Activity Balance Index

The Activity Balance Index (Danilevicz et al. 2024), a 0 to 1 transform of a detrended fluctuation analysis scaling exponent that peaks at the healthy \(\alpha = 1\) (1/f) balance: \(ABI(\alpha) = \exp(-|\alpha - 1| / e^{-2}) = \exp(-e^{2}\,|\alpha - 1|)\).

Usage

activity.balance.index(x)

Arguments

x

Either a numeric scaling exponent, or a fractal object with alpha (and optionally alpha1, alpha2) such as the result of the package's detrended fluctuation analysis.

Value

If x is numeric, the scalar ABI. If x is a fractal object, a list with ABI_overall, ABI_short, ABI_long.

References

Danilevicz IM, van Hees VT, van der Heide F, Jacob L, Landre B, Benadjaoud MA, Sabia S (2024). “Measures of fragmentation of rest activity patterns: mathematical properties and interpretability based on accelerometer real life data.” BMC Medical Research Methodology, 24, 132. doi:10.1186/s12874-024-02255-w .

Examples

activity.balance.index(1.0)   # perfect 1/f balance -> 1
#> [1] 1
activity.balance.index(0.7)
#> [1] 0.1089663