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# asr_variogram – Emperical variogram

###### Description

asr_varioGram calculates the empirical variogram from regular or irregular one or two dimensional data.

###### Usage
asr_varioGram(x, y, z, composite = TRUE, model = c("empirical"),
metric = c("euclidean", "manhattan"), angle = 0, angle.tol = 180,
nlag = 20, maxdist = 0.5, xlag = NA, lag.tol = 0.5, grid = TRUE)
###### Arguments
 x Numeric vector of x coordinates, may also be a matrix or data frame with 2 or 3 columns. If ncol(x) is 3, the columns are taken to be the x and y coordinates and the response (z), respectively. If ncol(x) is 2, the columns are taken to be the x coordinates and the response, respectively. In this case the y coordinates are generated as rep(1,nrow(x)). y Numeric vector of y coordinates. z The response vector. composite For data on a regular grid. If TRUE, the average of the variograms in quadrants (x,y) and (x,-y) is returned. Otherwise, both variograms are returned and identiﬁed as quadrants 1 and 4. model Can only be “empirical” at present. metric The distance between (x,y) points. Valid measures are “euclidean” or “manhattan“. angle A vector of directions. Angles are measured in degrees anticlockwise from the x axis. Default is 0. angle.tol The angle subtended by each direction. That is, an arc angle+- angle.tol/2. Default is 180 which gives an omnidirectional variogram. nlag The maximum number of lags; default is 20. maxdist The fraction of the maximum distance to include in the calculation. The default is half the maximum distance in the data. xlag The width of the lags. If missing, xlag is set to maxdist/nlag. lag.tol The distance tolerance. If missing, lag.tol is set to xlag/2. grid If FALSE, forces polar variograms if (x,y) speciﬁes a regular grid; default is TRUE.
###### Details

For one dimensional data the y coordinates need not be supplied and a vector of ones is generated. The function identiﬁes data on a complete regular array and in such cases only computes polar variograms If grid = FALSE. The data is assumed sorted with the x coordinates changing the fastest; the data is sorted internally if this is not the case.

###### Value
 A data frame including the following components: x The original x coordinates. y The original y coordinates. gamma The variogram estimate. distance The average distance for pairs in the lag. np The number of pairs in the lag. angle Direction if not a regular grid.
###### References

Webster W and Oliver MA (2001). Geostatistics for Environmental Scientists. John Wiley: West Sussex.

Updated on August 7, 2018