logistic2_gradient_2 {drda}

2-parameter logistic function gradient and Hessian

Description

Evaluate at a particular set of parameters the gradient and Hessian of the 2-parameter logistic function.

Usage

logistic2_gradient_2(x, theta, delta)

logistic2_hessian_2(x, theta, delta)

logistic2_gradient_hessian_2(x, theta, delta)

Arguments

x

numeric vector at which the function is to be evaluated.

theta

numeric vector with the two parameters in the form c(eta, phi).

delta

value of delta parameter (either 1 or -1).

Details

The 2-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. Only eta and phi are free to vary (therefore the name) while vector c(alpha, delta) is constrained to be either c(0, 1) (monotonically increasing curve) or c(1, -1) (monotonically decreasing curve).

This set of functions use a different parameterization from link[drda]{logistic2_gradient}. To avoid the non-negative constraints of parameters, the gradient and Hessian computed here are for the function with eta2 = log(eta).

Note that argument theta is on the original scale and not on the log scale.

Value

Gradient or Hessian of the alternative parameterization evaluated at the specified point.