acor
computes the additional standard correlation explained by each
canonical variable, taking into account the possible non-conjugacy of the
canonical vectors. The result of the analysis is returned as a list of class
nscancor
.
acor(x, xcoef, y, ycoef, xcenter = TRUE, ycenter = TRUE, xscale = FALSE,
yscale = FALSE)
acor
returns a list of class nscancor
containing the
following elements:
the additional correlation explained by each pair of canonical variables
copied from the input arguments
copied from the input arguments
the deflated data matrix corresponding to x
anologous to xp
a numeric matrix which provides the data from the first domain
a numeric data matrix with the canonical vectors related to
x
as its columns.
a numeric matrix which provides the data from the second domain
a numeric data matrix with the canonical vectors related to
y
as its columns.
a logical value indicating whether the empirical mean of (each
column of) x
should be subtracted. Alternatively, a vector of length
equal to the number of columns of x
can be supplied. The value is
passed to scale
.
analogous to xcenter
a logical value indicating whether the columns of x
should be scaled to have unit variance before the analysis takes place. The
default is FALSE
for consistency with cancor
. Alternatively,
a vector of length equal to the number of columns of x
can be
supplied. The value is passed to scale
.
analogous to xscale
The additional correlation is measured after projecting the corresponding canonical vectors to the ortho-complement space spanned by the previous canonical variables. This procedure ensures that the correlation explained by non-conjugate canonical vectors is not counted multiple times. See Mackey (2009) for a presentation of generalized deflation in the context of principal component analysis (PCA), which was adapted here to CCA.
acor
is also useful to build a partial CCA model, to be completed with
additional canonical variables computed using nscancor
.
Mackey, L. (2009) Deflation Methods for Sparse PCA. In Advances in Neural Information Processing Systems (pp. 1017--1024).