moranplotmap {GeoXp}R Documentation

Moran scatterplot and map

Description

The function `moranplotmap' draws a graphic used to detect spatial autocorrelation in the variable $var$. On the x-absis, is represented $(var-bar{var})$ and on the y-absis $W(var-bar{var})$, where $W$ is the spatial weight matrix. It also calcultes also 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 = 0, opt1 = 1, 
             locmoran = 0, listvar = NULL, listnomvar = NULL, 
             carte = NULL, criteria = NULL, label = "", symbol = 0, 
             labvar = "", axis = FALSE, lablong = "", lablat = "")

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 link neighbouring sites (0, no link (by default) and 1, link (for points or polygon))
opt1 2 for drawing regression line for model $W(X-bar{X})=β(X-bar{X})+u$ else 1
locmoran prints local Moran's $I$ statistic (0, no draw (by default) and 1, draw (for points or polygon))
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 variable $var$
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

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 give 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

The spatial weigth matrix has been normalized. Like that, the Moran'I statistic is equal to $β$ used in regression line for model $W(X-bar{X})=β(X-bar{X})+u$.

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 (2006), ``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,makedistanceW,normw,nonormmoran

Examples

# data baltimore
data(baltimore)
W <- makeneighborsw(baltimore$X,baltimore$Y,4)
moranplotmap(baltimore$X,baltimore$Y,baltimore$PRICE,W,label=baltimore$STATION,
criteria=(baltimore$PRICE>mean(baltimore$PRICE)),listvar=baltimore,
listnomvar=names(baltimore),axis=TRUE,lablong="X",lablat="Y",flower=1,locmoran=1,opt1=2)


[Package GeoXp version 1.0 Index]