# variogram: Sample variogram In SpATS: Spatial Analysis of Field Trials with Splines

### Description

Computes the sample variogram from an SpATS object.

### Usage

 1 2 ## 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.

SpATS, plot.variogram.SpATS

### Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 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) 

SpATS documentation built on May 19, 2017, 4:44 p.m.
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