AR: Asymptotic regression model

Description

Providing the mean function and the corresponding self starter function for the asymptotic regression model.

Usage

AR.2(fixed = c(NA, NA), names = c("d", "e"), ...)

  AR.3(fixed = c(NA, NA, NA), names = c("c", "d", "e"), ...)

Arguments

fixed

numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.

names

vector of character strings giving the names of the parameters (should not contain ":").

...

additional arguments to be passed from the convenience functions.

Value

A list of class drcMean, containing the mean function, the self starter function, the parameter names and other components such as derivatives and a function for calculating ED values.

Details

The asymptotic regression model is a three-parameter model with mean function: $$f(x) = c + (d-c)(1-\exp(-x/e))$$ The parameter $c$ is the lower limit (at $x=0$), the parameter $d$ is the upper limit and the parameter $e>0$ is determining the steepness of the increase as $x$.

Examples

Run this code

## First model
met.as.m1<-drm(gain ~ dose, product, data = methionine, fct = AR.3(), 
pmodels = list(~1, ~factor(product), ~factor(product)))
plot(met.as.m1, log = "", ylim = c(1450, 1800))
summary(met.as.m1)

## Calculating bioefficacy: approach 1
coef(met.as.m1)[5] / coef(met.as.m1)[4] * 100

## Calculating bioefficacy: approach 2
SI(met.as.m1, c(50,50))

## Simplified models
met.as.m2<-drm(gain ~ dose, product, data = methionine, fct = AR.3(), 
pmodels = list(~1, ~1, ~factor(product)))
anova(met.as.m2, met.as.m1)  # simplification not possible

met.as.m3 <- drm(gain ~ dose, product, data = methionine, fct = AR.3(), 
pmodels = list(~1, ~factor(product), ~1))
anova(met.as.m3, met.as.m1)  # simplification not possible