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 * 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.

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 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.

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

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)

[Package VGAM version 0.7-7 Index]