Return the perturbation-recovery metric definition table
Source:R/rri_recovery_metrics.R
rri_metric_table.RdReturns a publication-ready table defining the perturbation-recovery metrics
produced by rri_recovery_metrics(). The table is suitable for
R Markdown, Quarto, vignettes, and supplementary methods.
Examples
rri_metric_table()
#> symbol metric
#> 1 x(t) System state
#> 2 x0 Pre-perturbation baseline
#> 3 xmin_perturb Minimum perturbation state
#> 4 xmax_perturb Maximum perturbation state
#> 5 x_extreme Perturbation extremum
#> 6 perturb_direction Perturbation direction
#> 7 xmin_recovery Minimum recovery state
#> 8 xmax_recovery Maximum recovery state
#> 9 xeq Post-recovery equilibrium
#> 10 A Amplitude of change
#> 11 A_norm Normalized amplitude
#> 12 tau_lag Lag time
#> 13 O Direction-aware overshoot
#> 14 O_norm Normalized overshoot
#> 15 I Incomplete recovery
#> 16 I_norm Normalized incomplete recovery
#> 17 k Recovery rate constant
#> 18 k_r2 Recovery fit R-squared
#> 19 k_n Recovery fit sample size
#> 20 k_flag Recovery fit diagnostic flag
#> 21 tau_r Characteristic recovery time
#> 22 t_half Half-recovery time
#> 23 H Hysteresis
#> equation
#> 1 x(t)
#> 2 mean{x(t): t < t0}
#> 3 min{x(t): t0 <= t <= t1}
#> 4 max{x(t): t0 <= t <= t1}
#> 5 x(t*) where t* = arg max |x(t) - x0| during perturbation
#> 6 sign(x_extreme - x0)
#> 7 min{x(t): t > t1}
#> 8 max{x(t): t > t1}
#> 9 mean{x(t): final recovery window}
#> 10 max |x(t) - x0| during perturbation
#> 11 A / |x0|
#> 12 tdetect - t0
#> 13 Directional exceedance beyond baseline
#> 14 O / |x0|
#> 15 |xeq - x0|
#> 16 I / |x0|
#> 17 log|x(t)-xeq| = a - k(t-t1)
#> 18 1 - SSres / SStot
#> 19 Number of recovery observations used in k fit
#> 20 Diagnostic classification of k estimation
#> 21 1 / k
#> 22 log(2) / k
#> 23 H ≈ mean(|xrec(Fi) - xpert(Fi)|)
#> interpretation
#> 1 Observed RRI or resilience-associated system state.
#> 2 Estimated steady-state baseline before perturbation.
#> 3 Lowest observed state during perturbation.
#> 4 Highest observed state during perturbation.
#> 5 State farthest from baseline during perturbation.
#> 6 Direction of perturbation relative to baseline.
#> 7 Lowest observed state during recovery.
#> 8 Highest observed state during recovery.
#> 9 Estimated equilibrium after recovery.
#> 10 Magnitude of perturbation displacement from baseline.
#> 11 Dimensionless perturbation amplitude.
#> 12 Delay between perturbation onset and detectable response.
#> 13 Transient exceedance beyond baseline opposite the perturbation direction.
#> 14 Dimensionless overshoot metric.
#> 15 Persistent displacement from baseline after recovery.
#> 16 Dimensionless incomplete-recovery metric.
#> 17 Estimated first-order exponential recovery rate.
#> 18 Goodness-of-fit for exponential recovery approximation.
#> 19 Effective sample size used to estimate recovery kinetics.
#> 20 Diagnostic information describing recovery-rate estimation quality.
#> 21 Characteristic recovery timescale.
#> 22 Time required to recover half the remaining deviation.
#> 23 Path dependence between perturbation and recovery trajectories.