Exponential decay model

Exponential decay model with or without a nonzero lower limit.

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

  EXD.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 ":"). The default parameter names are: init, plateau, k.
...	additional arguments to be passed from the convenience functions.

Details

The exponential decay model is a three-parameter model with mean function:

$$f(x) = c + (d-c)(\exp(-x/e))$$

The parameter init is the upper limit (attained at \(x=0\)), the parameter plateau is the lower limit reached for x going to infinity and the parameter \(e>0\) is determining the steepness of the decay. The curve is monotonously decreasing in \(x\).

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.

References

Organisation for Economic Co-operation and Development (OECD) (2006) Current approaches in the statistical analysis of ecotoxicity data: A guidance to application - annexes, Paris: OECD (p. 80).

See also

Similar models giving exponential increasing curves are AR.2 and AR.3.

Examples

## Fitting an exponential decay model
ryegrass.m1<-drm(rootl~conc, data=ryegrass, fct=EXD.3())

plot(ryegrass.m1)

summary(ryegrass.m1)
#> 
#> Model fitted: Shifted exponential decay (3 parms)
#> 
#> Parameter estimates:
#> 
#>               Estimate Std. Error t-value   p-value    
#> c:(Intercept)  0.12945    0.36866  0.3511     0.729    
#> d:(Intercept)  8.23936    0.30335 27.1613 < 2.2e-16 ***
#> e:(Intercept)  4.53797    0.63886  7.1032 5.243e-07 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error:
#> 
#>  0.8384585 (21 degrees of freedom)