wheat | R Documentation |

Data from a 10-year experiment at the CIMMYT experimental station located in the Yaqui Valley near Ciudad Obregon, Sonora, Mexico — factorial design using 24 treatments in all. In each of the 10 years the experiment was arranged in a randomized complete block design with three replicates.

wheat

A data frame with 240 observations on the following 33 variables.

- yield
numeric, mean yield in kg/ha for 3 replicates

- year
a factor with levels

`1988:1997`

- tillage
a factor with levels

`T`

`t`

- summerCrop
a factor with levels

`S`

`s`

- manure
a factor with levels

`M`

`m`

- N
a factor with levels

`0`

`N`

`n`

- MTD
numeric, mean max temp sheltered (deg C) in December

- MTJ
same for January

- MTF
same for February

- MTM
same for March

- MTA
same for April

- mTD
numeric, mean min temp sheltered (deg C) in December

- mTJ
same for January

- mTF
same for February

- mTM
same for March

- mTA
same for April

- mTUD
numeric, mean min temp unsheltered (deg C)in December

- mTUJ
same for January

- mTUF
same for February

- mTUM
same for March

- mTUA
same for April

- PRD
numeric, total precipitation (mm) in December

- PRJ
same for January

- PRF
same for February

- PRM
same for March

- SHD
numeric, mean sun hours in December

- SHJ
same for January

- SHF
same for February

- EVD
numeric, total evaporation (mm) in December

- EVJ
same for January

- EVF
same for February

- EVM
same for March

- EVA
same for April

Tables A1 and A3 of
Vargas, M, Crossa, J, van Eeuwijk, F, Sayre, K D and Reynolds, M P
(2001). Interpreting treatment by environment interaction in agronomy
trials. *Agronomy Journal* **93**, 949–960.

set.seed(1) ## Scale yields to reproduce analyses reported in Vargas et al (2001) yield.scaled <- wheat$yield * sqrt(3/1000) ## Reproduce (up to error caused by rounding) Table 1 of Vargas et al (2001) aov(yield.scaled ~ year*tillage*summerCrop*manure*N, data = wheat) treatment <- interaction(wheat$tillage, wheat$summerCrop, wheat$manure, wheat$N, sep = "") mainEffects <- lm(yield.scaled ~ year + treatment, data = wheat) svdStart <- residSVD(mainEffects, year, treatment, 3) bilinear1 <- update(asGnm(mainEffects), . ~ . + Mult(year, treatment), start = c(coef(mainEffects), svdStart[,1])) bilinear2 <- update(bilinear1, . ~ . + Mult(year, treatment, inst = 2), start = c(coef(bilinear1), svdStart[,2])) bilinear3 <- update(bilinear2, . ~ . + Mult(year, treatment, inst = 3), start = c(coef(bilinear2), svdStart[,3])) anova(mainEffects, bilinear1, bilinear2, bilinear3) ## Examine the extent to which, say, mTF explains the first bilinear term bilinear1mTF <- gnm(yield.scaled ~ year + treatment + Mult(1 + mTF, treatment), family = gaussian, data = wheat) anova(mainEffects, bilinear1mTF, bilinear1) ## How to get the standard SVD representation of an AMMI-n model ## ## We'll work with the AMMI-2 model, which here is called "bilinear2" ## ## First, extract the contributions of the 5 terms in the model: ## wheat.terms <- termPredictors(bilinear2) ## ## That's a matrix, whose 4th and 5th columns are the interaction terms ## ## Combine those two interaction terms, to get the total estimated ## interaction effect: ## wheat.interaction <- wheat.terms[, 4] + wheat.terms[, 5] ## ## That's a vector, so we need to re-shape it as a 24 by 10 matrix ## ready for calculating the SVD: ## wheat.interaction <- matrix(wheat.interaction, 24, 10) ## ## Now we can compute the SVD: ## wheat.interaction.SVD <- svd(wheat.interaction) ## ## Only the first two singular values are nonzero, as expected ## (since this is an AMMI-2 model, the interaction has rank 2) ## ## So the result object can be simplified by re-calculating the SVD with ## just two dimensions: ## wheat.interaction.SVD <- svd(wheat.interaction, nu = 2, nv = 2)

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