pcamap {GeoXp}R Documentation

Generalized Principal Component Analysis and map

Description

The function `pcamap' draws the plots summarizing a generalized Principal Component Analysis (PCA), made with `genpca.r'. It draws the scatterplot of the individuals projected on a chosen principal component plane (with their percentage of inertia), together with the scatterplot of the variables projected into the same plane with the quality of representation in order to interpret the principal component axes. The individuals scatterplot interacts with the map.

Usage

pcamap(long,lat,dataset,name.dataset=NULL,direct=c(1,2),weight=rep(1/nrow(dataset),length=nrow(dataset)),
metric=diag(ncol(dataset)), center=NULL, reduce=TRUE,qualproj=FALSE,
listvar=NULL, listnomvar=NULL,criteria=NULL,carte=NULL,label="",cex.lab=1, pch=16, col="grey", 
axes=FALSE, xlab=as.character(direct[1]), ylab=as.character(direct[2]), lablong="", lablat="")

Arguments

long a vector $x$ of size $n$
lat a vector $y$ of size $n$
dataset matrix $n times p$ of variables
name.dataset List of Names of dataset
direct Two-dimension vector containing the numbers of principal axes to plot
weight vector of size $n$ of weight (by default : $weight=t(1/n,...,1/n)$)
metric matrix $p times p$ (by default : metric=Identity matrix)
center A vector of size p of the gravity center which by default is equal to $bar X$
reduce if TRUE, reduced PCA
qualproj if TRUE, print the quality of representation of individuals
listvar matrix of variables which permit to add graphics such as histogram, etc. and plot bubbles on map using the tlclk window
listnomvar names of variables from $listvar$
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 name of site. Names are printed on map after a selection
cex.lab character size of label
pch 16 by default, choice of representation of selected points
col "grey" by default, color of the two graphics
axes TRUE for drawing axes on the map
xlab a title for the two graphics x-axis
ylab a title for the two graphics y-axis
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

Let

D=diag(λ_1,...,λ_p)

1_p=(1,...,1)'

Let the coordinates of individuals in the principals components

CC=(C_1',...,C_n')'

with C_i=(C_i^1,...,C_i^p)
Let the coordinates of variables in the principals components

CC=(V_1',...,V_p')'

with V_i=(V_i^1,...,V_i^p)
Part of inertia :

(frac{λ_1}{sum_iλ_i},...,frac{λ_p}{sum_iλ_i})'

Quality of representation of individual k projected on plane (i,j):

Qu=sqrt{frac{(C_k^i)^2+(C_k^j)^2}{sum_l(C_k^l)^2}}

Quality of representation of variable k projected on plane (i,j):

VQu=sqrt{frac{(V_k^i)^2+(V_k^j)^2}{sum_l(V_k^l)^2}}

Value

Return `obs', vector of size $n$ of boolean with sites selected, `inertia' vector of size $p$ with percent of inertia of each component, `casecoord' matrix $n times p$ of indivuduals, `varcoord' matrix $p times p$ of principal components.

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''

Caussinus H., Fekri M., Hakam S., Ruiz-Gazen A. (2003) , ``A monitoring display of Multivariate Outliers'', Computational Statistics and Data Analysis, vol. 44, 1-2, 237-252.

See Also

clustermap,genpca

Examples

# Data Colombus
example(columbus)
coords <- coordinates(columbus)
cont<-spdf2list(columbus)$poly

obs<-pcamap(coords[,1], coords[,2],columbus@data[,6:12],
label=columbus@data$NEIGNO, carte=cont,listvar=columbus@data,
qualproj=TRUE,listnomvar=names(columbus@data),name.dataset=names(columbus@data[,6:12]),
cex.lab=0.7, pch=6, col="purple")

# data boston
data(boston)
obs<-pcamap(boston.utm[,1],boston.utm[,2],boston.c[,12:15],label=boston.c$TOWN, 
listvar=boston.c,listnomvar=names(boston.c),name.dataset=names(boston.c[,12:15]),
cex.lab=0.3,center=c(0,0,0,0))


[Package GeoXp version 1.3 Index]