biomassTill | R Documentation |

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.

`data("biomassTill", package="robustbase")`

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”.

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

```
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))
```

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