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 with TRUE on specific sites (these for non interactive selection)
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, choice of representation of 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}=frac{1}{2}(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)=frac{1}{2|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 $ε$ between points are set as follows :

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

and :

ε=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 $g_{α}$ (in that case the points below this quantile curve are not drawn).

Value

A matrix of boolean of size $n times n$. 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 (2008), ``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)
#bin=c(0,50,100,250,500,750,1000,1250,1500,1750,2000) )
#points(meuse.riv, type = "l", asp = 1)

[Package GeoXp version 1.3 Index]