MM                    package:drc                    R Documentation

_M_i_c_h_a_e_l_i_s-_M_e_n_t_e_n _m_o_d_e_l

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

     The functions can be used to fit (shifted) Michaelis-Menten models
     that are used for modeling enzyme kinetics, weed densities etc.

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

      
       MM.2(fixed = c(NA, NA), names = c("d", "e"), ...)
       
       MM.3(fixed = c(NA, NA, NA), names = c("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: a vector of character strings giving the names of the
          parameters (should not contain ":").  The order of the
          parameters is: y0, Vm, K (see under 'Details').

     ...: additional arguments from convenience functions to
          'llogistic'.

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

     The model is given by the mean function


               f(x, (c, d, e)) = c + frac{d-c}{1+(e/x)}


     It is a decreasing three-parameter model. The two-parameter
     Michaelis-Menten model ('MM.2') is obtained by setting c equal to
     0.

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

     A list of class 'drcMean', containing the mean function, the self
     starter function, the parameter names and other components such as
     derivatives and a function for calculating ED values.

_N_o_t_e:

     At the moment the implementation cannot deal with infinite
     concentrations.

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

     Christian Ritz

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

     Related models are the asymptotic regression models 'AR.2' and
     'AR.3'.

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

     ## Fitting Michaelis-Menten model
     met.mm.m1 <- drm(gain~dose, product, data=methionine, fct=MM.3(), 
     pmodels = list(~1, ~factor(product), ~factor(product)))
     plot(met.mm.m1, log = "", ylim=c(1450, 1800))
     summary(met.mm.m1)
     ED(met.mm.m1, c(10, 50))

     ## Calculating bioefficacy: approach 1
     coef(met.mm.m1)[4] / coef(met.mm.m1)[5] * 100

     ## Calculating bioefficacy: approach 2
     SI(met.mm.m1, c(50,50))

     ## Simplified models
     met.mm.m2a <- drm(gain~dose, product, data=methionine, fct=MM.3(), pmodels = list(~1, ~factor(product), ~1))
     anova(met.mm.m2a, met.mm.m1)  # model reduction not possible

     met.mm.m2b <- drm(gain~dose, product, data=methionine, fct=MM.3(), pmodels = list(~1, ~1, ~factor(product)))
     anova(met.mm.m2b, met.mm.m1)  # model reduction not possible

