E_DHx_HmDm_HT_CIdHt.f {TapeR}

Estimate diameter and exact confidence and prediction intervals

Description

Calibrates a taper curve based on at least one diameter measurement and returns the expected diameters and exact variances

Usage

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

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

Details

calibrates the tree specific taper curve and calculates 'exact' confidence intervals, which can be useful for plotting. Attention: this function is somewhat time-consuming.

Value

a matrix with six columns:

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

• q_DHx_u: Lower confidence interval (cm). (95% CI except for estimates close to the stem tip.)

• DHx: Diameter estimate (cm).

• q_DHx_o: Upper CI (cm).

• cP_DHx_u: Probability of observations <q_DHx_u.

• cP_DHx_o: Probability of observations <q_DHx_o.

Author(s)

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.

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)

## Calculate "exact" CIs. Careful: This takes a while!
#library(pracma)# for numerical integration with gaussLegendre()

tc.tree1.exact <- E_DHx_HmDm_HT_CIdHt.f(Hx=1:tree1$Ht[1],
                                        Hm=tree1$Hx[3],
                                        Dm=tree1$Dx[3],
                                        mHt=tree1$Ht[1],
                                        sHt=1,
                                        par.lme=SK.par.lme)
#add exact confidence intervals to approximate intervals above - fits
#quite well
lines(tc.tree1.exact[,1], tc.tree1.exact[,2], lty=2,col=2)
lines(tc.tree1.exact[,1], tc.tree1.exact[,4], lty=2,col=2)