vgram: Traditional or robust variogram methods for spatial data

Description

vgram computes pairwise squared differences as a function of distance. Returns an S3 object of class "vgram" with either raw values or statistics from binning. crossCoVGram is the same as vgram but differences are taken across different variables rather than the same variable.

plot.vgram and boxplotVGram create lineplots and boxplots of vgram objects output by the vgram function. boxplotVGram plots the base R boxplot function, and plots estimates of the mean over the boxplot.

The getVGMean function returns the bin centers and means of the vgram object based on the bin breaks provided by the user.

Usage

vgram(loc, y, id = NULL, d = NULL, lon.lat = FALSE, 
                    dmax = NULL, N = NULL, breaks = NULL, prettyBins = FALSE,
                    type=c("variogram", "covariogram", "correlogram"))
crossCoVGram(loc1, loc2, y1, y2, id = NULL, d = NULL, lon.lat = FALSE, 
                        dmax = NULL, N = NULL, breaks = NULL, 
                        type=c("cross-covariogram", "cross-correlogram"),
                        prettyBins = FALSE)
boxplotVGram(x, N=10, breaks = pretty(x$d, N, eps.correct = 1), plot=TRUE, plot.args, ...)
# S3 method for vgram
plot(x, N=10, breaks = pretty(x$d, N, eps.correct = 1), add=FALSE, ...)
getVGMean(x, N = 10, breaks = pretty(x$d, N, eps.correct = 1))

Value

vgram and crossCoVGram return a "vgram" object containing the following values:

vgram: Variogram or covariogram values
d: Pairwise distances
call: Calling string
stats: Matrix of statistics for values in each bin. Rows are the summaries returned by the stats function or describe. If not either breaks or N arguments are not supplied then this component is not computed.
centers: Bin centers.

If boxplotVGram is called with plot=FALSE, it returns a list with the same components as returned by bplot.xy

Arguments

loc: Matrix where each row is the coordinates of an observed point of the field
y: Value of the field at locations
loc1: Matrix where each row is the coordinates of an observed point of field 1
loc2: Matrix where each row is the coordinates of an observed point of field 2
y1: Value of field 1 at locations
y2: Value of field 2 at locations
id: A 2 column matrix that specifies which variogram differnces to find. If omitted all possible pairing are found. This can used if the data has an additional covariate that determines proximity, for example a time window.
d: Distances among pairs indexed by id. If not included distances from from directly from loc.
lon.lat: If true, locations are assumed to be longitudes and latitudes and distances found are great circle distances (in miles see rdist.earth). Default is FALSE.
dmax: Maximum distance to compute variogram.
N: Number of bins to use. The break points are found by the pretty function and so ther may not be exactly N bins. Specify the breaks explicity if you want excalty N bins.
breaks: Bin boundaries for binning variogram values. Need not be equally spaced but must be ordered.
x: An object of class "vgram" (an object returned by vgram)
add: If TRUE, adds empirical variogram lineplot to current plot. Otherwise creates new plot with empirical variogram lineplot.
plot: If TRUE, creates a plot, otherwise returns variogram statistics output by bplot.xy.
plot.args: Additional arguments to be passed to plot.vgram.
prettyBins: If FALSE creates exactly N-1 bins. If TRUE you are at the mercy of giving N to the pretty function!
type: One of "variogram", "covariogram", "correlogram", "cross-covariogram", and "cross-correlogram". vgram supports the first three of these and crossCoVGram supports the last two.
...: Additional argument passed to plot for plot.vgram or to bplot.xy for boxplotVGram.

Author

John Paige, Doug Nychka

References

See any standard reference on spatial statistics. For example Cressie, Spatial Statistics

Examples

Run this code

#
# compute variogram for the midwest ozone field  day 16
# (BTW this looks a bit strange!)
#
data( ozone2)
good<- !is.na(ozone2$y[16,])
x<- ozone2$lon.lat[good,] 
y<- ozone2$y[16,good]

look<-vgram( x,y, N=15, lon.lat=TRUE) # locations are in lon/lat so use right
#distance
# take a look:
plot(look, pch=19)
#lines(look$centers, look$stats["mean",], col=4)

brk<- seq( 0, 250,, (25 + 1) ) # will give 25 bins.
 
## or some boxplot bin summaries using base R graphics
look<-vgram( x,y, N=45, lon.lat=TRUE) 
bplot.xy( look$d, look$vgram,
          breaks=look$breaks, outline=FALSE,
          xlim=c( 0,250), xlab="miles", 
          ylim=c( 0, 2000), ylab="Variogram")
lines( look$centers, look$stats[2,], type="b",
col="magenta", pch=16)

#
# compute equivalent covariogram, but leave out the boxplots
#
look<-vgram( x,y, N=15, lon.lat=TRUE, type="covariogram")
plot(look, breaks=brk, col=4)

#
# compute equivalent cross-covariogram of the data with itself 
#(it should look almost exactly the same as the covariogram of 
#the original data, except with a few more points in the 
#smallest distance boxplot and points are double counted)
#
look = crossCoVGram(x, x, y, y, N=15, lon.lat=TRUE, type="cross-covariogram")
plot(look, breaks=brk, col=4)

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