Example of yield stability analysis
Translation of an example that may be found at
https://www.r-bloggers.com/2019/06/genotype-experiments-fitting-a-stability-variance-model-with-r/,
based on yield of eight durum wheat genotypes over seven years, following a randomised block design with three replicates.
A genotype-in-year random effect is used to quantify genotype-by-environment interactions.
In the first fit (constvar), the variance of this random effect is constant over genotypes.
In the second fit (varvar), different variances are fitted for the distinct genotypes, to assess the relative stability of yield of the different genotypes over environments. This second model can be fitted as a
constrained random-coefficient model, where the constraint describes a diagonal covariance matrix for the random coefficients.
This example uses the fact that the argument fixed=list(ranCoefs=<...>) can be used to fit a
covariance matrix with an arbitrary set of constrained elements. Only elements
left as 'NA' (here the diagonal elements of the matrix) are fitted.
if (spaMM.getOption("example_maxtime")>1.5 &&
requireNamespace("agridat", quietly = TRUE)) {
data("onofri.winterwheat", package="agridat")
(constvar <- fitme(
yield ~ gen + (1|year) + (1|block %in% year)+(1|gen %in% year),
data=onofri.winterwheat, method="REML"))
# Diagonal matrix of NA's, represented as vector for its lower triangle:
ranCoefs_for_diag <- function(nlevels) {
## Conceptual version
# diagmat <- matrix(NA, ncol=nlevels,nrow=nlevels)
# diagmat[lower.tri(diagmat,diag=FALSE)] <- 0
# diagmat[lower.tri(diagmat,diag=TRUE)]
## which amount to:
vec <- rep(0,nlevels*(nlevels+1L)/2L)
vec[cumsum(c(1L,rev(seq(nlevels-1L)+1L)))] <- NA
vec
}
(varvar <- fitme(
yield ~ gen + (1|year) + (1|block %in% year)+(0+gen|gen %in% year), method="REML",
data=onofri.winterwheat, fixed=list(ranCoefs=list("3"=ranCoefs_for_diag(8L)))))
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