Biomass Tillage Data

Description

An agricultural experiment in which different tillage methods were implemented. The effects of tillage on plant (maize) biomass were subsequently determined by modeling biomass accumulation for each tillage treatment using a 3 parameter Weibull function.

A datset where the total biomass is modeled conditional on a three value factor, and hence vector parameters are used.

Usage

data("biomassTill")

Format

A data frame with 58 observations on the following 3 variables.

Tillage

Tillage treatments, a factor with levels

CA-:

a no-tillage system with plant residues removed

CA+:

a no-tillage system with plant residues retained

CT:

a conventionally tilled system with residues incorporated

DVS

the development stage of the maize crop. A DVS of 1 represents maize anthesis (flowering), and a DVS of 2 represents physiological maturity. For the data, numeric vector with 5 different values between 0.5 and 2.

Biomass

accumulated biomass of maize plants from each tillage treatment.

Biom.2

the same as Biomass, but with three values replaced by “gross errors”.

Source

From Strahinja Stepanovic and John Laborde, Department of Agronomy & Horticulture, University of Nebraska-Lincoln, USA

Examples

data(biomassTill)
str(biomassTill)
require(lattice)
## With long tailed errors
xyplot(Biomass ~ DVS | Tillage, data = biomassTill, type=c("p","smooth"))
## With additional 2 outliers:
xyplot(Biom.2 ~ DVS | Tillage, data = biomassTill, type=c("p","smooth"))

### Fit nonlinear Regression models: -----------------------------------

## simple starting values, needed:
m00st <- list(Wm = rep(300,  3),
               a = rep( 1.5, 3),
               b = rep( 2.2, 3))

robm <- nlrob(Biomass ~ Wm[Tillage] * (-expm1(-(DVS/a[Tillage])^b[Tillage])),
              data = biomassTill, start = m00st, maxit = 200)
##                                               -----------
summary(robm) ## ... 103 IRWLS iterations
plot(sort(robm$rweights), log = "y",
     main = "ordered robustness weights (log scale)")
mtext(getCall(robm))

## the classical (only works for the mild outliers):
cl.m <- nls(Biomass ~ Wm[Tillage] * (-expm1(-(DVS/a[Tillage])^b[Tillage])),
            data = biomassTill, start = m00st)

## now for the extra-outlier data: -- fails with singular gradient !!
try(
rob2 <- nlrob(Biom.2 ~ Wm[Tillage] * (-expm1(-(DVS/a[Tillage])^b[Tillage])),
              data = biomassTill, start = m00st)
)
## use better starting values:
m1st <- setNames(as.list(as.data.frame(matrix(
                coef(robm), 3))),
                c("Wm", "a","b"))
try(# just breaks a bit later!
rob2 <- nlrob(Biom.2 ~ Wm[Tillage] * (-expm1(-(DVS/a[Tillage])^b[Tillage])),
              data = biomassTill, start = m1st, maxit= 200, trace=TRUE)
)

## Comparison  {more to come} % once we have  "MM" working...
rbind(start = unlist(m00st),
      class = coef(cl.m),
      rob   = coef(robm))