gompertz: Gompertz growth functions

In mnirs: Muscle Near-Infrared Spectroscopy Processing and Analysis

Gompertz growth functions

Description

Calculate 4-parameter Gompertz (asymmetric sigmoidal) curves. Model families fit by analyse_kinetics() with method = "sigmoidal" and shape = "gompertz" or "gompertz_left", and by stats::nls() via the self-starting wrappers SSgompertz() and SSgompertz_left().

Usage

gompertz(t, A, B, xmid, slope)

gompertz_left(t, A, B, xmid, slope)

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.

Details

gompertz() (right-Gompertz) is asymmetric with the inflection point xmid closer to the starting asymptote A: early acceleration away from A, and a slow approach to the ending asymptote B. Appropriate for fast-onset, slow-tail responses.

gompertz_left() (left-Gompertz) has the inflection point closer to the ending asymptote B: slow departure from A, and late acceleration toward B. Appropriate for slow-onset, fast-tail responses.

Model equations

Both forms are re-parameterised so xmid is the time at inflection and slope is the response rate dx/dt at the inflection, with k = slope * e / (B - A).

• gompertz(): A + (B - A) * exp(-exp(-k * (t - xmid))). Inflection height fixed at A + (B - A) / e; 36.8% of the amplitude.

• gompertz_left(): A + (B - A) * (1 - exp(-exp(k * (t - xmid)))). Inflection height fixed at A + (B - A) * (1 - 1/e); 63.2% of the amplitude.

Value

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

See Also

analyse_kinetics(), SSgompertz(), SSgompertz_left(), logistic(), sigmoidal_drift()

Examples

## create a Gompertz curve with random noise
set.seed(15)
t <- 1:60
x <- gompertz(t, A = 10, B = 100, xmid = 30, slope = 4) +
    rnorm(length(t), 0, 2)
data <- data.frame(t, x)

## fit with the self-starting wrapper
model <- nls(x ~ SSgompertz(t, A, B, xmid, slope), data = data)
summary(model)

y <- predict(model, data)


    if (requireNamespace("ggplot2", quietly = TRUE)) {
        ggplot2::ggplot(data, ggplot2::aes(t, x)) +
            theme_mnirs() +
            ggplot2::geom_point() +
            ggplot2::geom_line(ggplot2::aes(y = y))
    }

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