Michaelis-Menten Model
Fits a Michaelis-Menten nonlinear regression model.
micmen(rpar = 0.001, divisor = 10, init1 = NULL, init2 = NULL,
imethod = 1, oim = TRUE, link1 = "identitylink", link2 = "identitylink",
firstDeriv = c("nsimEIM", "rpar"), probs.x = c(0.15, 0.85),
nsimEIM = 500, 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
|
init1, init2 |
Numerical. Optional 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 |
dispersion |
Numerical. Dispersion parameter. |
firstDeriv |
Character. Algorithm for computing the first derivatives and working weights. The first is the default. |
imethod, probs.x |
See |
nsimEIM, zero |
See |
oim |
Use the OIM?
See |
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.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
This function is not (nor could ever be) entirely reliable. Plotting the fitted function and monitoring convergence is recommended.
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, therefore omit the intercept term.
The LHS of the formula form2 is ignored.
To predict the response at new values of u_i one must assign
the @extra$Xm2 slot in the fitted object these values, e.g.,
see the example below.
Numerical problems may occur. If so, try setting some initial values for the parameters. In the future, several self-starting initial values will be implemented.
T. W. Yee
Seber, G. A. F. and Wild, C. J. (1989). Nonlinear Regression, New York: Wiley.
Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika, 61, 439–447.
Bates, D. M. and Watts, D. G. (1988). Nonlinear Regression Analysis and Its Applications, New York: Wiley.
mfit <- vglm(velocity ~ 1, micmen, data = enzyme, trace = TRUE,
crit = "coef", form2 = ~ conc - 1)
summary(mfit)
## Not run: plot(velocity ~ conc, enzyme, xlab = "concentration", las = 1,
col = "blue", main = "Michaelis-Menten equation for the enzyme data",
ylim = c(0, max(velocity)), xlim = c(0, max(conc)))
points(fitted(mfit) ~ conc, enzyme, col = "red", pch = "+", cex = 1.5)
# This predicts the response at a finer grid:
newenzyme <- data.frame(conc = seq(0, max(with(enzyme, conc)), len = 200))
mfit@extra$Xm2 <- newenzyme$conc # This assignment is needed for prediction
lines(predict(mfit, newenzyme, "response") ~ conc, newenzyme, col = "red")
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.