Four-Parameter Log-Logistic (Dose-Response) Forward Function

Classical Hill-equation parameterisation for positive-valued x: $$y = a + \frac{d - a}{1 + (c / x)^b}$$

Usage

loglogistic4(x, a, b, c, d)

Arguments

x: Numeric vector. Independent variable (typically log10-concentration).
a: Numeric scalar. Lower asymptote (baseline response).
b: Numeric scalar. Scale parameter ($b > 0$); controls steepness.
c: Numeric scalar. Inflection-point location on the x-axis.
d: Numeric scalar. Upper asymptote (saturation response).

Value

Numeric vector of predicted response values.

Details

Here $c$ is the EC50 (inflection on the concentration scale) and $b > 0$ is the Hill coefficient. Requires $x > 0$ and $c > 0$.

Domain restriction

This model requires positive x. When the independent variable is log10-transformed (and can be negative), use logistic4() instead — on the log scale the two models are algebraically equivalent.