micmen {VGAM} | R Documentation |
Fits a Michaelis-Menten nonlinear regression model.
micmen(rpar = 0.001, divisor = 10, init1 = NULL, init2 = NULL, link1 = "identity", link2 = "identity", earg1=list(), earg2=list(), dispersion = 0, zero = NULL)
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.
|
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.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
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$uvec
slot in the fitted object these values, e.g.,
see the example below.
Numerical problems may occur. If so, try setting some initial values for the parameters. In the future, several self-starting initial values will be implemented.
T. W. Yee
Seber, G. A. F. and Wild, C. J. (1989) Nonlinear Regression, New York: Wiley.
Wedderburn, R. W. M. (1974) Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika, 61, 439–447.
Bates, D. M. and Watts, D. G. (1988) Nonlinear Regression Analysis and Its Applications, New York: Wiley.
Documentation accompanying the VGAM package at http://www.stat.auckland.ac.nz/~yee contains further information and examples.
data(enzyme) fit = vglm(velocity ~ 1, micmen, enzyme, trace=TRUE, crit="c", regressor=enzyme$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)