Multi-environment trial of wheat
Yield of 10 spring wheat varieties for 17 locations in 1976.
A data frame with 134 observations on the following 3 variables.
gen
genotype, 10 levels
env
environment, 17 levels
yield
yield (t/ha)
Yield of 10 spring wheat varieties for 17 locations in 1976.
Used to illustrate modified joint regression.
Digby, P.G.N. (1979). Modified joint regression analysis for incomplete variety x environment data. Journal of Agricultural Science, 93, 81-86. https://doi.org/10.1017/S0021859600086159
Hans-Pieter Piepho, 1997. Analyzing Genotype-Environment Data by Mixed-Models with Multiplicative Terms. Biometrics, 53, 761-766. https://doi.org/10.2307/2533976
RJOINT procedure in GenStat. https://www.vsni.co.uk/software/genstat/htmlhelp/server/RJOINT.htm
## Not run: library(agridat) data(digby.jointregression) dat <- digby.jointregression # Simple gen means, ignoring unbalanced data. # Matches Digby table 2, Unadjusted Mean round(tapply(dat$yield, dat$gen, mean),3) # Two-way model. Matches Digby table 2, Fitting Constants m00 <- lm(yield ~ 0 + gen + env, dat) round(coef(m00)[1:10]-2.756078+3.272,3) # Adjust intercept # genG01 genG02 genG03 genG04 genG05 genG06 genG07 genG08 genG09 genG10 # 3.272 3.268 4.051 3.724 3.641 3.195 3.232 3.268 3.749 3.179 n.gen <- nlevels(dat$gen) n.env <- nlevels(dat$env) # Estimate theta (env eff) m0 <- lm(yield ~ -1 + env + gen, dat) thetas <- coef(m0)[1:n.env] thetas <- thetas-mean(thetas) # center env effects # Add env effects to the data dat$theta <- thetas[match(paste("env",dat$env,sep=""), names(thetas))] # Initialize beta (gen slopes) at 1 betas <- rep(1, n.gen) done <- FALSE while(!done){ betas0 <- betas # M1: Fix thetas (env effects), estimate beta (gen slope) m1 <- lm(yield ~ -1 + gen + gen:theta, data=dat) betas <- coef(m1)[-c(1:n.gen)] dat$beta <- betas[match(paste("gen",dat$gen,":theta",sep=""), names(betas))] # print(betas) # M2: Fix betas (gen slopes), estimate theta (env slope) m2 <- lm(yield ~ env:beta + gen -1, data=dat) thetas <- coef(m2)[-c(1:n.gen)] thetas[is.na(thetas)] <- 0 # Change last coefficient from NA to 0 dat$theta <- thetas[match(paste("env",dat$env,":beta",sep=""), names(thetas))] # print(thetas) # Check convergence chg <- sum(((betas-betas0)/betas0)^2) cat("Relative change in betas",chg,"\n") if(chg < .0001) done <- TRUE } libs(lattice) xyplot(yield ~ theta|gen, data=dat, xlab="theta (environment effect)", main="digby.jointregression - stability plot") # Dibgy Table 2, modified joint regression # Genotype sensitivities (slopes) round(betas,3) # Match Digby table 2, Modified joint regression sensitivity # genG01 genG02 genG03 genG04 genG05 genG06 genG07 genG08 genG09 genG10 # 0.953 0.739 1.082 1.024 1.142 0.877 1.089 0.914 1.196 0.947 # Env effects. Match Digby table 3, Modified joint reg round(thetas,3)+1.164-.515 # Adjust intercept to match # envE01 envE02 envE03 envE04 envE05 envE06 envE07 envE08 envE09 envE10 # -0.515 -0.578 -0.990 -1.186 1.811 1.696 -1.096 0.046 0.057 0.825 # envE11 envE12 envE13 envE14 envE15 envE16 envE17 # -0.576 1.568 -0.779 -0.692 0.836 -1.080 0.649 # Using 'gnm' gives similar results. # libs(gnm) # m3 <- gnm(yield ~ gen + Mult(gen,env), data=dat) # slopes negated # round(coef(m3)[11:20],3) # Using 'mumm' gives similar results, though gen is random and the # coeffecients are shrunk toward 0 a bit. libs(mumm) m1 <- mumm(yield ~ -1 + env + mp(gen, env), dat) round(1 + ranef(m1)$`mp gen:env`,2) ## End(Not run)
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