Barley heights and environmental covariates in Norway

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

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.

Used with permission of Harald Martens.

Source

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

References

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

Examples

# \dontrun{

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

libs(reshape2, pls)
#> 
#> Attaching package: 'pls'
#> The following object is masked from 'package:stats':
#> 
#>     loadings
  
  # 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
#> [1] 10165.55
  sv <- svd(Z)$d
  round(100 * sv^2/sum(sv^2),1) # Prop of variance each axis
#> [1] 74.4  7.9  5.0  4.8  3.6  2.1  1.4  0.7  0.0
  # 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
  # Proportion of variance on each axis
  round(100 * sv^2/sum(sv^2),1)
#> [1] 33.5 18.4 16.5 13.9  8.8  4.4  2.4  2.1  0.0

  # Now, PLS relating the two matrices
  m1 <- plsr(Z~U)
  loadings(m1)
#> 
#> Loadings:
#>    Comp 1 Comp 2 Comp 3 Comp 4 Comp 5 Comp 6 Comp 7 Comp 8
#> R1 -0.131  0.232 -0.345  0.411         0.140 -0.157  0.130
#> R2  0.141        -0.139  0.549 -0.343         0.148       
#> R3                0.505  0.231 -0.125        -0.163       
#> R4  0.358               -0.174  0.123  0.103 -0.182  0.420
#> R5  0.152  0.425  0.150         0.141  0.141  0.495 -0.300
#> R6  0.230 -0.362 -0.211  0.173  0.148 -0.129              
#> S1  0.172 -0.427  0.191                0.331  0.124       
#> S2        -0.122        -0.509  0.281 -0.554  0.106       
#> S3        -0.135 -0.388 -0.226  0.230  0.297        -0.448
#> S4 -0.284 -0.290 -0.238        -0.157                     
#> S5 -0.345 -0.206                       0.250 -0.320 -0.138
#> S6 -0.349  0.249                       0.138  0.132 -0.120
#> ST  0.299 -0.117               -0.417         0.110 -0.239
#> T1  0.243 -0.169  0.316  0.175 -0.209  0.196  0.106 -0.271
#> T2  0.156  0.197        -0.353 -0.440 -0.261 -0.217       
#> T3  0.318 -0.144 -0.244                       0.239  0.410
#> T4 -0.110 -0.315        -0.201 -0.482  0.151  0.266  0.143
#> T5 -0.239 -0.105  0.331 -0.105        -0.388  0.274  0.325
#> T6 -0.267  0.170 -0.131  0.331         0.318  0.467  0.184
#> 
#>                Comp 1 Comp 2 Comp 3 Comp 4 Comp 5 Comp 6 Comp 7 Comp 8
#> SS loadings     1.025  1.024  1.020  1.230  1.013  1.055  1.000  1.000
#> Proportion Var  0.054  0.054  0.054  0.065  0.053  0.056  0.053  0.053
#> Cumulative Var  0.054  0.108  0.162  0.226  0.280  0.335  0.388  0.440
  # 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)

  # 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"

  libs(gnm)
  dath <- aastveit.barley.height
  dath$year = factor(dath$year)

  set.seed(42)
  m2 <- gnm(height ~ year + gen + Mult(year, gen), data = dath)
#> Initialising
#> Running start-up iterations..
#> Running main iterations........
#> Done
  # 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)  
#>         [,1]   [,2]   [,3]
#>  [1,] -0.227 -0.337 -0.116
#>  [2,] -0.514 -0.609 -0.418
#>  [3,] -0.439 -0.539 -0.339
#>  [4,]  0.200  0.090  0.311
#>  [5,]  0.533  0.440  0.627
#>  [6,] -0.142 -0.254 -0.030
#>  [7,]  0.332  0.226  0.439
#>  [8,]  0.176  0.064  0.287
#>  [9,]  0.079 -0.034  0.192
  round(cbind(delta[,1], delta[, 1] +
                           outer(delta[, 2], c(-1.96, 1.96))) ,3)
#>         [,1]   [,2]   [,3]
#>  [1,] -0.079 -0.195  0.037
#>  [2,] -0.008 -0.124  0.109
#>  [3,] -0.170 -0.284 -0.055
#>  [4,]  0.047 -0.069  0.163
#>  [5,] -0.181 -0.296 -0.067
#>  [6,] -0.129 -0.245 -0.014
#>  [7,] -0.014 -0.130  0.103
#>  [8,]  0.422  0.318  0.527
#>  [9,]  0.271  0.159  0.382
#> [10,]  0.335  0.226  0.444
#> [11,]  0.376  0.269  0.483
#> [12,] -0.285 -0.396 -0.174
#> [13,]  0.168  0.054  0.283
#> [14,] -0.293 -0.404 -0.182
#> [15,] -0.460 -0.563 -0.358
# }