Canonical OMI analysis
Description
This function performs a canonical OMI analysis (outlying mean index).
Usage
1 2 3 4 5 
Arguments
dudiX 
an object of class 
Y 
a a data frame Resource unitsanimals according to

scannf 
a logical value indicating whether the eigenvalues bar plot should be displayed 
nf 
if scannf FALSE, an integer indicating the number of kept axes 
x 
an object of class 
xax 
the number of the xaxis 
yax 
the number of the xaxis 
... 
further arguments passed to or from other methods 
Details
The canonical OMI analysis is similar to the function niche
,
from the package ade4
. The principle of this analysis is the
following. A set of N resource units (RUs) are available to the
animals of the study. Each resource unit is described by P
environmental variables. Therefore, the N resource units define a
cloud of N points in the Pdimensionnal space defined by the P
variables. We call this space "ecological space".
Moreover, the use of the N resource units is known (or sampled) for
a sample of K animals (e.g., using radiotracking). These utilization
weights for each RU (rows) and each animal (column) define a table
Y
. For a given animal, the set of resource units used define
the "niche" of the animal. The vector connecting the centroid (mean)
of the available RUs to the centroid of the RUs used by this animal is
named "marginality vector" (and its squared length is named
"marginality" or "outlying mean index").
The canomi
first distorts the ecological space so that the
available resource units take a standard spherical shape (by first
performing a principal component analysis). Then, in this distorted
space, a noncentred principal component analysis of the marginality
vectors is performed. The canonical OMI analysis finds the directions
in the distorted ecological space where the marginality is, in
average, the largest.
Value
canomi
returns a list of the class canomi
, with the
following components:
call 
original call. 
rank 
an integer indicating the rank of the studied matrix 
nf 
an integer indicating the number of kept axes 
eig 
a vector with all the eigenvalues of the analysis. 
tab 
a data frame with n rows (n animals) and p columns (p environmental variables). 
li 
animals coordinates, data frame with n rows and nf columns. 
l1 
animals normed coordinates, data frame with n rows and nf columns. 
c1 
column scores, data frame with p rows and nf columns. 
cor 
the correlation between the canomi axes and the original variables 
ls 
a data frame with the resource units coordinates 
cm 
The variables metric used in the analysis (e.g.

as 
a data frame with the axis upon niche axis 
Author(s)
Clement Calenge clement.calenge@oncfs.gouv.fr
References
Chessel, D. 2006. Calcul de l'outlier mean index. Consultation statistique avec le logiciel R.
See Also
dudi
for class dudi
,
niche
for classical OMI analysis
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  ## The data
data(puech)
locs < puech$relocations
maps < puech$maps
## the maps
mimage(maps)
## the relocations of the wild boar:
image(maps)
points(locs, col=as.numeric(slot(locs, "data")[,1]))
## count the number of relocations
## in each pixel of the maps
cp < count.points(locs, maps)
## gets the data:
dfavail < slot(maps, "data")
dfused < slot(cp, "data")
## a preliminary principal component analysis of the data:
dud < dudi.pca(dfavail, scannf=FALSE)
## The analysis:
nic < canomi(dud, dfused, scannf=FALSE)
nic
## Plot the results:
plot(nic)

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