SSsigmoidal_drift: Self-starting sigmoidal-drift model

In mnirs: Muscle Near-Infrared Spectroscopy Processing and Analysis

Self-starting sigmoidal-drift model

Description

Creates initial coefficient estimates for a selfStart wrapper around sigmoidal_drift(), for use with stats::nls(): a 4-parameter sigmoid (A, B, xmid, slope) with a linear drift slope_B at its ending asymptote from the onset fraction drift_fraction.

Usage

SSsigmoidal_drift(t, A, B, xmid, slope, slope_B, drift_fraction, shape)

Arguments

t	A numeric vector of the predictor variable (time).
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

Model formula

x ~ SSsigmoidal_drift(t, A, B, xmid, slope, slope_B, drift_fraction = 0.95, shape = "gompertz")

drift_fraction should be written as a constant, and shape is a string constant ("symmetric" when omitted); neither is estimated. The hinge at the drift onset is not differentiable, so algorithm = "port" with control = nls.control(warnOnly = TRUE) is recommended.

Starting estimates seed the sigmoid as for SSgompertz(), resolve the drift onset from that seed, and regress the residual past the onset on time to seed slope_B and correct the asymptote B.

Fixing parameters

Any parameter may be held constant by writing a value in place of its name in the formula, e.g. x ~ SSsigmoidal_drift(t, A = 0, B, xmid, slope, slope_B, drift_fraction = 0.95) fixes the starting asymptote at A = 0. Fixed parameters are excluded from estimation and are not returned by stats::coef().

Value

A numeric vector of predicted values the same length as the predictor variable t.

See Also

sigmoidal_drift(), analyse_kinetics(), stats::nls(), stats::selfStart(), SSlogistic(), SSgompertz(), SSexponential_drift()

Examples

## create a Gompertz curve with late linear drift and random noise
set.seed(13)
t <- 1:120
x <- sigmoidal_drift(
    t, A = 10, B = 100, xmid = 40, slope = 4,
    slope_B = -0.4, drift_fraction = 0.95, shape = "gompertz"
) + rnorm(length(t), 0, 2)
data <- data.frame(t, x)

## fit with the drift onset held at 95% of the amplitude
model <- nls(
    x ~ SSsigmoidal_drift(
        t, A, B, xmid, slope, slope_B,
        drift_fraction = 0.95, shape = "gompertz"
    ),
    data = data,
    algorithm = "port",
    control = nls.control(warnOnly = TRUE)
)
summary(model)

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