rm.coef(mat, indices)The definition of the RM coefficient is as follows: $$RM = \sqrt{\frac{\mathrm{tr}(X^t P_v X)}{\mathrm{X^t X}}}$$ {RM = sqrt(tr(X' Pv X)/tr(X'X))} where $X$ is the full (column-centered) data matrix and $P_v$ is the matrix of orthogonal projections on the subspace spanned by a k-variable subset.
This definition is equivalent to:
$$RM = \sqrt{\frac{\sum\limits_{i=1}^{p}\lambda_i
(r)_i^2}{\sum\limits_{j=1}^{p}\lambda_j}}$$
where $\lambda_i$ stands for the $i$-th largest
eigenvalue of the covariance matrix defined by X and
$r$ stands for the multiple correlation between the
i-th Principal Component and the k-variable subset.
These definitions are also equivalent to the expression used in the code, which only requires the covariance (or correlation) matrix of the data under consideration.
McCabe, G.P. (1986) "Prediction of Principal Components by Variable Subsets", Technical Report 86-19, Department of Statistics, Purdue University.
Ramsay, J.O., ten Berge, J. and Styan, G.P.H. (1984), "Matrix Correlation", Psychometrika, 49, 403-423.
data(iris3)
x<-iris3[,,1]
rm.coef(var(x),c(1,3))
## [1] 0.8724422Run the code above in your browser using DataLab