Canonical OMI analysis

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Description

This function performs a canonical OMI analysis (outlying mean index).

Usage

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canomi(dudiX, Y, scannf = TRUE, nf = 2)
## S3 method for class 'canomi'
print(x, ...)
## S3 method for class 'canomi'
 plot(x, xax = 1, yax = 2, ...)

Arguments

dudiX

an object of class dudi

Y

a a data frame Resource units-animals according to dudiX$tab with no columns of zero

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 canomi returned by the function canomi

xax

the number of the x-axis

yax

the number of the x-axis

...

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 P-dimensionnal 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 radio-tracking). 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 non-centred 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. ls = dudiX\$tab%*%cm%*%c1)

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

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## 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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