OptimModel (version 2.0-1)

hill_model: Four-parameter Hill model, gradient, starting values, and back-calculation functions

Description

Four-parameter Hill model, gradient, starting values, and back-calculation functions.

Usage

hill_model(theta, x)

Value

Let N = length(x). Then

• hill_model(theta, x) returns a numeric vector of length N.

• attr(hill_model, "gradient")(theta, x) returns an N x 4 matrix.

• attr(hill_model, "start")(x, y) returns a numeric vector of length 4 with starting values for \((e_{\min}, e_{\max}, \text{lec50}, m)\).

• attr(hill_model, "backsolve")(theta, y) returns a numeric vector of length=length(y).

Arguments

theta

Vector of four parameters: \((e_{\min}, e_{\max}, \text{lec50}, m)\). See details.

x

Vector of concentrations for the Hill model.

Author

Steven Novick

Details

The four parameter Hill model is given by: $$y = e_{\min} + \frac{(e_{\max}-e_{\min})}{( 1 + \exp( m\log(x) - m*\text{lec50} ) )}\text{, where }$$

\(e_{\min} = \min y\) (minimum y value), \(e_{\max} = \max y\) (maximum y value), \(\text{lec50} = \log( \text{ec5} )\), and m is the shape parameter. Note: ec50 is defined such that hill.model(theta, ec50) = .5*( emin+ emax ).

See Also

optim_fit, rout_fitter

Examples

set.seed(123L)
x = rep( c(0, 2^(-4:4)), each=4 )
theta = c(0, 100, log(.5), 2)
y = hill_model(theta, x)  + rnorm( length(x), mean=0, sd=1 )
attr(hill_model, "gradient")(theta, x)
attr(hill_model, "start")(x, y)
attr(hill_model, "backsolve")(theta, 50)