OptimModel (version 2.0-1)

gompertz_model: Four-parameter Gompertz model, gradient, starting values, and back-calculation functions

Description

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

Usage

gompertz_model(theta, x)

Value

Let N = length(x). Then

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

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

• attr(gompertz_model, "start")(x, y) returns a numeric vector of length 4 with starting values for (A, B, m, offset).

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

Arguments

theta

Vector of four parameters: (A, B, m, offset). See details.

x

Vector of concentrations for the Gompertz model.

Author

Steven Novick

Details

The four parameter Gompertz model is given by:

$$y = A + (B-A)\times\exp( -\exp( m(x-\text{offset}) ) )\text{, where}$$

\(A = \min y\) (minimum y value), \(A+(B-A)\exp(-\exp( -m*\text{offset} ))\) is the maximum y value, m is the shape parameter, and offset shifts the curve, relative to the concentration x.

See Also

optim_fit, rout_fitter

Examples

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