aastveit.barley {agridat} | R Documentation |

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.

`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 date

`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

`value`

value of the covariate

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

`year`

year, 9

`gen`

genotype, 15 levels

`height`

height (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) ## End(Not run)

[Package *agridat* version 1.18 Index]