variocloudmap {GeoXp} | R Documentation |
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.
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)
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 |
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).
A matrix of boolean of size n x n. TRUE if the couple of site was in the last selection of points.
Thomas-Agnan C., Aragon Y., Ruiz-Gazen A., Laurent T., Robidou L.
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.
# 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)