Find the Tucker's coefficient of congruence between two sets of factor loadings.
Factor congruences are the cosines of pairs of vectors defined by the loadings matrix
and based at the origin. Thus, for loadings that differ only by a scaler
(e.g. the size of the eigen value), the factor congruences will be 1.
For factor loading vectors of X and Y the measure of factor congruence, phi, is
$$
\phi = \frac{\sum X Y}{\sqrt{\sum(X^2)\sum(Y^2)}}
.$$
If y=NULL and x is a numeric matrix, the congruence
coefficients between the columns of the matrix x are returned.
The result is a symmetric matrix with ones on the diagonal. If two matrices
are provided, they must have the same size and the result is a square matrix containing the
congruence coefficients between all pairs of columns of the two matrices.