Sample variogram

Description

Computes the sample variogram from an SpATS object.

Usage

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## S3 method for class 'SpATS'
variogram(x, ...)

Arguments

x

an object of class SpATS as produced by SpATS().

...

further arguments passed to or from other methods. Not yet implemented

Details

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).

Value

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

References

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.

See Also

SpATS, plot.variogram.SpATS

Examples

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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)