moranplotmap {GeoXp}R Documentation

Moran scatterplot and map

Description

The function `moranplotmap' draws a moran plot, used to detect spatial autocorrelation in the variable $var$. On the x-axis, is represented $(var-bar{var})$ and on the y-axis $W(var-bar{var})$, where $W$ is the spatial weight matrix. It also calcultes Moran's $I$ statistic (see nonnormoran.r) and give a p-value associated to the autocorrelation test (gaussian version and permutation version).

Usage

moranplotmap(long, lat, var, W, flower=FALSE, locmoran=FALSE, listvar=NULL, listnomvar=NULL,
carte=NULL, criteria=NULL, label="", cex.lab=1, col="blue",pch=16, xlab=expression((X-bar(X))),
ylab=expression(W(X-bar(X))), axes=FALSE, lablong="", lablat="",
names.arg=c("H.-H.","L.-H.","L.-L.","H.-L."))

Arguments

long a vector $x$ of size $n$
lat a vector $y$ of size $n$
var a vector of numeric values of size $n$
W A spatial weigth matrix of size $n times n$
flower if TRUE, link neighbouring sites
locmoran if TRUE, print local Moran's $I$ statistic on the Moran plot
listvar matrix of variables which permit to plot bubbles on map or add a graphic using the tk window
listnomvar a list with names of variables $listvar$
carte matrix with 2 columns for drawing spatial polygonal contours : $x$ and $y$ coordinates of the vertices of the polygon
criteria a vector of size $n$ of boolean with TRUE on specific sites (these for non interactive selection)
label a list of character of size $n$ with name of site. Names are printed on map after a selection
cex.lab character size of label
col "blue" by default, color of bars on the histogram
pch 16 by default, choice of representation of selected points
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
names.arg names of quadrants of the Moran plot

Details

For the permutation test, for each drawing the values of the variable $var$ are randomly assigned to the sites. We then calculate Moran'I statistic associated to each drawing and we give the frequency of drawings when Moran'I statistic is lower or equal to the observed Moran'$I$ statistic. Moreover, the function gives the opportunity to link neighbouring sites and gives Local Moran's I statistic. For a site $i$:

I_i=(var_i-bar{var})sum_{j}W_{ij}(var_j-bar{var})

with $j$ not equal to $i$.

Value

Returns $obs$, vector of size $n$ of boolean with selected sites, and Moran'I statistic $MORAN$.

Note

In the case of the spatial weigth matrix is not normalized, the Moran'I statistic is not equal to $β$ used in regression line for model $W(X-bar{X})=β(X-bar{X})+u$. That is why the regression line is only drawn in the case of W normalized.

Author(s)

Aragon Y., Thomas-Agnan C., 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''

Jim Lesage, ``Spatial Econometrics Toolbox'', http://www.spatial-econometrics.com/

See Also

neighbourmap,makeneighborsw,normw,nonormmoran

Examples

# data baltimore
data(baltimore)
W <- makeneighborsw(baltimore$X,baltimore$Y,method="neighbor",4)
moranplotmap(baltimore$X,baltimore$Y,baltimore$PRICE,W,label=baltimore$STATION,
criteria=(baltimore$PRICE>mean(baltimore$PRICE)),listvar=baltimore,
listnomvar=names(baltimore),flower=TRUE,locmoran=TRUE,cex.lab=0.7,pch=5)


[Package GeoXp version 1.3 Index]