Computes the symmetric relative difference of a numeric vector with respect
to its first element. Unlike the standard relative change
(relChange), this metric is bounded in \([-1, 1]\) and
remains well-defined when the baseline value is small.
Arguments
- v
A
numericvector with length greater than 1 and first element > 0.
Value
A numeric vector of symmetric relative differences, bounded in
\([-1, 1]\). Returns NA where the denominator
\(x_t + x_0 = 0\).
Details
The symmetric relative difference is defined as:
$$D_{sym}(t) = \frac{x_t - x_0}{x_t + x_0}$$
This formulation is preferred over the standard relative change when:
The baseline value \(x_0\) is small, causing the standard formula to produce arbitrarily large values (common for rare species or freshly colonised habitat).
Symmetric treatment of gains and losses is required: a change from \(a\) to \(b\) has the same magnitude (opposite sign) as from \(b\) to \(a\).
A bounded, directly comparable index across species or regions with very different baseline areas is needed.
Examples
x <- c(20, 6, 2, 1, 15, 25)
relChangeSym(x)
#> [1] 0.0000000 -0.5384615 -0.8181818 -0.9047619 -0.1428571 0.1111111