logistic4_gradient: 4-parameter logistic function gradient and Hessian

In drda: Dose-Response Data Analysis

4-parameter logistic function gradient and Hessian

Description

Evaluate at a particular set of parameters the gradient and Hessian of the 4-parameter logistic function.

Usage

logistic4_gradient(x, theta)

logistic4_hessian(x, theta)

logistic4_gradient_hessian(x, theta)

Arguments

x	numeric vector at which the function is to be evaluated.
theta	numeric vector with the four parameters in the form c(alpha, delta, eta, phi).

Details

The 4-parameter logistic function ⁠f(x; theta)⁠ is defined here as

⁠g(x; theta) = 1 / (1 + exp(-eta * (x - phi)))⁠ ⁠f(x; theta) = alpha + delta g(x; theta)⁠

where theta = c(alpha, delta, eta, phi) and eta > 0. When delta is positive (negative) the curve is monotonically increasing (decreasing).

Value

Gradient or Hessian evaluated at the specified point.

drda documentation built on April 3, 2025, 6 p.m.