mvar | R Documentation |
Compute the metric variance, covariance, correlation or standard deviation.
mvar(x,...)
mcov(x,...)
mcor(x,...)
msd(x,...)
## Default S3 method:
mvar(x,y=NULL,...)
## Default S3 method:
mcov(x,y=x,...)
## Default S3 method:
mcor(x,y,...)
## Default S3 method:
msd(x,y=NULL,...)
x |
a dataset, eventually of amounts or compositions |
y |
a second dataset, eventually of amounts or compositions |
... |
further arguments to
|
The metric variance (mvar
) is defined by the trace of the
variance in the natural geometry of the data, or also by the generalized
variance in natural geometry. The natural geometry is equivalently
given by the cdt
or idt
transforms.
The metric standard deviation (msd
) is not the square root
of the metric variance, but the square root of the mean of the eigenvalues of the
variance matrix. In this way it can be interpreted in units of the original
natural geometry, as the radius of a sperical ball around
the mean with the same volume as the 1-sigma ellipsoid of the data set.
The metric covariance (mvar
) is the sum over the absolute
singular values of the covariance of two datasets in their respective
geometries. It is always positive. The metric covariance of a dataset
with itself is its metric variance. The interpretation of a metric
covariance is quite difficult, but useful in regression problems.
The metric correlation (mcor
) is the metric covariance of the
datasets in their natural geometry normalized to unit variance matrix. It is a
number between 0 and the smaller dimension of both natural spaces. A
number of 1 means perfect correlation in 1 dimension, but only partial
correlations in higher dimensions.
a scalar number, informing of the degree of variation/covariation of one/two datasets.
K.Gerald v.d. Boogaart http://www.stat.boogaart.de, Raimon Tolosana-Delgado
Daunis-i-Estadella, J., J.J. Egozcue, and V. Pawlowsky-Glahn
(2002) Least squares regression in the Simplex on the simplex, Terra
Nostra, Schriften der Alfred Wegener-Stiftung, 03/2003
Pawlowsky-Glahn, V. and J.J. Egozcue (2001) Geometric approach to
statistical analysis on the simplex. SERRA 15(5), 384-398
var
, cov
,
mean.acomp
, acomp
, rcomp
,
aplus
, rplus
data(SimulatedAmounts)
mvar(acomp(sa.lognormals))
mvar(rcomp(sa.lognormals))
mvar(aplus(sa.lognormals))
mvar(rplus(sa.lognormals))
msd(acomp(sa.lognormals))
msd(rcomp(sa.lognormals))
msd(aplus(sa.lognormals))
msd(rplus(sa.lognormals))
mcov(acomp(sa.lognormals5[,1:3]),acomp(sa.lognormals5[,4:5]))
mcor(acomp(sa.lognormals5[,1:3]),acomp(sa.lognormals5[,4:5]))
mcov(rcomp(sa.lognormals5[,1:3]),rcomp(sa.lognormals5[,4:5]))
mcor(rcomp(sa.lognormals5[,1:3]),rcomp(sa.lognormals5[,4:5]))
mcov(aplus(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5]))
mcor(aplus(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5]))
mcov(rplus(sa.lognormals5[,1:3]),rplus(sa.lognormals5[,4:5]))
mcor(rplus(sa.lognormals5[,1:3]),rplus(sa.lognormals5[,4:5]))
mcov(acomp(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5]))
mcor(acomp(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5]))
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