multicorrelation {multivariance} | R Documentation |
Computes various types of sample distance multicorrelation as defined in [3].
multicorrelation(x, vec = 1:ncol(x), type = "m.multi.2", multicorrelation.type = "unnormalized", squared = TRUE, ...)
x |
either a data matrix or a list of centered distance matrices |
vec |
if x is a matrix, then this indicates which columns are treated together as one sample; if x is a list, these are the indexes for which the multivariance is calculated. The default is all columns and all indexes, respectively. |
type |
one of |
multicorrelation.type |
one of |
squared |
if |
... |
these are passed to |
The unnormalized and normalized versions coincide if an even number of variables is considered (in particular always for 2-multivariance). They usually differ if an odd number of variables is considered (always for 3-multivariance). If all variables are related by similarity transforms the unnormalized "unnormalized"
multicorrelations are 1.
For "m.multi.2"
the empirical 2-multicorrelation is computed. Which is a dependence measure for pairwise dependence, i.e. the 3-multicorrelation is 0 if and only if all variables are pairwise independent.
For total multicorrelation there is currently only a feasible empirical estimator for a lower bound ("(lower bound) total"
). But it still characterizes dependence in the sense that the population version of this bound is 0 if and only if the variables are independent.
A value of 0 of multicorrelation "multi"
or 3-multicorrelation "m.multi.3"
does not characterize independence.
Value of the multicorrelation.
For the theoretic background see the references given on the main help page of this package: multivariance-package.
y = rnorm(100) x = cbind(y,y*2,(y-2)/3,y+1,y*5) # all variables are related by similarity transforms # compute all types of correlations for x: for (ty in c("(lower bound) total","m.multi.2","m.multi.3","multi")) for (mty in c("normalized","unnormalized")) print(paste(format(multicorrelation(x,type=ty,multicorrelation.type = mty) ,digits=3,nsmall = 3,width = 7),mty,ty,"correlation"))