Time Delay Stability across a multivariate physiological series

Computes pairwise Time Delay Stability (TDS) for every pair of columns in X. Each column is treated as one physiological node (e.g. an EEG band-power, heart rate, respiration, an EMG envelope). The result is a symmetric matrix of TDS strengths (percentage of time each pair is stably coupled).

Usage

timeDelayStability(
  X,
  sampling_rate = 1,
  window = NULL,
  step = NULL,
  max_lag = NULL,
  window_sec = NULL,
  step_sec = NULL,
  max_lag_sec = NULL,
  stability_tol = 1L,
  min_stable = 4L,
  nodes = NULL
)

Arguments

X

A numeric matrix or data frame, time (rows) by nodes (columns), or an object accepted by physioNodeMatrix() (named list of equal-length vectors).

sampling_rate

Sampling rate in Hz of the rows of X (default 1).

window, step, max_lag

Window length, step, and maximum lag in samples (override the *_sec arguments when supplied).

window_sec, step_sec, max_lag_sec

The same quantities in seconds. Defaults: window_sec = 60, step = window/2, max_lag = window/4.

stability_tol

Maximum change in optimal lag (in samples) between consecutive windows for the pair to be considered stable (default 1).

min_stable

Minimum number of consecutive windows forming a stable period (default 4).

nodes

Optional character vector of node names (defaults to the column names of X).

Value

An object of class "tds": a list with tds (nodes x nodes TDS percentage matrix, diagonal 0), stable_lag (nodes x nodes dominant stable lag in samples), pairs (per-pair detail incl. tau0 and in_stable), nodes, n_windows, and params.

Details

Windowing may be given in samples (window, step, max_lag) or in seconds (window_sec, step_sec, max_lag_sec, using sampling_rate). Sample arguments take precedence. Sensible defaults derive step and max_lag from the window when unspecified.

References

Bashan et al. (2012) doi:10.1038/ncomms1705 .

Examples

set.seed(1)
n <- 3000
x <- as.numeric(stats::filter(rnorm(n), rep(1/5, 5), sides = 2))
x[is.na(x)] <- 0
y <- c(rep(0, 5), x[seq_len(n - 5)]) + rnorm(n, sd = 0.3)  # y lags x by 5
z <- rnorm(n)                                              # unrelated
X <- cbind(x = x, y = y, z = z)
res <- timeDelayStability(X, window = 100, step = 50, max_lag = 20,
                          min_stable = 3)
res$tds
#>           x          y         z
#> x   0.00000 100.000000 15.254237
#> y 100.00000   0.000000  5.084746
#> z  15.25424   5.084746  0.000000