digby.jointregression {agridat} | R Documentation

## Multi-environment trial of wheat

### Description

Yield of 10 spring wheat varieties for 17 locations in 1976.

### Format

A data frame with 134 observations on the following 3 variables.

`gen`

  genotype, 10 levels

`env`

  environment, 17 levels

`yield`

  yield (t/ha)

### Details

Yield of 10 spring wheat varieties for 17 locations in 1976.

Used to illustrate modified joint regression.

### Source

Digby, P.G.N. (1979). Modified joint regression analysis for incomplete variety x environment data. Journal of Agricultural Science, 93, 81-86. http://doi.org/10.1017/S0021859600086159

### References

Hans-Pieter Piepho, 1997. Analyzing Genotype-Environment Data by Mixed-Models with Multiplicative Terms. Biometrics, 53, 761-766. http://doi.org/10.2307/2533976

RJOINT procedure in GenStat. http://www.vsni.co.uk/software/genstat/htmlhelp/server/RJOINT.htm

### Examples

    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

    }

    require(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

    # How to use gnm package for this?
    # require(gnm)
    # m3 <- gnm(yield ~ gen + Mult(gen,env), data=dat) # slopes negated

[Package agridat version 1.16 Index]