variogram | R Documentation |
Computes the sample variogram from an SpATS
object.
## S3 method for class 'SpATS'
variogram(x, ...)
x |
an object of class |
... |
further arguments passed to or from other methods. Not yet implemented |
The present function computes the sample variogram on the basis of the (deviance) residuals of the fitted model. Currently, the function can only be applied for regular two-dimensional data, i.e, when the plots of the field are arranged in a regular two-dimensional array (usually defined by the column and row positions).
For each pair of (deviance) residuals e_i
and e_j
, the half-squared difference is computed
v_{ij} = 0.5(e_i - e_j)^2,
as well as the corresponding column (cd_{ij}
) and row displacements (rd_{ij}
), with
cd_{ij} = |c_i - c_j|
and
rd_{ij} = |r_i - r_j|,
where c_k
and r_k
denote the column and row position of plot k
respectively. The sample variogram is then defined as the triplet
(cd_{ij}, rd_{ij}, \bar{v}_{ij}),
where \bar{v}_{ij}
denotes the average of the v_{ij}
that share the same column and row displacements.
For a more detailed description, see Gilmour et al. (1997).
An object of class variogram.SpATS
with the following components:
data |
data frame including the following information: “value”: the value of the sample variogram at each pair of column and row displacements; and “length”: the number of observations used to compute the sample variogram at the corresponding pair of displacements. |
col.displacement |
numerical vector containing the column displacements |
row.displacement |
numerical vector containing the row displacements |
Gilmour, A.R., Cullis, B.R., and Verbyla, A.P. (1997). Accounting for Natural and Extraneous Variation in the Analysis of Field Experiments. Journal of Agricultural, Biological, and Environmental Statistics, 2, 269 - 293.
Stefanova, K.T., Smith, A.B. and Cullis, B.R. (2009). Enhanced Diagnostics for the Spatial Analysis of Field Trials. Journal of Agricultural, Biological, and Environmental Statistics, 14, 392 - 410.
SpATS
, plot.variogram.SpATS
library(SpATS)
data(wheatdata)
wheatdata$R <- as.factor(wheatdata$row)
wheatdata$C <- as.factor(wheatdata$col)
m0 <- SpATS(response = "yield", spatial = ~ SAP(col, row, nseg = c(10,20), degree = 3, pord = 2),
genotype = "geno", fixed = ~ colcode + rowcode, random = ~ R + C, data = wheatdata,
control = list(tolerance = 1e-03))
# Compute the variogram
var.m0 <- variogram(m0)
# Plot the variogram
plot(var.m0)
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