Barley heights and environmental covariates in Norway

Average height for 15 genotypes of barley in each of 9 years. Also 19 covariates in each of the 9 years.

Usage

data("aastveit.barley.covs")
data("aastveit.barley.height")

Format

The 'aastveit.barley.covs' dataframe has 9 observations on the following 20 variables.

year: year
R1: avg rainfall (mm/day) in period 1
R2: avg rainfall (mm/day) in period 2
R3: avg rainfall (mm/day) in period 3
R4: avg rainfall (mm/day) in period 4
R5: avg rainfall (mm/day) in period 5
R6: avg rainfall (mm/day) in period 6
S1: daily solar radiation (ca/cm^2) in period 1
S2: daily solar radiation (ca/cm^2) in period 2
S3: daily solar radiation (ca/cm^2) in period 3
S4: daily solar radiation (ca/cm^2) in period 4
S5: daily solar radiation (ca/cm^2) in period 5
S6: daily solar radiation (ca/cm^2) in period 6
ST: sowing time, measured in days after April 1
T1: avg temp (deg Celsius) in period 1
T2: avg temp (deg Celsius) in period 2
T3: avg temp (deg Celsius) in period 3
T4: avg temp (deg Celsius) in period 4
T5: avg temp (deg Celsius) in period 5
T6: avg temp (deg Celsius) in period 6

The 'aastveit.barley.height' dataframe has 135 observations on the following 3 variables.

year: year, 9 years spanning from 1974 to 1982
gen: genotype, 15 levels
height: height (cm)

Details

Experiments were conducted at As, Norway.

The height dataframe contains average plant height (cm) of 15 varieties of barley in each of 9 years.

The growth season of each year was divided into eight periods from sowing to harvest. Because the plant stop growing about 20 days after ear emergence, only the first 6 periods are included here.

Used with permission of Harald Martens.

Source

Aastveit, A. H. and Martens, H. (1986). ANOVA interactions interpreted by partial least squares regression. Biometrics, 42, 829–844. https://doi.org/10.2307/2530697

References

J. Chadoeuf and J. B. Denis (1991). Asymptotic variances for the multiplicative interaction model. J. App. Stat., 18, 331-353. https://doi.org/10.1080/02664769100000032

Examples

if (FALSE) { # \dontrun{

library(agridat)
data("aastveit.barley.covs")
data("aastveit.barley.height")

libs(reshape2, pls)
  
  # First, PCA of each matrix separately

  Z <- acast(aastveit.barley.height, year ~ gen, value.var="height")
  Z <- sweep(Z, 1, rowMeans(Z))
  Z <- sweep(Z, 2, colMeans(Z)) # Double-centered
  sum(Z^2)*4 # Total SS = 10165
  sv <- svd(Z)$d
  round(100 * sv^2/sum(sv^2),1) # Prop of variance each axis
  # Aastveit Figure 1.  PCA of height
  biplot(prcomp(Z),
         main="aastveit.barley - height", cex=0.5)
  
  U <- aastveit.barley.covs
  rownames(U) <- U$year
  U$year <- NULL
  U <- scale(U) # Standardized covariates
  sv <- svd(U)$d
  # Proportion of variance on each axis
  round(100 * sv^2/sum(sv^2),1)

  # Now, PLS relating the two matrices
  m1 <- plsr(Z~U)
  loadings(m1)
  # Aastveit Fig 2a (genotypes), but rotated differently
  biplot(m1, which="y", var.axes=TRUE)
  # Fig 2b, 2c (not rotated)
  biplot(m1, which="x", var.axes=TRUE)

  # Adapted from section 7.4 of Turner & Firth,
  # "Generalized nonlinear models in R: An overview of the gnm package"
  # who in turn reproduce the analysis of Chadoeuf & Denis (1991),
  # "Asymptotic variances for the multiplicative interaction model"

  libs(gnm)
  dath <- aastveit.barley.height
  dath$year = factor(dath$year)

  set.seed(42)
  m2 <- gnm(height ~ year + gen + Mult(year, gen), data = dath)
  # Turner: "To obtain parameterization of equation 1, in which sig_k is the
  # singular value for component k, the row and column scores must be constrained
  # so that the scores sum to zero and the squared scores sum to one.
  # These contrasts can be obtained using getContrasts"
  gamma <- getContrasts(m2, pickCoef(m2, "[.]y"),
                        ref = "mean", scaleWeights = "unit")
  delta <- getContrasts(m2, pickCoef(m2, "[.]g"),
                        ref = "mean", scaleWeights = "unit")
  # estimate & std err
  gamma <- gamma$qvframe
  delta <- delta$qvframe
  # change sign of estimate
  gamma[,1] <- -1 * gamma[,1]
  delta[,1] <- -1 * delta[,1]
  # conf limits based on asymptotic normality, Chadoeuf table 8, p. 350, 
  round(cbind(gamma[,1], gamma[, 1] +
                           outer(gamma[, 2], c(-1.96, 1.96))) ,3)  
  round(cbind(delta[,1], delta[, 1] +
                           outer(delta[, 2], c(-1.96, 1.96))) ,3)
} # }