micmen {VGAM} | R Documentation

## Michaelis-Menten Model

### Description

Fits a Michaelis-Menten nonlinear regression model.

### Usage

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

### Arguments

`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.

### Details

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.

### Value

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

### Note

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.

### Author(s)

T. W. Yee

### References

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 http://www.stat.auckland.ac.nz/~yee contains further information and examples.

### See Also

`enzyme`.

### Examples

    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)

[Package VGAM version 0.7-9 Index]