exp_decay_pl {OptimModel}

Three-parameter exponential decay with initial plateau, gradient, starting values, and back-calculation functions

Description

Three-parameter exponential decay with initial plateau, gradient, starting values, and back-calculation functions.

Usage

 
        exp_decay_pl(theta, x)

Arguments

theta

Vector of four parameters: (x0, yMax, yMin, k). See details.

x

Vector of concentrations.

Details

The three-parameter exponential decay with initial plateau model is given by y = \text{yMax} whenever x\le 0 otherwise

y = \text{yMin} + (\text{yMax}-\text{yMin})\times\exp(-K(x-X0))\text{ if } x > X0,

where X0 = \exp(x0) is an inflection point between plateau and exponential decay curve, \text{yMin} = \min y (min response), \text{yMax} = \max y (maximum response), and K = \exp(k) is the shape parameter.

Value

Let N = length(x). Then

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

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

• attr(exp_decay_pl, "start")(x, y) returns a numeric vector of length 4 with starting values for (x0, yMax, yMin, k).

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

Author(s)

Steven Novick

See Also

optim_fit, rout_fitter

Examples

set.seed(100)
x = 2^(-4:4)
theta = c(0.4, 75, 10, log(3))
y = exp_decay_pl(theta, x)  + rnorm( length(x), mean=0, sd=1 )
attr(exp_decay_pl, "gradient")(theta, x)
attr(exp_decay_pl, "start")(x, y)
attr(exp_decay_pl, "backsolve")(theta, 38)