acor {nscancor}

Additional Explained Correlation

Description

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.

Usage

acor(
  x,
  xcoef,
  y,
  ycoef,
  xcenter = TRUE,
  ycenter = TRUE,
  xscale = FALSE,
  yscale = FALSE
)

Arguments

x

a numeric matrix which provides the data from the first domain

xcoef

a numeric data matrix with the canonical vectors related to x as its columns.

y

a numeric matrix which provides the data from the second domain

ycoef

a numeric data matrix with the canonical vectors related to y as its columns.

xcenter

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.

ycenter

analogous to xcenter

xscale

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.

yscale

analogous to xscale

Details

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.

Value

A list of class nscancor containing the following elements:

cor

the additional correlation explained by each pair of canonical variables

xcoef

copied from the input arguments

ycoef, ycenter, yscale

copied from the input arguments

xp

the deflated data matrix corresponding to x

yp

analogous to xp

References

Mackey, L. (2009) Deflation Methods for Sparse PCA. In Advances in Neural Information Processing Systems (pp. 1017–1024).

Examples

data(nutrimouse, package = "CCA")

x <- nutrimouse$gene[ , 1:5]
y <- nutrimouse$lipid
cc <- cancor(x, y)

# Re-compute explained correlation
ac <- acor(x, cc$xcoef, y, cc$ycoef)

# Results should agree
print(cc$cor)
print(ac$cor)