Asymptotic regression model

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

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.

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 \(x\).

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.

Note

The functions are for use with the function drm.

See also

A very similar, but monotonously decreasing model is the exponential decay model: EXD.2 and EXD.3.

Examples

## First model
met.as.m1<-drm(gain ~ dose, product, data = methionine, fct = AR.3(),
pmodels = list(~1, ~factor(product), ~factor(product)))
#> Control measurements detected for level: control
plot(met.as.m1, log = "", ylim = c(1450, 1800))
summary(met.as.m1)
#> 
#> Model fitted: Shifted asymptotic regression (3 parms)
#> 
#> Parameter estimates:
#> 
#>                 Estimate Std. Error  t-value   p-value    
#> c:(Intercept) 1.4536e+03 1.0764e+01 135.0395 1.804e-08 ***
#> d:DLM         1.6892e+03 9.8280e+00 171.8804 6.873e-09 ***
#> d:MHA         1.7541e+03 2.1369e+01  82.0855 1.320e-07 ***
#> e:DLM         4.5386e-02 7.4128e-03   6.1226  0.003605 ** 
#> e:MHA         9.2668e-02 1.6516e-02   5.6109  0.004957 ** 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error:
#> 
#>  11.20328 (4 degrees of freedom)

## Calculating bioefficacy: approach 1
coef(met.as.m1)[5] / coef(met.as.m1)[4] * 100
#>    e:MHA 
#> 204.1797 

## Calculating bioefficacy: approach 2
EDcomp(met.as.m1, c(50,50))
#> 
#> Estimated ratios of effect doses
#> 
#>                 Estimate Std. Error    t-value    p-value
#> DLM/MHA:50/50  0.4897647  0.1091974 -4.6725956  0.0094999

## Simplified models
met.as.m2<-drm(gain ~ dose, product, data = methionine, fct = AR.3(),
pmodels = list(~1, ~1, ~factor(product)))
#> Control measurements detected for level: control
anova(met.as.m2, met.as.m1)  # simplification not possible
#> 
#> 1st model
#>  fct:     AR.3()
#>  pmodels: ~1, ~1, ~factor(product)
#> 2nd model
#>  fct:     AR.3()
#>  pmodels: ~1, ~factor(product), ~factor(product)
#> 
#> ANOVA table
#> 
#>           ModelDf     RSS Df F value p value
#> 1st model       5 1861.77                   
#> 2nd model       4  502.05  1 10.8332  0.0302

met.as.m3 <- drm(gain ~ dose, product, data = methionine, fct = AR.3(),
pmodels = list(~1, ~factor(product), ~1))
#> Control measurements detected for level: control
anova(met.as.m3, met.as.m1)  # simplification not possible
#> 
#> 1st model
#>  fct:     AR.3()
#>  pmodels: ~1, ~factor(product), ~1
#> 2nd model
#>  fct:     AR.3()
#>  pmodels: ~1, ~factor(product), ~factor(product)
#> 
#> ANOVA table
#> 
#>           ModelDf     RSS Df F value p value
#> 1st model       5 1878.73                   
#> 2nd model       4  502.05  1 10.9683  0.0296