Neill's lack-of-fit test for dose-response models

neill.test provides a lack-of-fit test for non-linear regression models. It is applicable both in cases where there are replicates (in which case it reduces to the standard lack-of-fit test against an ANOVA model) and in cases where there are no replicates, though then a grouping has to be provided.

Usage

neill.test(
  object,
  grouping,
  method = c("c-finest", "finest", "percentiles"),
  breakp = NULL,
  display = TRUE
)

Arguments

object: object of class 'drc' or 'nls'.
grouping: character or numeric vector that provides the grouping of the dose values.
method: character string specifying the method to be used to generate a grouping of the dose values.
breakp: numeric vector of break points for generating dose intervals that form a grouping.
display: logical. If TRUE results are displayed. Otherwise they are not (useful in simulations).

Value

The function returns an object of class anova which is displayed using print.anova.

Details

The functions use the methods df.residual and residuals and the data component of object (only for determining the number of observations).

Note

A clustering technique could be employed to determine the grouping to be used in cases where there are no replicates. There should at most be ceiling(n/2) clusters as otherwise some observations will not be used in the test. At the other end there need to be more clusters than parameters in the model.

References

Neill, J. W. (1988) Testing for lack of fit in nonlinear regression, Ann. Statist., 16, 733–740

Author

Christian Ritz

Examples

### Example with 'drc' object

## Lack-of-fit test against ANOVA
ryegrass.m1 <-drm(rootl~conc, data = ryegrass, fct = LL.4())
modelFit(ryegrass.m1)
#> Lack-of-fit test
#> 
#>           ModelDf    RSS Df F value p value
#> ANOVA          17 5.1799                   
#> DRC model      20 5.4002  3  0.2411  0.8665

## The same test using 'neill.test'
neill.test(ryegrass.m1, ryegrass$conc)
#> Grouping used
#> 
#>    0 0.94 1.88 3.75  7.5   15   30 
#>    6    3    3    3    3    3    3 
#> 
#> Neill's lack-of-fit test
#> 
#>  F value p value
#>   0.2411  0.8665

## Generating a grouping
neill.test(ryegrass.m1, method="c-finest")
#> Grouping used
#> 
#> 1 2 3 4 5 6 7 
#> 6 3 3 3 3 3 3 
#> 
#> Neill's lack-of-fit test
#> 
#>  F value p value
#>   0.2411  0.8665
neill.test(ryegrass.m1, method="finest")
#> Grouping used
#> 
#>  1  2  3  4  5  6  7  8  9 10 11 12 
#>  2  2  2  2  2  2  2  2  2  2  2  2 
#> 
#> Neill's lack-of-fit test
#> 
#>  F value p value
#>   1.0625  0.4462
neill.test(ryegrass.m1, method="perc")
#> Grouping used
#> 
#>    (-Inf,0]    (0,1.88] (1.88,3.75]   (3.75,15]   (15, Inf] 
#>           6           6           3           6           3 
#> 
#> Neill's lack-of-fit test
#> 
#>  F value p value
#>   0.7545  0.3959