Cedergreen-Ritz-Streibig Model with Lower Limit Fixed at 0 and Alpha = 1 (Deprecated)

This function is deprecated as of version 3.3.0. Please use CRS.5() instead, which provides a more general and flexible interface.

A four-parameter Cedergreen-Ritz-Streibig (CRS) hormesis model where the lower asymptote (c) is fixed at 0 and the alpha parameter controlling the steepness of the hormetic component is fixed at 1. The four free parameters are b, d, e, and f.

Usage

CRS.4a(names = c("b", "c", "d", "e", "f"), fixed = c(NA, 0, NA, NA, NA), ...)

Arguments

names

A character vector of length 5 specifying the names of the model parameters in the following order:

b

Hill slope (steepness of the dose-response curve).

c

Lower asymptote (fixed at 0 via the fixed argument).

d

Upper asymptote.

e

Effective dose producing a response midway between c and d (ED50).

f

Hormesis parameter controlling the magnitude of the stimulatory effect at low doses.

Defaults to c("b", "c", "d", "e", "f").

fixed

A numeric vector of length 5 specifying fixed (non-estimated) parameter values. Use NA for parameters that should be estimated freely. Defaults to c(NA, 0, NA, NA, NA), which fixes the lower asymptote c at 0.

...

Additional arguments passed to cedergreen().

Value

A list of class "drcMean" as returned by cedergreen(), containing the model definition including the mean function, its gradient, parameter names, and fixed values. This object is intended for use as the fct argument in drm().

See also

• CRS.5() — the recommended replacement for this deprecated function.

• cedergreen() — the underlying model constructor.

• CRS.5a() — the five-parameter CRS model with alpha = 1.

• UCRS.4a() — the unconstrained four-parameter CRS model with alpha = 1.

Author

Christian Ritz, Hannes Reinwald

Examples

# NOTE: CRS.4a() is deprecated. Use CRS.5() instead.
# The example below is retained for backward compatibility illustration only.

lettuce.crsm1 <- drm( lettuce[, c(2, 1)], fct = CRS.4a() )
summary(lettuce.crsm1)
#> 
#> Model fitted: Cedergreen-Ritz-Streibig with lower limit 0 (alpha=1) (4 parms)
#> 
#> Parameter estimates:
#> 
#>                 Estimate Std. Error t-value   p-value    
#> b:(Intercept) 7.7892e-01 2.5343e-01  3.0735   0.01177 *  
#> d:(Intercept) 1.1091e+00 7.8336e-02 14.1586 6.081e-08 ***
#> e:(Intercept) 2.8572e+01 3.1328e+01  0.9120   0.38322    
#> f:(Intercept) 5.5833e-04 4.1209e-01  0.0014   0.99895    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error:
#> 
#>  0.155635 (10 degrees of freedom)
ED(lettuce.crsm1, c(50))
#> 
#> Estimated effective doses
#> 
#>      Estimate Std. Error
#> e:50   28.608     11.751

# Recommended replacement:
fct_spec <- CRS.5(alpha_type = "a", fixed = c(NA, 0, NA, NA, NA))
lettuce.crs5 <- drm(lettuce[, c(2, 1)], fct = fct_spec)
summary(lettuce.crs5)
#> 
#> Model fitted: Cedergreen-Ritz-Streibig (alpha=1) (4 parms)
#> 
#> Parameter estimates:
#> 
#>                 Estimate Std. Error t-value   p-value    
#> b:(Intercept) 7.7892e-01 2.5343e-01  3.0735   0.01177 *  
#> d:(Intercept) 1.1091e+00 7.8336e-02 14.1586 6.081e-08 ***
#> e:(Intercept) 2.8572e+01 3.1328e+01  0.9120   0.38322    
#> f:(Intercept) 5.5833e-04 4.1209e-01  0.0014   0.99895    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error:
#> 
#>  0.155635 (10 degrees of freedom)
ED(lettuce.crs5, c(50))
#> 
#> Estimated effective doses
#> 
#>      Estimate Std. Error
#> e:50   28.608     11.751