aastveit.barley {agridat} | R Documentation

## Barley heights and environmental covariates in Norway

### Description

Average height for 15 genotypes of barley in each of 9 years. Also 19 covariates in each of the 9 years.

### Usage

    data("aastveit.barley.covs")
    data("aastveit.barley.height")

### Format

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)

### Details

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.

### Source

Aastveit, A. H. and Martens, H. (1986). ANOVA interactions interpreted by partial least squares regression. Biometrics, 42, 829–844. http://doi.org/10.2307/2530697

Used with permission of Harald Martens.

### References

J. Chadoeuf and J. B. Denis (1991). Asymptotic variances for the multiplicative interaction model. J. App. Stat. 18, 331-353. http://doi.org/10.1080/02664769100000032

### Examples

    data("aastveit.barley.covs")
    data("aastveit.barley.height")

    if(require(reshape2) & require(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
      round(100 * sv^2/sum(sv^2),1) # Proportion of variance on each axis

      ## Not run:
      # 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)

    ## End(Not run)

    }

    ## Not run:
      # 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"

      require(agridat)
      require(gnm)
      data("aastveit.barley.height")
      dath <- aastveit.barley.height
      dath$year = factor(dath$year)

      set.seed(1)
      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 1.16 Index]