logistic4_gradient_2 {drda}  R Documentation 
4parameter logistic function gradient and Hessian
Description
Evaluate at a particular set of parameters the gradient and Hessian of the 4parameter logistic function.
Usage
logistic4_gradient_2(x, theta)
logistic4_hessian_2(x, theta)
logistic4_gradient_hessian_2(x, theta)
Arguments
x 
numeric vector at which the function is to be evaluated. 
theta 
numeric vector with the four parameters in the form

Details
The 4parameter 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).
This set of functions use a different parameterization from
link[drda]{logistic4_gradient}
. To avoid the nonnegative
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.