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 = "", symbol = 0,labvar = "", axis = FALSE, lablong = "", lablat = "")
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 |
vector of character of size $n$ with names of sites |
symbol |
0 (by default) or 1, choice of representation of selected points. If 0, selected points are circles, if 1, selected points are stars |
labvar |
name of $var$ |
axis |
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 |
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).
A matrix of boolean of size $n times n$. 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 (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.
# data meuse data(meuse.all) data(meuse.riv) obs<-variocloudmap(meuse.all$x,meuse.all$y, meuse.all$zinc,quantiles=0.95,listvar=meuse.all, listnomvar=names(meuse.all)) #points(meuse.riv, type = "l", asp = 1)