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.
data("aastveit.barley.covs")
data("aastveit.barley.height")The 'aastveit.barley.covs' dataframe has 9 observations on the following 20 variables.
yearyear
R1avg rainfall (mm/day) in period 1
R2avg rainfall (mm/day) in period 2
R3avg rainfall (mm/day) in period 3
R4avg rainfall (mm/day) in period 4
R5avg rainfall (mm/day) in period 5
R6avg rainfall (mm/day) in period 6
S1daily solar radiation (ca/cm^2) in period 1
S2daily solar radiation (ca/cm^2) in period 2
S3daily solar radiation (ca/cm^2) in period 3
S4daily solar radiation (ca/cm^2) in period 4
S5daily solar radiation (ca/cm^2) in period 5
S6daily solar radiation (ca/cm^2) in period 6
STsowing date
T1avg temp (deg Celsius) in period 1
T2avg temp (deg Celsius) in period 2
T3avg temp (deg Celsius) in period 3
T4avg temp (deg Celsius) in period 4
T5avg temp (deg Celsius) in period 5
T6avg temp (deg Celsius) in period 6
valuevalue of the covariate
The 'aastveit.barley.height' dataframe has 135 observations on the following 3 variables.
yearyear, 9
gengenotype, 15 levels
heightheight (cm)
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.
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
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
## 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)
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