agridat (version 1.8.1)

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.

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. 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

# 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
# Aastveit Figure 1.  PCA of height
biplot(prcomp(Z), main="aastveit.barley - 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)