TapeR (version 0.5.3)

E_DHx_HmDm_HT.f: 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

Usage

E_DHx_HmDm_HT.f(
  Hx,
  Hm,
  Dm,
  mHt,
  sHt = 0,
  par.lme,
  Rfn = list(fn = "sig2"),
  ...
)

Value

a list holding nine elements:

• DHx: Numeric vector of diameters (cm) (expected value) along the heights given by Hx.

• Hx: Numeric vector of heights (m) along which to return the expected diameter.

• MSE_Mean: Mean squared error for the expected value of the diameter.

• 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.

• KOV_Mean: Variance-Covariance matrix for the expected value of the diameter.

• MSE_Pred: Mean squared error for the prediction of the diameter.

• CI_Pred: 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.

• KOV_Pred: Variance-Covariance matrix for the prediction of the diameter.

• Rfn: Function applied for estimated or assumed residual variance.

Arguments

Hx

Numeric vector of stem heights (m) along which to return the expected diameter.

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 Dm.

Dm

Numeric vector of diameter measurements (cm) taken for calibration. Can be of length 1. Must be of same length as Hm.

mHt

Scalar. Tree height (m).

sHt

Scalar. Standard deviation of stem height. Can be 0 if height was measured without error.

par.lme

List of taper model parameters obtained by TapeR_FIT_LME.f.

Rfn

list with function name to provide estimated or assumed residual variances for the given measurements, optionally parameters for such functions

...

not currently used

Author

Edgar Kublin and Christian Vonderach

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 Rfn the taper curve can be forced through the measured diameters, c.f. resVar.

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.

See Also

TapeR_FIT_LME.f

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, 6)
tc.tree1 <- E_DHx_HmDm_HT.f(Hx=seq(0, tree1$Ht[1], 0.1), 
                            Hm=tree1$Hx[i],
                            Dm=tree1$Dx[i], 
                            mHt = tree1$Ht[1], 
                            sHt = 0, 
                            par.lme = SK.par.lme,
                            Rfn=list(fn="sig2"))
tc.tree2 <- E_DHx_HmDm_HT.f(Hx=seq(0, tree1$Ht[1], 0.1), 
                            Hm=tree1$Hx[i],
                            Dm=tree1$Dx[i], 
                            mHt = tree1$Ht[1], 
                            sHt = 0, 
                            par.lme = SK.par.lme,
                            Rfn=list(fn="zero"))
# 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)
# closer window
plot(tc.tree1$Hx, tc.tree1$DHx, type="l", las=1, xlim=c(0, 8), ylim=c(24, 30))
# 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)

## apply yet another residual variance function
i <- c(1, 2, 3) # calibrating with 0.5, 1m and 2m, assuming no error in 0.5m
zrv <- tree1$Hx[1] / tree1$Ht[1] # assumed zero resiudal variance
# assumed residual variance per measurement
TapeR:::resVar(relH = tree1$Hx[i] / tree1$Ht[1], fn = "dlnorm", 
               sig2 = SK.par.lme$sig2_eps, par = list(zrv=zrv))
tc.tree3 <- E_DHx_HmDm_HT.f(Hx=seq(0, tree1$Ht[1], 0.1), 
                            Hm=tree1$Hx[i],
                            Dm=tree1$Dx[i], 
                            mHt = tree1$Ht[1], 
                            sHt = 0, 
                            par.lme = SK.par.lme,
                            Rfn=list(fn="dlnorm", par=list(zrv=zrv)))
plot(tc.tree1$Hx, tc.tree1$DHx, type="l", las=1, xlim=c(0, 4))
points(x=tc.tree3$Hx, y=tc.tree3$DHx, type="l", lty=2)
points(tree1$Hx[i], tree1$Dx[i], pch=3, col=2)
points(tree1$Hx, tree1$Dx)