Variation matrix: the pairwise log-ratio variances

Sample variances (denominator n-1) throughout, matching the sibling modules aitcen and aittvr.

Usage

Compvar(X)

Arguments

X

One composition per row; strictly positive.

Value

List with variation (D x D, zero diagonal), totvar, n, D.

Details

Formula: tau_ij = var( log(x_i / x_j) ), totvar = (1/D) sum_{i<j} tau_ij

References

Aitchison (1986), The Statistical Analysis of Compositional Data, Chapter 4. The relation totvar = (1/D) sum_{i<j} tau_ij is the one already used by the sibling module aittvr in this package.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Compvar(V)
#> $variation
#>      [,1]
#> [1,]    0
#> 
#> $totvar
#> [1] 0
#> 
#> $n
#> [1] 8
#> 
#> $D
#> [1] 1
#> 
#> $method
#> [1] "Compositional variation matrix"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"