lnormal                 package:drc                 R Documentation

_L_o_g-_n_o_r_m_a_l _d_o_s_e-_r_e_s_p_o_n_s_e _m_o_d_e_l

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

     'lnormal' and the accompanying convenience functions provide a
     general framework for specifying  the mean function of the
     decreasing or incresing log-normal dose-response model.

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

       lnormal(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), 
       method = c("1", "2", "3", "4"), ssfct = NULL,
       fctName, fctText, loge = FALSE)
       
       LN.2(upper = 1, fixed = c(NA, NA), names = c("b", "e"), ...)
       
       LN.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)
       
       LN.3u(upper = 1, fixed = c(NA, NA, NA), names = c("b", "c", "e"), ...)
       
       LN.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)

_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: 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' for the precise
          meaning of each parameter).

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

   ssfct: a self starter function to be used.

 fctName: character string used internally by convenience functions
          (optional).

 fctText: character string used internally by convenience functions
          (optional).

    loge: logical indicating whether or not ED50 or log(ED50) should be
          a parameter in the model.  By default ED50 is a model
          parameter.

   upper: numeric specifying the upper horizontal asymptote in the
          convenience function.  The default is 1.

     ...: additional arguments to be passed from the convenience
          functions to 'lnormal'.

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

     For the case where log(ED50), denoted e in the equation below, is
     a parameter in the model,  the mean function is:


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


     and the mean function is:


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


     in case ED50, which is also denoted e, is a parameter in the
     model. If the former model is fitted any estimated ED values will
     need to be back-transformed subsequently in order to obtain
     effective doses on the original scale.

     The mean functions above yield the same models as those described
     by Bruce and Versteeg (1992), but in a different parameterisations
     (among other things the natural logarithm is used).

     For the case c=0 and d=1, the log-normal model reduces the classic
     probit model (Finney, 1971)  with log dose as explanatory variable
     (mostly used for quantal data). This special case is available
     through the convenience function 'LN.2'.

     The case c=0 is available as the function 'LN.3', whereas the
     'LN.3u' corresponds to the special case where the upper horizontal
     asymptote is fixed (default is 1). The full four-parameter model
     is available through 'LN.4'.

_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 function is for use with the function 'drm', but typically the
     convenience functions 'link{LN.2}', 'link{LN.3}', 'link{LN.3u}',
     and 'link{LN.4}' should be used.

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

     Christian Ritz

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

     Finney, D. J. (1971) _Probit analysis_, London: Cambridge
     University Press.

     Bruce, R. D. and Versteeg, D. J. (1992) A statistical procedure
     for modeling continuous toxicity data, _Environ. Toxicol. Chem._,
     *11*, 1485-1494.

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

     The log-logistic model ('llogistic') is very similar to the
     log-normal model at least in the middle, but they may differ in
     the tails and thus provide different estimates of low effect
     concentrations EC/ED.

     Examples are provided in the help pages of the datasets
     'S.capricornutum', 'P.promelas', and 'M.bahia'.

