lmfor (version 1.6)

ImputeHeights: Impute missing tree heights into a forest data using a nonlinear (mixed-effects) model.

Description

A function to impute tree heights in a forest inventory situation where all trees have been measured for diameter but only some trees have been measured for height.

Usage

ImputeHeights(d, h, plot, modelName = "naslund", nranp = 2, varf = TRUE, 
              addResidual = FALSE, makeplot=TRUE, level = 1,
              start=NA, bh=1.3, control=list(),random=NA)

Arguments

d

A numerical vector of tree diameters, usually given in cm.

h

A numerical vector of tree heights, usually given in meters. Should be of the same length as d.

plot

A vector of type numeric or factor, defining the groups of the data; usually the plot indices. Should be of the same length as d and h.

modelName

Either (i) a character vector specifying the name of the nonlinear function or (ii) the formula specifying a linear model. In case (i) the name should be one of the functions documented on the help page of HDmodels. In case (ii), it should be the linear formula in the form that is entered to the function lme, for example model=h~d+I(d^2)-1

nranp

Parameters nranp and random specify two alternative ways to specify the random effects of the model. An easy but restricted way is to use argument nranp. It is an integer between 0 and the number of fixed parameters, and has the the following meaning in the case of nonlinear model:

• If nranp=0, then a model without random parameters is fitted. Results to a fixed-effects model, and argument plot is not used.

• If nranp=1, then parameter a of a nonlinear function or the first coefficient of the linear formula is assumed to vary among plots.

• If nranp=2, then a and b or the first two terms of the linear formula are assumed to vary among plots or

• If nranp=3, then a b, and c of a three-parameter nonlinear model or three first coefficients of a linear model are assumed to vary among plots

In the case of linear model, the constant (if exists) it always counted as the first term.

As an alternative to nranp, argument random can be used to express the random part as a nlme formula, but without specification of the grouping structure. The provided formula is passed to the lme or nlme function. Argument random is always used when provided, so nranp has effect only if random=NA (the default).

varf

Numeric with values 0, 1 or 2. If 0 or FALSE, no variance function is used. If varf=1, 2 or TRUE, then the power- type variance function var(e)=sigma^2*w^(2*delta) is used. where weight w is the raw diameter (when varf=1 or TRUE), or w=max(1,dsd+3) (when varf=2), where dsd=(d-D)/SDD. Here d is tree diameter, D and SDD are the mean and standard deviation of diameters on the plot in question.

addResidual

Boolean. If TRUE, a random residual is added to the imputed height from a normal distribution using the estimated variance function. If also level=0 or if the plot did not include any measured heights to predict the random effects, then also a randomly selected plot effect from among the predicted plot effects is added. The added plot effect is the same for all trees of a given plot.

makeplot

Should a residual plot of the fitted model be produced for evaluation of goodness of fit? The plot is produced using the default arguments of function plot.hdmod, and is not affected by the value of arguments level and addResidual.

level

The level of prediction. 0 means fixed-effect prediction and 1 means plot-level prediction using the random effects. Has no effect if nranp=0.

start, bh, control, random

Arguments passed to fithd. See documentation of fithd.

Value

A list of components

h

A vector of tree heights, including the measured heights for the trees with known height and imputed heights for the others.

imputed

A booelan vector of the same length as h, having value TRUE for imputed heights. Produced as is.na(data$h)

model

The fitted model that was used in imputation. Fitted using fithd which in turn calls nlme or gnls

predType

A vector of the same length as h, including information on the level of prediction. Value 0 means a measured height (no model prediction is used), value 1 means the plot-level prediction has been done using the estimated plot effects. Value 2 means that no sample trees were available and the prediction is based on fixed part only (if level=0) or on a simulated plot effect (if level=1).

hpred

Predicted heights for all trees. Equals to vector h for trees that had missing heights.

Details

The function predicts the missing heights using a nonlinear mixed-effects model or a nonlinear fixed-effects model. In mixed-effects model, plot-specific random effects can be used if other tree heights have been measured from the same plot. Also random, normally distributed residual can be added to the heights according to the estimated constant or heteroscedastic residual variance structure.

References

Mehtatalo, L., Gregoire, T.G., and de Miguel, S. Modeling Height-diameter curves for height prediction. Canadian Journal of Forest Research, 45(7): 826-837, 10.1139/cjfr-2015-0054

See Also

fithd for model fitting and plot.hdmod for plotting.

Examples

# NOT RUN {
data(spati) 

ImpFixed<-ImputeHeights(spati$d,spati$h,spati$plot,level=0)
ImpRandom<-ImputeHeights(spati$d,spati$h,spati$plot,level=1,makeplot=FALSE)
# Try also
# ImpRanRes<-ImputeHeights(spati$d,spati$h,spati$plot,level=1,addResidual=TRUE,makeplot=FALSE)

plot(spati$d[!is.na(spati$h)],
     spati$h[!is.na(spati$h)],
     col=spati$plot[!is.na(spati$h)],
     main="Observations", xlab="d, cm", ylab="h, m",
     ylim=c(0,30))

plot(spati$d[ImpFixed$imputed],
     ImpFixed$h[ImpFixed$imputed],
     col=spati$plot[ImpFixed$imputed],
     main="Imputed, Naslund, Fixed", xlab="d, cm", ylab="h, m",
     ylim=c(0,30))
       
plot(spati$d[ImpRandom$imputed],
     ImpRandom$h[ImpRandom$imputed],
     col=spati$plot[ImpRandom$imputed],
     main="Imputed, Naslund, Fixed + Plot", xlab="d, cm", ylab="h, m",
     ylim=c(0,30))

# Try also
# plot(spati$d[ImpRanRes$imputed],
#     ImpRanRes$h[ImpRanRes$imputed],
#     col=spati$plot[ImpRanRes$imputed],
#     main="Imputed, Naslund, Fixed + Plot + Tree", xlab="d, cm", ylab="h, m",
#     ylim=c(0,30))
# }