llogistic                package:drc                R Documentation

_T_h_e _l_o_g-_l_o_g_i_s_t_i_c _f_u_n_c_t_i_o_n

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

     'llogistic' provides a very general way of specifying log-logistic
     models, under various constraints on the parameters.

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

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

       llogistic2(fixed = c(NA, NA, NA, NA, NA), 
       names = c("b", "c", "d", "e", "f"),
       ss = c("1", "2", "3"), 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, f  (see under 'Details').

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

      ss: 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:

     The default arguments yields the five-parameter log-logistic
     function given by the expression


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


     If the parameter f differs from 1 then the function is asymmetric;
     otherwise it is symmetric (on log scale). This function is fitted
     using 'llogistic'.

     The log-logistic function with log(e) rather than e as a
     parameter, that is using the parameterisation


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


     is fitted using 'llogistic2'.

     Sometimes the log-logistic models are also called Hill models.

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

     The value returned is a list containing the nonlinear 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:

     Finney, D. J. (1979) Bioassay and the Practise of Statistical
     Inference,  _Int. Statist. Rev._, *47*, 1-12.

     Seber, G. A. F. and Wild, C. J. (1989) _Nonlinear Regression_, New
     York: Wiley & Sons (p. 330).

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

     For convenience several special cases are available:  'LL.2',
     'LL.3', 'LL.4' and 'LL.5'.  Examples are provided in the help
     pages for these functions.

