if TRUE) or not (if FALSE).}
#' }
#' @author Edgar Kublin
#' @references Kublin, E., Breidenbach, J., Kaendler, G. (2013) A flexible stem
#' taper and volume prediction method based on mixed-effects B-spline
#' regression, Eur J For Res, 132:983-997.
#' @seealso \code{\link{TapeR_FIT_LME.f}}
#' @export
#'
#' @examples
#' #example data
#' data(DxHx.df)
#' taper curve parameters based on all measured trees
#' data(SK.par.lme)
#'
#' #select data of first tree
#' Idi <- (DxHx.df[,"Id"] == unique(DxHx.df$Id)[1])
#' (tree1 <- DxHx.df[Idi,])
#'
#' ## Predict the taper curve based on the diameter measurement in 2 m
#' ## height and known height
#' tc.tree1 <- E_DHx_HmDm_HT.f(Hx=1:tree1$Ht[1],
#' Hm=tree1$Hx[3],
#' Dm=tree1$Dx[3],
#' mHt = tree1$Ht[1],
#' sHt = 0,
#' par.lme = SK.par.lme)
#' #plot the predicted taper curve
#' plot(tc.tree1$Hx, tc.tree1$DHx, type="l", las=1)
#' #lower CI
#' lines(tc.tree1$Hx, tc.tree1$CI_Mean[,1], lty=2)
#' #upper CI
#' lines(tc.tree1$Hx, tc.tree1$CI_Mean[,3], lty=2)
#' #lower prediction interval
#' lines(tc.tree1$Hx, tc.tree1$CI_Pred[,1], lty=3)
#' #upper prediction interval
#' lines(tc.tree1$Hx, tc.tree1$CI_Pred[,3], lty=3)
#' #add measured diameter used for calibration
#' points(tree1$Hx[3], tree1$Dx[3], pch=3, col=2)
#' #add the observations
#' points(tree1$Hx, tree1$Dx)
#'
#' ## feature of forcing taper curve through measured diameters
#' i <- c(3, 5)
#' tc.tree1 <- E_DHx_HmDm_HT.f(Hx=1:tree1$Ht[1],
#' Hm=tree1$Hx[i],
#' Dm=tree1$Dx[i],
#' mHt = tree1$Ht[1],
#' sHt = 0,
#' par.lme = SK.par.lme,
#' R0=FALSE)
#' tc.tree2 <- E_DHx_HmDm_HT.f(Hx=1:tree1$Ht[1],
#' Hm=tree1$Hx[i],
#' Dm=tree1$Dx[i],
#' mHt = tree1$Ht[1],
#' sHt = 0,
#' par.lme = SK.par.lme,
#' R0=TRUE)
#' #plot the predicted taper curve
#' plot(tc.tree1$Hx, tc.tree1$DHx, type="l", las=1)
#' #added taper curve through measurement
#' points(x=tc.tree2$Hx, y=tc.tree2$DHx, type="l", lty=2)
#' #add measured diameter used for calibration
#' points(tree1$Hx[i], tree1$Dx[i], pch=3, col=2)
#' #add the observations
#' points(tree1$Hx, tree1$Dx)
E_DHx_HmDm_HT.f <-
function( Hx, Hm, Dm, mHt, sHt = 0, par.lme, R0=FALSE, ...){
if(sHt > 0){
# SK.par.lme = par.lme
mw_HtT = mHt
sd_HtT = sHt
nx = c(30,20)
Ht_u = mw_HtT - 2*sd_HtT
Ht_m = mw_HtT
Ht_o = mw_HtT + 2*sd_HtT
# ------------------------------------------------------------------------
# CI_SK_u
# ------------------------------------------------------------------------
# SK_u :..................................................................
hx = seq(0,1,length.out = sum(nx))
SK_u = SK_EBLUP_LME.f(xm = Hm/Ht_u, ym = Dm, xp = hx, par.lme, R0) # Kalibrierung/LME
u.ssp = smooth.spline(x = hx*Ht_u, y = SK_u$yp, df=10)
u.ssp$fit$coef[length(u.ssp$fit$coef)] = 0 # u.ssp(Ht_u)=0
# CI_u(SK_m) :............................................................
SK_m = SK_EBLUP_LME.f(xm = Hm/Ht_m, ym = Dm, xp = hx, par.lme, R0)
m.ssp = smooth.spline(x = hx*Ht_m, y = SK_m$CI_Pred[,1] , df=10)
m.ssp$fit$coef[length(u.ssp$fit$coef)] = 0 # m.ssp(Ht_m)=0
# CI_SK_u (Approximation):................................................
# nx = c(30,20)
hx = c(seq(0,0.3*Ht_u,length.out = nx[1]),seq(0.6*Ht_u,Ht_u,length.out = nx[2]))
qu = predict(u.ssp,x = hx, deriv = 0)$y; qu = apply(cbind(0,qu),1,max)
qm = predict(m.ssp,x = hx, deriv = 0)$y; qm = apply(cbind(0,qm),1,max)
qmin = apply(cbind(qu,qm),1,min); qmin = apply(cbind(qmin,0),1,max)
qD_u.ssp = smooth.spline(x = hx, y = qmin, df=10); qD_u.ssp$fit$coef[length(qD_u.ssp$fit$coef)] = 0
# ----------------------------------------------------------------------------------------
# CI_SK_o
# ----------------------------------------------------------------------------------------
hx = seq(0,1,length.out = sum(nx))
SK_o = SK_EBLUP_LME.f(xm = Hm/Ht_o, ym = Dm, xp = hx, par.lme, R0)
o.ssp = smooth.spline(x = hx*Ht_o, y = SK_o$yp, df=10); o.ssp$fit$coef[length(u.ssp$fit$coef)] = 0 # u.ssp(Ht_u)=0
# ----------------------------------------------------------------------------------------
SK_m = SK_EBLUP_LME.f(xm = Hm/Ht_m, ym = Dm, xp = hx, par.lme, R0)
m.ssp = smooth.spline(x = hx*Ht_m, y = SK_m$CI_Pred[,3] , df=10)
# CI_SK_o (Approximation):................................................................
# nx=c(30,20)
hx = c(seq(0,0.3*Ht_o,length.out = nx[1]),seq(min(Ht_u,0.6*Ht_o),Ht_o,length.out=nx[2]))
qm = predict(m.ssp,x = hx, deriv = 0)$y; qm = apply(cbind(0,qm),1,max)
qo = predict(o.ssp,x = hx, deriv = 0)$y; qo = apply(cbind(0,qo),1,max)
qmax = apply(cbind(qm,qo),1,max)
qD_o.ssp = smooth.spline(x = hx, y = qmax, df=10); qD_o.ssp$fit$coef[length(qD_o.ssp$fit$coef)] = 0
# ----------------------------------------------------------------------------------------
HHx = Hx[order(Hx)]
qD_u = qD_o = list(x=0,y=0)
hx = HHx/Ht_m; hx = apply(cbind(hx,1),1,min)
SK_m = SK_EBLUP_LME.f(xm = Hm/Ht_m, ym = Dm, xp = hx, par.lme, R0)
DHx = SK_m$yp
MSE_Mean = SK_m$MSE_Mean
MSE_Pred = SK_m$MSE_Pred
HHx = Hx[order(Hx)]; HHx = apply(cbind(Ht_u,HHx),1,min)
qD_u[["x"]] = HHx
qD_u[["y"]] = predict(qD_u.ssp,x = HHx)$y
HHx = Hx[order(Hx)]; HHx = apply(cbind(Ht_o,HHx),1,min)
qD_o[["x"]] = HHx
qD_o[["y"]] = predict(qD_o.ssp,x = HHx)$y
CI_Mean = cbind(qD_u[["y"]],DHx,qD_o[["y"]])
sig2_eps = par.lme$sig2_eps
dfRes = par.lme$dfRes
c_alpha = qt(p=0.025, df=dfRes, ncp=0, lower.tail = F, log.p = FALSE)
CI_Pred = CI_Mean
# qD_u = CI_Mean[,2] - c_alpha*sqrt(MSE_Mean)
# sqrt(MSE_Mean) = (CI_Mean[,2]-qD_u)/c_alpha
dci = sqrt(((DHx - qD_u[["y"]])/c_alpha)^2 + sig2_eps)
CI_Pred[,1] = DHx - c_alpha*dci
CI_Pred[,1] = apply(cbind(CI_Pred[,1],0),1,max)
# ii = (Ht_u<=Hx); CI_Pred[ii,1] = 0
dci = sqrt(((qD_o[["y"]] - DHx)/c_alpha)^2 + sig2_eps)
CI_Pred[,3] = DHx + c_alpha*dci
CI_Pred[,3] = apply(cbind(CI_Pred[,3],0),1,max)
# ii = (Ht_o<=Hx); CI_Pred[ii,3]=0
if(F){
plot(Hx,CI_Mean[,3],type="n")
matlines(Hx,CI_Mean, col = "blue", lwd=2, lty=1)
matlines(Hx,CI_Pred,col = "red", lwd=2, lty=1)
cbind(CI_Pred[,1],CI_Mean[,1])
cbind(CI_Mean[,3],CI_Pred[,3])
}
}else{ # mHt=DxHx.df[Idi,"Ht"][1]gemessen
xm = Hm/mHt
ym = Dm
hx = Hx[order(Hx)]/mHt
hx = apply(cbind(1,hx),1,min)
# ----------------------------------------------------------------------------------------
SK_m = SK_EBLUP_LME.f(xm = Hm/mHt, ym = Dm, xp = hx, par.lme, R0) # Kalibrierung/LME
# ----------------------------------------------------------------------------------------
DHx = SK_m$yp
MSE_Mean = SK_m$MSE_Mean
MSE_Pred = SK_m$MSE_Pred
dfRes = par.lme$dfRes
c_alpha = qt(p=0.025, df=dfRes, ncp=0, lower.tail = F, log.p = FALSE)
CI_Mean = cbind(DHx - c_alpha*sqrt(MSE_Mean),DHx,DHx + c_alpha*sqrt(MSE_Mean))
CI_Pred = cbind(DHx - c_alpha*sqrt(MSE_Pred),DHx,DHx + c_alpha*sqrt(MSE_Pred))
}
return(list(DHx = DHx, Hx = Hx[order(Hx)],
MSE_Mean = MSE_Mean, CI_Mean = CI_Mean,
MSE_Pred = MSE_Pred, CI_Pred = CI_Pred,
R0=R0))
}
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