micmen                 package:VGAM                 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:

     Fits a Michaelis-Menten nonlinear regression model.

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

     micmen(rpar = 0.001, divisor = 10, init1 = NULL, init2 = NULL,
            link1 = "identity", link2 = "identity",
            earg1=list(), earg2=list(),
            dispersion = 0, zero = NULL)

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

    rpar: Numeric. Initial positive ridge parameter. This is used to
          create positive-definite weight matrices.

 divisor: Numerical. The divisor used to divide the ridge parameter at
          each iteration until it is very small but still positive. 
          The value of 'divisor' should be greater than one.

init1, init2: Numerical. Initial value for the first and second
          parameters, respectively.  The default is to use a
          self-starting value.

link1, link2: Parameter link function applied to the first and second
          parameters, respectively. See 'Links' for more choices.

earg1, earg2: List. Extra argument for each of the links. See 'earg' in
          'Links' for general information.

dispersion: Numerical. Dispersion parameter.

    zero: An integer-valued vector specifying which linear/additive
          predictors are modelled as intercepts only. The values must
          be from the set {1,2}. A 'NULL' means none.

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

     The Michaelis-Menten Model is given by

                E(Y_i) = theta1 * u_i / (theta2 + u_i)

     where theta1 and theta2 are the two parameters.

     The relationship between iteratively reweighted least squares and
     the Gauss-Newton algorithm is given in Wedderburn (1974). However,
     the algorithm used by this family function is different. Details
     are given at the Author's web site.

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

     An object of class '"vglmff"' (see 'vglmff-class'). The object is
     used by modelling functions such as 'vglm', and 'vgam'.

_N_o_t_e:

     The regressor values u_i are inputted as the RHS of the 'form2'
     argument. It should just be a simple term; no smart prediction is
     used. It should just a single vector so omit the intercept term.
     The LHS is ignored.

     Numerical problems may occur. If so, try setting some initial
     values for the parameters. In the future, several self-starting
     initial values will be implemented.

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

     T. W. Yee

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

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

     Wedderburn, R. W. M. (1974) Quasi-likelihood functions,
     generalized linear models, and the Gauss-Newton method.
     _Biometrika_, *61*, 439-447.

     Bates, D. M. and Watts, D. G. (1988) _Nonlinear Regression
     Analysis and Its Applications_, New York: Wiley.

     Documentation accompanying the 'VGAM' package at <URL:
     http://www.stat.auckland.ac.nz/~yee> contains further information
     and examples.

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

     'enzyme'.

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

     fit = vglm(velocity ~ 1, micmen, enzyme, trace=TRUE, crit="c",
                form2 = ~ conc - 1)
     ## Not run: 
     with(enzyme, plot(conc, velocity, xlab="concentration", las=1,
                       main="Enzyme data", ylim=c(0,max(velocity)),
                       xlim=c(0,max(conc))))
     with(enzyme, points(conc, fitted(fit), col="blue", pch="+"))

     # This predicts the response at a finer grid:
     newenzyme = data.frame(conc = with(enzyme, seq(0, max(conc),len=200)))
     with(newenzyme, lines(conc, predict(fit, newenzyme, type="response"),
                           col="red"))
     ## End(Not run)
     summary(fit)

