weibull1                 package:drc                 R Documentation

_W_e_i_b_u_l_l _m_o_d_e_l _f_u_n_c_t_i_o_n_s

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

     'weibull' and 'weibull2' provide a very general way of specifying
     Weibull dose response functions, under various constraints on the
     parameters.

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

       weibull1(fixed = c(NA, NA, NA, NA), 
                names = c("b", "c", "d", "e"),
                method = c("1", "2", "3", "4"), 
                ssfct = NULL,
                fctName, fctText)
      
       weibull2(fixed = c(NA, NA, NA, NA), 
                names = c("b", "c", "d", "e"),
                method = c("1", "2", "3", "4"), 
                ssfct = NULL,
                fctName, fctText)

_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 default is
          reasonable (see under 'Usage'). The order of the parameters
          is: b, c, d, e (see under 'Details').

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

   ssfct: a self starter function to be used.

 fctName: optional character string used internally by convenience
          functions.

 fctText: optional character string used internally by convenience
          functions.

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

     As pointed out in Seber and Wild (1989), there exist two different
     parameterisations of the Weibull model. They do not yield the same
     fitted curve for a given dataset (see under Examples).

     One four-parameter Weibull model ('weibull1') is

            f(x) = c + (d-c) exp(-exp(b(log(x)-log(e)))).


     Another four-parameter Weibull model ('weibull2') is

         f(x) = c + (d-c) (1 - exp(-exp(b(log(x)-log(e))))).


     Both four-parameter functions are asymmetric with inflection point
     at the dose 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 function 'drm'.

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

     Christian Ritz

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

     Seber, G. A. F. and Wild, C. J (1989)  _Nonlinear Regression_, 
     New York: Wiley & Sons (pp. 338-339).

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

     For convenience several special cases of the function 'weibull1'
     are available:  'W1.2', 'W1.3' and 'W1.4'.  

     Special cases of 'weibull2' are:  'W2.2', 'W2.3' and 'W2.4'.  

     These convenience functions should be used rather than the
     underlying functions  'weibull1' and 'weibull2'.

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

     ## Fitting two different Weibull models
     ryegrass.m1 <- drm(ryegrass, fct = W1.4())
     plot(ryegrass.m1, conLevel=0.5)

     ryegrass.m2 <- drm(ryegrass, fct = W2.4())
     plot(ryegrass.m2, conLevel=0.5, add = TRUE, type = "none", col = 2)
     # you could also look at the ED values to see the difference

     ## A four-parameter Weibull model with b fixed at 1
     ryegrass.m3 <- drm(ryegrass, fct = W1.4(fixed = c(1, NA, NA, NA)))
     summary(ryegrass.m3)

     ## A four-parameter Weibull model with the constraint b>3
     ryegrass.m4 <- drm(ryegrass, fct = W1.4(), lowerl = c(3, -Inf, -Inf, -Inf), 
     control = drmc(constr=TRUE))
     summary(ryegrass.m4)

