Barley heights and environmental covariates in Norway

Description

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

## Not run: 

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)

## End(Not run)