VGAM (version 1.1-14)

micmen: Michaelis-Menten Model

Description

Fits a Michaelis-Menten nonlinear regression model.

Usage

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)

Value

An object of class "vglmff"

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

Details

The Michaelis-Menten model is given by $$E(Y_i) = (\theta_1 u_i) / (\theta_2 + u_i)$$ where \(\theta_1\) and \(\theta_2\) 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.

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.

See Also

enzyme.

Examples

mfit <- vglm(velocity ~ 1, micmen, data = enzyme, trace = TRUE,
             crit = "coef", form2 = ~ conc - 1)
summary(mfit)

if (FALSE) {
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 = 2, pch = "+", cex = 2)

# 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 is needed for prediction
lines(predict(mfit, newenzyme, "response") ~ conc, newenzyme,
      col = "red") }