agridat (version 1.5)

aastveit.barley: Barley heights and environmental covariates in Norway

Description

Average height for 15 genotypes of barley in each of 9 years. A second matrix contains 19 covariates in each of 9 years.

Usage

data(aastveit.barley)

format

A list of two matrices, height and covs. See details below.

source

Aastveit, A. H. and Martens, H. (1986). ANOVA interactions interpreted by partial least squares regression. Biometrics, 42, 829--844. Used with permission of Harald Martens.

Details

Experiments were conducted at As, Norway. Four blocks per year. The height matrix contains average plant height (cm) of 15 varieties of barley in each of 9 years. The covs matrix contains 19 environmental covariates for each year. ll{ ST Sowing date T1-T6 Avg temp (deg Celsius) in period 1, ..., 6 R1-R6 Avg rainfall (mm/day) in period 1, ..., 6 S1-S6 Daily solar radiation (ca/cm^2) in period 1, ..., 6 }

References

Chadoeuf, J and Denis, J B (1991). Asymptotic variances for the multiplicative interaction model. J. App. Stat. 18, 331--353.

Examples

data(aastveit.barley)

# First, PCA of each matrix separately

Z <- aastveit.barley$height
Z <- sweep(Z, 1, rowMeans(Z))
Z <- sweep(Z, 2, colMeans(Z)) # Double-centered
sum(Z^2)*4 # Total SS
sv <- svd(Z)$d
round(100 * sv^2/sum(sv^2),1) # Prop of variance each axis
biplot(prcomp(Z)) # Aastveit Figure 1.  PCA of height

U <- aastveit.barley$covs
U <- scale(U) # Standardized covariates
sv <- svd(U)$d
round(100 * sv^2/sum(sv^2),1) # Prop variance each axis

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