beta_model {OptimModel} | R Documentation |
Beta hook-effect model, gradient, starting values, and back-calculation functions
Description
Five-parameter hook-effect model for dose-response curve fitting
Usage
beta_model(theta, x)
Arguments
theta |
Vector of five parameters: |
x |
Vector of concentrations for the Beta model. |
Details
The five-parameter Beta model is given by:
where
and
Note that the Beta model depends on the maximum x value. For a particular data set, this may be set by
attr(theta), "maxX") = max(x).
Value
Let N = length(x). Then
beta_model(theta, x) returns a numeric vector of length N.
attr(beta_model, "gradient")(theta, x) returns an N x 5 matrix.
attr(beta_model, "start")(x, y) returns a numeric vector of length 5 with starting values for
attr(beta_model, "backsolve")(theta, y) returns a numeric vector of length=length(y) with the first x such that beta_model(theta, x)=y.
Author(s)
Steven Novick
See Also
Examples
set.seed(123L)
x = rep( c(0, 2^(-4:4)), each=4 )
theta = c(emin=0, emax=115, ldelta1=-1.5, ldelta2=9, ldelta3=11.5)
y = beta_model(theta, x) + rnorm( length(x), mean=0, sd=1 )
beta_model(theta, x)
attr(beta_model, "gradient")(theta, x)
attr(beta_model, "start")(x, y)
attr(theta, "maxX") = max(x)
attr(beta_model, "backsolve")(theta, 50)
[Package OptimModel version 2.0-1 Index]