hildebrand.systems {agridat} | R Documentation

## Multi-environment trial of maize for four cropping systems

### Description

Maize yields for four cropping systems at 14 on-farm trials.

### Format

A data frame with 56 observations on the following 4 variables.

`village`

  village, 2 levels

`farm`

  farm, 14 levels

`system`

  cropping system

`yield`

  yield, t/ha

### Details

Yields from 14 on-farm trials in Phalombe Project region of south-eastern Malawi. The farms were located near two different villages.

On each farm, four different cropping systems were tested. The systems were: LM = Local Maize, LMF = Local Maize with Fertilizer, CCA = Improved Composite, CCAF = Improved Composite with Fertilizer.

### Source

P. E. Hildebrand, 1984. Modified Stability Analysis of Farmer Managed, On-Farm Trials. Agronomy Journal, 76, 271–274. https://doi.org/10.2134/agronj1984.00021962007600020023x

### References

H. P. Piepho, 1998. Methods for Comparing the Yield Stability of Cropping Systems. Journal of Agronomy and Crop Science, 180, 193–213. http://doi.org/10.1111/j.1439-037X.1998.tb00526.x

### Examples

    data(hildebrand.systems)
    dat <- hildebrand.systems

    # Piepho 1998 Fig 1
    require(lattice)
    dotplot(yield ~ system, dat, groups=village, auto.key=TRUE,
            main="hildebrand.systems", xlab="cropping system by village")

    # Plot of risk of 'failure' of System 2 vs System 1
    s11 = .30;  s22 <- .92; s12 = .34
    mu1 = 1.35; mu2 = 2.70
    lambda <- seq(from=0, to=5, length=20)
    system1 <- pnorm((lambda-mu1)/sqrt(s11))
    system2 <- pnorm((lambda-mu2)/sqrt(s22))

    # A simpler view
    plot(lambda, system1, type="l", xlim=c(0,5), ylim=c(0,1),
         xlab="Yield level", ylab="Prob(yield < level)",
         main="hildebrand.systems - risk of failure for each system")
    lines(lambda, system2, col="red")

    # Prob of system 1 outperforming system 2. Table 8
    pnorm((mu1-mu2)/sqrt(s11+s22-2*s12))
    # .0331

    # ----------------------------------------------------------------------------

    ## Not run:
      # asreml3
      require(asreml)
      # Environmental variance model, unstructured correlations

      dat <- dat[order(dat$system, dat$farm),]
      m1 <- asreml(yield ~ system, data=dat, rcov = ~us(system):farm)

      # Means, table 5
      p1 <- predict(m1, data=dat, classify="system")$predictions$pvals
      ##  system pred.value std.error  est.stat
      ##     CCA      1.164    0.2816 Estimable
      ##    CCAF      2.657    0.3747 Estimable
      ##      LM      1.35     0.1463 Estimable
      ##     LMF      2.7      0.2561 Estimable

      # Variances, table 5
      require(lucid)
      vc(m1)[c(2,4,7,11),]
      ##              effect component std.error z.ratio constr
      ##    R!system.CCA:CCA    1.11      0.4354     2.5    pos
      ##  R!system.CCAF:CCAF    1.966     0.771      2.5    pos
      ##      R!system.LM:LM    0.2996    0.1175     2.5    pos
      ##    R!system.LMF:LMF    0.9185    0.3603     2.5    pos

      # Stability variance model
      m2 <- asreml(yield ~ system, data=dat,
                   random = ~ farm,
                   rcov = ~ at(system):units)
      p2 <- predict(m2, data=dat, classify="system")$predictions$pvals

      # Variances, table 6
      vc(m2)
      ##                effect component std.error z.ratio constr
      ##         farm!farm.var 0.2996       0.1175     2.5    pos
      ##   system_CCA!variance 0.4136       0.1622     2.5    pos
      ##  system_CCAF!variance 1.267        0.4969     2.5    pos
      ##    system_LM!variance 0.0000002        NA      NA  bound
      ##   system_LMF!variance 0.5304       0.208      2.5    pos

    ## End(Not run)

    # ----------------------------------------------------------------------------

    ## Not run:
      ## require(asreml4)
      ## # Environmental variance model, unstructured correlations

      ## dat <- dat[order(dat$system, dat$farm),]
      ## m1 <- asreml(yield ~ system, data=dat,
      ##              resid = ~us(system):farm)

      ## # Means, table 5
      ## p1 <- predict(m1, data=dat, classify="system")$pvals
      ## ##  system pred.value std.error  est.stat
      ## ##     CCA      1.164    0.2816 Estimable
      ## ##    CCAF      2.657    0.3747 Estimable
      ## ##      LM      1.35     0.1463 Estimable
      ## ##     LMF      2.7      0.2561 Estimable

      ## # Variances, table 5
      ## require(lucid)
      ## vc(m1)[c(2,4,7,11),]
      ## ##              effect component std.error z.ratio constr
      ## ##    R!system.CCA:CCA    1.11      0.4354     2.5    pos
      ## ##  R!system.CCAF:CCAF    1.966     0.771      2.5    pos
      ## ##      R!system.LM:LM    0.2996    0.1175     2.5    pos
      ## ##    R!system.LMF:LMF    0.9185    0.3603     2.5    pos

      ## # Stability variance model
      ## m2 <- asreml(yield ~ system, data=dat,
      ##              random = ~ farm,
      ##              resid = ~ dsum( ~ units|system))
      ## m2 <- update(m2)
      ## p2 <- predict(m2, data=dat, classify="system")$pvals

      ## # Variances, table 6
      ## vc(m2)
      ## ##                effect component std.error z.ratio constr
      ## ##         farm!farm.var 0.2996       0.1175     2.5    pos
      ## ##   system_CCA!variance 0.4136       0.1622     2.5    pos
      ## ##  system_CCAF!variance 1.267        0.4969     2.5    pos
      ## ##    system_LM!variance 0.0000002        NA      NA  bound
      ## ##   system_LMF!variance 0.5304       0.208      2.5    pos

    ## End(Not run)

[Package agridat version 1.16 Index]