cedergreen                package:drc                R Documentation

_T_h_e _C_e_d_e_r_g_r_e_e_n-_R_i_t_z-_S_t_r_e_i_b_i_g _m_o_d_e_l

_D_e_s_c_r_i_p_t_i_o_n:

     'cedergreen' provides a very general way of specifying then
     Cedergreen-Ritz-Streibig  modified log-logistic model for
     describing hormesis, under various constraints on the parameters.

     'CRS.6' is the extension of 'link{cedergreen}' with freely varying
     alpha parameter.

     For u-shaped hormesis data 'ucedergreen' provides a very general
     way of specifying the  Cedergreen-Ritz-Streibig modified
     log-logistic model, under various constraints on the parameters.

_U_s_a_g_e:

       cedergreen(fixed = c(NA, NA, NA, NA, NA), 
       names = c("b", "c", "d", "e", "f"), 
       method = c("1", "2", "3", "4"), ssfct = NULL,
       alpha)
       
       CRS.6(fixed = c(NA, NA, NA, NA, NA, NA), 
       names = c("b","c","d","e","f","g"),
       method = c("1", "2", "3", "4"), ssfct = NULL)
       
       ucedergreen(fixed = c(NA, NA, NA, NA, NA), 
       names = c("b", "c", "d", "e", "f"), 
       method = c("1", "2", "3", "4"), ssfct = NULL,
       alpha)

_A_r_g_u_m_e_n_t_s:

   fixed: numeric vector. Specifies which parameters are fixed and at
          what value they are fixed.  NAs for parameter that are not
          fixed.

   names: a vector of character strings giving the names of the
          parameters (should not contain ":").  The order of the
          parameters is: b, c, d, e, f (see under 'Details').

  method: character string indicating the self starter function to use.

   ssfct: a self starter function to be used.

   alpha: numeric value between 0 and 1, reflecting the steepness of
          the hormesis peak.  This argument needs to be specified.

_D_e_t_a_i_l_s:

     The model is given by the expression


 f(x) = c + frac{d-c+f exp(-1/(x^{alpha}))}{1+exp(b(log(x)-log(e)))}


     which is a five-parameter model (alpha is fixed or freely
     varying). Not all features (eg EC/ED calculation)  are available
     for the model with freely varying alpha.

     It is a modification of the four-parameter logistic curve to take
     hormesis into account.

     The u-shaped model is given by the expression


 f(x) = cd - frac{d-c+f exp(-1/x^{alpha})}{1+exp(b(log(x)-log(e)))}

_V_a_l_u_e:

     The value returned is a list containing the non-linear function,
     the self starter function and the parameter names.

_N_o_t_e:

     The functions are for use with the functions 'drm'.

_A_u_t_h_o_r(_s):

     Christian Ritz

_R_e_f_e_r_e_n_c_e_s:

     Cedergreen, N. and Ritz, C. and Streibig, J. C. (2005)  Improved
     empirical models describing hormesis,  _Environmental Toxicology
     and Chemistry_  *24*, 3166-3172.

_S_e_e _A_l_s_o:

     For fixed alpha, several special cases are handled by the
     following convenience functions  'CRS.4a', 'CRS.4b',  'CRS.4c',
     'CRS.5a', 'CRS.5b', 'CRS.5c', 'UCRS.4a', 'UCRS.4b', 'UCRS.4c',
     'UCRS.5a', 'UCRS.5b', 'UCRS.5c' where a, b and c correspond to 
     the pre-specified alpha values 1, 0.5 and 0.25, respectively.

_E_x_a_m_p_l_e_s:

     ## Estimating CRS model with alpha unknown
     lettuce.crsm1 <- drm(weight~conc, data = lettuce, fct = CRS.6())
     summary(lettuce.crsm1)
     plot(lettuce.crsm1)  # oops: not increasing until hormesis peak

