logistic6_gradient_2 {drda}  R Documentation 
6parameter logistic function gradient and Hessian
Description
Evaluate at a particular set of parameters the gradient and Hessian of the 6parameter logistic function.
Usage
logistic6_gradient_2(x, theta)
logistic6_hessian_2(x, theta)
logistic6_gradient_hessian_2(x, theta)
Arguments
x 
numeric vector at which the function is to be evaluated. 
theta 
numeric vector with the six parameters in the form

Details
The 6parameter logistic function f(x; theta)
is defined here as
g(x; theta) = 1 / (xi + nu * exp(eta * (x  phi)))^(1 / nu)
f(x; theta) = alpha + delta g(x; theta)
where theta = c(alpha, delta, eta, phi, nu, xi)
, eta > 0
, nu > 0
, and
xi > 0
. When delta
is positive (negative) the curve is monotonically
increasing (decreasing).
This set of functions use a different parameterization from
link[drda]{logistic6_gradient}
. To avoid the nonnegative
constraints of parameters, the gradient and Hessian computed here are for
the function with eta2 = log(eta)
, nu2 = log(nu)
, and xi2 = log(xi)
.
Note that argument theta
is on the original scale and not on the log scale.
Note: The 6parameter logistic function is overparameterized and nonidentifiable from data. It is available only for theoretical research.
Value
Gradient or Hessian of the alternative parameterization evaluated at the specified point.