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\name{biomassTill}
\alias{biomassTill}
\docType{data}
\title{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 \emph{vector} parameters are used.
}
\usage{data("biomassTill", package="robustbase")}
\format{
A data frame with 58 observations on the following 3 variables.
\describe{
\item{\code{Tillage}}{Tillage treatments, a \code{\link{factor}}
with levels \describe{
\item{\code{CA-}:}{a no-tillage system with plant residues removed}
\item{\code{CA+}:}{a no-tillage system with plant residues retained}
\item{\code{CT}:}{a conventionally tilled system with residues incorporated}
}
}
\item{\code{DVS}}{the development stage of the maize crop. A DVS of
\code{1} represents maize anthesis (flowering), and a DVS of \code{2}
represents physiological maturity. For the data, numeric vector with
5 different values between 0.5 and 2.}
\item{\code{Biomass}}{accumulated biomass of maize plants from each
tillage treatment.}
\item{\code{Biom.2}}{the same as \code{Biomass}, but with three
values replaced by \dQuote{gross errors}.}
}
}
\source{
From Strahinja Stepanovic and John Laborde, Department of Agronomy &
Horticulture, University of Nebraska-Lincoln, USA
}
%% \references{
%% %% ~~ possibly secondary sources and usages ~~
%% }
\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))
}
\keyword{datasets}
|
