Cedergreen-Ritz-Streibig Five-Parameter Model with Alpha = 0.5 (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 five-parameter Cedergreen-Ritz-Streibig (CRS) hormesis model where the alpha parameter controlling the steepness of the hormetic component is fixed at 0.5. All five parameters b, c, d, e, and f are freely estimated.

Usage

CRS.5b(names = c("b", "c", "d", "e", "f"), fixed = c(NA, NA, 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 (freely estimated).

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, NA, NA, NA, NA), meaning all five parameters are freely estimated.

...

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.4b() — the four-parameter CRS model with lower limit fixed at 0 and alpha = 0.5.

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

Author

Christian Ritz, Hannes Reinwald

Examples

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

lettuce.m2 <- drm( lettuce[, c(2, 1)], fct = CRS.5b() )
summary(lettuce.m2)
#> 
#> Model fitted: Cedergreen-Ritz-Streibig (alpha=0.5) (5 parms)
#> 
#> Parameter estimates:
#> 
#>               Estimate Std. Error t-value   p-value    
#> b:(Intercept) 0.806096   0.537800  1.4989    0.1681    
#> c:(Intercept) 0.316586   0.199024  1.5907    0.1461    
#> d:(Intercept) 0.971581   0.081936 11.8577 8.523e-07 ***
#> e:(Intercept) 0.814111   2.969068  0.2742    0.7901    
#> f:(Intercept) 3.288976   8.216399  0.4003    0.6983    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error:
#> 
#>  0.1167711 (9 degrees of freedom)
ED(lettuce.m2, c(50))
#> 
#> Estimated effective doses
#> 
#>      Estimate Std. Error
#> e:50   11.550      8.603

# Recommended replacement:
lettuce.crs5 <- drm( lettuce[, c(2, 1)], fct = CRS.5(alpha_type = "b") )
summary(lettuce.crs5)
#> 
#> Model fitted: Cedergreen-Ritz-Streibig (alpha=0.5) (5 parms)
#> 
#> Parameter estimates:
#> 
#>               Estimate Std. Error t-value   p-value    
#> b:(Intercept) 0.806096   0.537800  1.4989    0.1681    
#> c:(Intercept) 0.316586   0.199024  1.5907    0.1461    
#> d:(Intercept) 0.971581   0.081936 11.8577 8.523e-07 ***
#> e:(Intercept) 0.814111   2.969068  0.2742    0.7901    
#> f:(Intercept) 3.288976   8.216399  0.4003    0.6983    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error:
#> 
#>  0.1167711 (9 degrees of freedom)
ED(lettuce.crs5, c(50))
#> 
#> Estimated effective doses
#> 
#>      Estimate Std. Error
#> e:50   11.550      8.603