loglogistic6_gradient: 6-parameter log-logistic function gradient and Hessian

In drda: Dose-Response Data Analysis

6-parameter log-logistic function gradient and Hessian

Description

Evaluate at a particular set of parameters the gradient and Hessian of the 6-parameter log-logistic function.

Usage

loglogistic6_gradient(x, theta)

loglogistic6_hessian(x, theta)

loglogistic6_gradient_hessian(x, theta)

Arguments

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

Details

The 6-parameter log-logistic function ⁠f(x; theta)⁠ is defined here as

⁠g(x; theta) = (x^eta / (xi * x^eta + nu * phi^eta))^(1 / nu)⁠ ⁠f(x; theta) = alpha + delta g(x; theta)⁠

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

Note: The 6-parameter log-logistic function is over-parameterized and non-identifiable from data. It is available only for theoretical research.

Value

Gradient or Hessian evaluated at the specified point.

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