asdev computes the additional standard deviation explained by each
principal component, taking into account the possible non-orthogonality of
the pseudo-rotation matrix \(\mathbf{W}\).
asdev(x, w, center = TRUE, scale. = FALSE)a numeric data matrix with the observations as rows
a numeric data matrix with the principal axes as columns
a logical value indicating whether the empirical mean 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.
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 prcomp. Alternatively,
a vector of length equal to the number of columns of x can be
supplied. The value is passed to scale.
asdev returns a list with class (nsprcomp, prcomp)
containing the following elements:
the additional standard deviation explained by each component
copied from the
input argument w
the scores matrix \(\mathbf{XW}\), containing the principal components as columns (after centering and scaling if requested)
the centering and scaling used
the deflated data matrix corresponding to x
an orthonormal basis for the principal subspace
The additional standard deviation of a component is measured after projecting the corresponding principal axis to the ortho-complement space spanned by the previous principal axes. This procedure ensures that the variance explained by non-orthogonal principal axes is not counted multiple times. If the principal axes are pairwise orthogonal (e.g. computed using standard PCA), the additional standard deviations are identical to the standard deviations of the columns of the scores matrix \(\mathbf{XW}\).
asdev is also useful to build a partial PCA model from
\(\mathbf{W}\), to be completed with additional components computed
using nsprcomp.
Mackey, L. (2009) Deflation Methods for Sparse PCA. In Advances in Neural Information Processing Systems (pp. 1017--1024).