biomassTill: Biomass Tillage Data

Description Usage Format Source Examples

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

1
data("biomassTill", package="robustbase")

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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
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))

Example output

'data.frame':	58 obs. of  4 variables:
 $ Tillage: Factor w/ 3 levels "CA-","CA+","CT": 1 1 1 1 1 1 1 1 1 1 ...
 $ DVS    : num  0.49 0.49 0.49 0.49 0.749 ...
 $ Biomass: num  0.541 1.309 7.03 2.03 5.911 ...
 $ Biom.2 : num  108.25 261.8 7.03 2.03 5.91 ...
Loading required package: lattice

Call:
nlrob(formula = Biomass ~ Wm[Tillage] * (-expm1(-(DVS/a[Tillage])^b[Tillage])), 
    data = biomassTill, start = m00st, maxit = 200, algorithm = "default")

Residuals:
     Min       1Q   Median       3Q      Max 
-124.369  -23.776   -5.418   28.073  340.556 

Parameters:
     Estimate Std. Error t value Pr(>|t|)    
Wm1 219.84347   78.59343   2.797 0.007346 ** 
Wm2 265.91513   97.32363   2.732 0.008722 ** 
Wm3 343.38787   26.39224  13.011  < 2e-16 ***
a1    1.46076    0.41373   3.531 0.000913 ***
a2    1.49303    0.44386   3.364 0.001500 ** 
a3    1.29362    0.07733  16.728  < 2e-16 ***
b1    2.88871    1.35760   2.128 0.038409 *  
b2    2.83763    1.18395   2.397 0.020401 *  
b3    4.04557    0.87533   4.622 2.79e-05 ***
---
Signif. codes:  0***0.001**0.01*0.05.’ 0.1 ‘ ’ 1

Robust residual standard error: 36.9 
Convergence in 103 IRWLS iterations

Robustness weights: 
 43 weights are ~= 1. The remaining 15 ones are summarized as
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.1457  0.3444  0.5338  0.5237  0.6462  0.9266 
Error in nls(formula, data = data, start = start, algorithm = algorithm,  : 
  singular gradient
robust iteration 1 
132570.9 :  219.843474 265.915134 343.387869   1.460763   1.493028   1.293623   2.888710   2.837634   4.045572
128604.8 :  256.127352 173.157194 344.261838   1.655889   1.209569   1.295166   1.999126   3.086581   4.040089
127364.3 :  368.479748 193.182438 344.252014   2.339725   1.242377   1.295119   1.649138   3.262429   4.040244
127273.3 :  681.452425 194.093282 344.252334   4.117628   1.245100   1.295120   1.466655   3.186278   4.040239
127051.6 :  1869.218371  194.045018  344.252325   10.057611    1.244583    1.295120    1.371602    3.202393    4.040239
127026.5 :  2484.683939  194.046190  344.252325   12.615147    1.244593    1.295120    1.368390    3.202187    4.040239
127020.4 :  3015.934037  194.046735  344.252325   14.670637    1.244597    1.295120    1.366952    3.202091    4.040239
127014.7 :  3401.068572  194.046998  344.252325   16.088674    1.244600    1.295120    1.366277    3.202045    4.040239
127013.6 :  3885.722557  194.047256  344.252325   17.818019    1.244602    1.295120    1.365625    3.202000    4.040239
127010.3 :  4198.986993  194.047383  344.252325   18.897890    1.244603    1.295120    1.365310    3.201978    4.040239
127008.1 :  4562.578888  194.047509  344.252325   20.125916    1.244604    1.295120    1.365002    3.201956    4.040239
127007.5 :  4989.344972  194.047633  344.252325   21.536235    1.244605    1.295120    1.364699    3.201935    4.040239
127005.4 :  5243.095172  194.047695  344.252325   22.355415    1.244605    1.295120    1.364550    3.201924    4.040239
127003.6 :  5522.375785  194.047757  344.252325   23.245252    1.244606    1.295120    1.364403    3.201913    4.040239
127002.2 :  5831.171414  194.047818  344.252325   24.215723    1.244606    1.295120    1.364257    3.201903    4.040239
127001.2 :  6174.356430  194.047879  344.252325   25.278894    1.244607    1.295120    1.364113    3.201892    4.040239
127000.8 :  6557.902485  194.047940  344.252325   26.449330    1.244608    1.295120    1.363970    3.201881    4.040239
126999.6 :  6773.580658  194.047970  344.252325   27.097148    1.244608    1.295120    1.363899    3.201876    4.040239
126998.5 :  7003.255902  194.048000  344.252325   27.781106    1.244608    1.295120    1.363829    3.201871    4.040239
126997.5 :  7248.331209  194.048030  344.252325   28.504499    1.244608    1.295120    1.363759    3.201866    4.040239
126996.6 :  7510.407587  194.048060  344.252325   29.271054    1.244609    1.295120    1.363689    3.201860    4.040239
126995.8 :  7791.268345  194.048090  344.252325   30.084858    1.244609    1.295120    1.363620    3.201855    4.040239
126995.2 :  8093.020649  194.048120  344.252325   30.950743    1.244609    1.295120    1.363551    3.201850    4.040239
126994.7 :  8418.045597  194.048150  344.252325   31.874084    1.244609    1.295120    1.363483    3.201845    4.040239
126994.3 :  8769.124882  194.048180  344.252325   32.861118    1.244610    1.295120    1.363414    3.201840    4.040239
126994.2 :  9149.451240  194.048209  344.252325   33.918905    1.244610    1.295120    1.363346    3.201835    4.040239
126993.6 :  9356.137681  194.048224  344.252325   34.487352    1.244610    1.295120    1.363313    3.201832    4.040239
126993 :  9572.080048  194.048239  344.252325   35.077743    1.244610    1.295120    1.363279    3.201829    4.040239
126992.5 :  9797.889275  194.048254  344.252325   35.691382    1.244610    1.295120    1.363246    3.201827    4.040239
126992 :  10034.243206   194.048269   344.252325    36.329713     1.244610     1.295120     1.363212     3.201824     4.040239
126991.5 :  10281.938028   194.048283   344.252325    36.994458     1.244610     1.295120     1.363179     3.201822     4.040239
126991.1 :  10541.771919   194.048298   344.252325    37.687285     1.244611     1.295120     1.363145     3.201819     4.040239
126990.7 :  10814.626049   194.048313   344.252325    38.410030     1.244611     1.295120     1.363112     3.201817     4.040239
126990.4 :  11101.557097   194.048327   344.252325    39.164934     1.244611     1.295120     1.363079     3.201814     4.040239
126990.1 :  11403.651755   194.048342   344.252325    39.954239     1.244611     1.295120     1.363046     3.201812     4.040239
126989.9 :  11722.149649   194.048357   344.252325    40.780508     1.244611     1.295120     1.363013     3.201809     4.040239
126989.7 :  12058.411503   194.048371   344.252325    41.646524     1.244611     1.295120     1.362980     3.201806     4.040239
126989.6 :  12413.895514   194.048386   344.252325    42.555219     1.244611     1.295120     1.362947     3.201804     4.040239
126989.5 :  12790.355654   194.048401   344.252325    43.510169     1.244611     1.295120     1.362915     3.201801     4.040239
Error in nls(formula, data = data, start = start, algorithm = algorithm,  : 
  step factor 0.000488281 reduced below 'minFactor' of 0.000976562
           Wm1      Wm2      Wm3       a1       a2       a3       b1       b2
start 300.0000 300.0000 300.0000 1.500000 1.500000 1.500000 2.200000 2.200000
class 489.9173 615.5279 380.0640 2.342740 2.189602 1.371278 2.397332 2.594862
rob   219.8435 265.9151 343.3879 1.460763 1.493028 1.293623 2.888710 2.837634
            b3
start 2.200000
class 3.594968
rob   4.045572

robustbase documentation built on June 2, 2021, 5:07 p.m.