variocloudmap {GeoXp}R Documentation

Interactive variocloud and map

Description

The function variocloudmap() draws a semi-variocloud (directional or omnidirectional) and a map. It is used to detect spatial autocorrelation. Possibility to draw the empirical semi-variogram and a robust empirical semi-variogram.

Usage

variocloudmap(long, lat, var, bin=NULL, quantiles=NULL, listvar=NULL, listnomvar=NULL,
criteria=NULL, carte = NULL, label = "", cex.lab=1, pch = 16, col="grey", xlab = "",
ylab="", axes=FALSE, lablong = "", lablat = "", xlim=NULL, ylim=NULL)

Arguments

long a vector x of size n
lat a vector y of size n
var a vector of numeric values of size n
bin list of values where empirical variogram is evaluated
quantiles list of values of quantile orders (the regression quantile is obtained by spline smoothing)
listvar matrix of variables
listnomvar names of variables listvar
criteria a vector of size n of boolean which permit to represent preselected sites with a cross, using the tcltk window
carte matrix with 2 columns for drawing spatial polygonal contours : x and y coordinates of the vertices of the polygon
label a list of character of size n with names of sites
cex.lab character size of label
pch 16 by default, symbol for selected points
col "grey" by default, colors of points on the angle plot
xlab a title for the graphic x-axis
ylab a title for the graphic y-axis
axes a boolean with TRUE for drawing axes on the map
lablong name of the x-axis that will be printed on the map
lablat name of the y-axis that will be printed on the map
xlim the x limits of the plot
ylim the y limits of the plot

Details

For some couple of sites (s_i,s_j), the graph represents on the y-axis the semi squared difference between var_i and var_j :

gamma_ij=0.5(var_i-var_j)^2

and on the x-absis the distance h_(ij) between s_i and s_j. The semi Empirical variogram has been calculated as :

gamma(h)=0.5/|N(h)|sum_(N(h))(Z(s_i)-Z(s_j))^2

where

N(h)={(s_i,s_j):s_i-s_j=h;i,j=1,...,n}

and the robust version :

gamma(h)=frac(1)(2(0.457+frac(0.494)(|N(h)|)))(frac(1)(|N(h)|)sum_(N(h))|Z(s_i)-Z(s_j)|^(1/2))^4

The number N of points to evaluate the empirical variogram and the distance epsilon between points are set as follows :

N=frac(1)(max(30/n^2,0.08,d/D))

and :

epsilon=frac(D)(N)

with :

D=max(h_ij)-min(h_ij)

and :

d=max(h_ij^(l)-h_ij^(l+1)),

where h^(l) is the vector of sorted distances. In options, possibility to represent a regression quantile smoothing spline g_alpha (in that case the points below this quantile curve are not drawn).

Value

A matrix of boolean of size n x n. TRUE if the couple of site was in the last selection of points.

Author(s)

Thomas-Agnan C., Aragon Y., Ruiz-Gazen A., Laurent T., Robidou L.

References

Aragon Yves, Perrin Olivier, Ruiz-Gazen Anne, Thomas-Agnan Christine (2009), Statistique et Econométrie pour données géoréférencées : modèles et études de cas

Cressie N. and Hawkins D. (1980), Robust estimation of the variogram, in Journal of the international association for mathematical geology, 13, 115-125.

See Also

angleplotmap, driftmap

Examples

# data meuse
data(meuse)
data(meuse.riv)
obs<-variocloudmap(meuse$x,meuse$y,meuse$zinc,
quantiles=0.75,listvar=meuse,listnomvar=names(meuse),
xlim=c(0,2000),ylim=c(0,500000),pch=2,carte=meuse.riv[c(21:65,110:153),])
#bin=c(0,50,100,250,500,750,1000,1250,1500,1750,2000) )
#points(meuse.riv, type = "l", asp = 1)

[Package GeoXp version 1.4 Index]