sigdrift_texc: Excursion point of the sigmoidal-drift model

In mnirs: Muscle Near-Infrared Spectroscopy Processing and Analysis

Excursion point of the sigmoidal-drift model

Description

The time past the inflection at which the drift rate overtakes the decaying sigmoid rate, ⁠|S'(t)| = |slope_B|⁠, floored at the drift onset (see sigdrift_onset()): the turning point of the curve when the phases oppose, or where the linear trend takes over a monotonic response. A drift at least as fast as the peak sigmoid rate slope takes over from the onset. Scalar parameters only.

Usage

sigdrift_texc(A, B, xmid, slope, slope_B, drift_fraction, shape)

Arguments

A	A numeric parameter for the starting asymptote of the response variable.
B	A numeric parameter for the ending asymptote of the response variable.
xmid	A numeric parameter for the time at the inflection point (the steepest point) of the curve, in units of the predictor variable t.
slope	A numeric parameter for the response rate dx/dt at the inflection xmid.
slope_B	A numeric parameter for the linear drift rate dx/dt of the secondary phase at the ending asymptote B, in response units per unit of the predictor variable t.
drift_fraction	A numeric fraction of the primary amplitude B - A in ⁠(0.5, 1)⁠ at which the linear drift begins, where the sigmoid reaches A + drift_fraction * (B - A).
shape	Character; the 4-parameter sigmoidal shape. One of "symmetric" (default; logistic()), "gompertz" (gompertz()), or "gompertz_left" (gompertz_left()).

Details

With ⁠ratio = |slope_B / slope|⁠ and u = k * (t - xmid) (see sigdrift_rate()), the sigmoid rate relative to its peak is 4 * L * (1 - L) with L = 1 / (1 + exp(-u)) for "symmetric", solved as u = 2 * atanh(sqrt(1 - r)); exp(1 - u - exp(-u)) for "gompertz"; and exp(1 + u - exp(u)) for "gompertz_left". The Gompertz forms have no closed inverse and are solved by stats::uniroot() on a bracket containing the single post-inflection root.

Value

A numeric excursion time.

mnirs documentation built on Sept. 13, 2026, 1:06 a.m.