R: Wheat Yields from Mexican Field Trials

wheat {gnm} | R Documentation

## Wheat Yields from Mexican Field Trials

### Description

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.

### Usage

    wheat

### Format

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

### Source

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.

### Examples

    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)

[Package gnm version 1.1-2 Index]