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 * x_i / (theta2 + x_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 x_i are inputted as a vector in the
     'regressor' argument. To predict the response at new values of x_i
     one must assign the '@extra$uvec' slot in the fitted object these
     values, e.g., see the example below.

     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:

     data(enzyme)
     fit = vglm(velocity ~ 1, micmen, enzyme, trace=TRUE, crit="c",
                regressor=enzyme$conc)
     ## Not run: 
     attach(enzyme)
     plot(conc, velocity, xlab="concentration", las=1, main="Enzyme data")
     lines(conc, fitted(fit), col="blue") # Join up the fitted values
     detach(enzyme)

     # Predict the response at other concentrations and add it to the plot
     newdata = new=data.frame(concentration=seq(0, 2, len=200))
     fit@extra$uvec = newdata$concentration
     lines(newdata$conc, predict(fit, new=newdata, type="res"), col="red")
     ## End(Not run)
     summary(fit)

