| % File src/library/stats/man/SSmicmen.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2017 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{SSmicmen} |
| \encoding{UTF-8} |
| \title{Self-Starting Nls Michaelis-Menten Model} |
| \usage{ |
| SSmicmen(input, Vm, K) |
| } |
| \alias{SSmicmen} |
| \arguments{ |
| \item{input}{a numeric vector of values at which to evaluate the model.} |
| \item{Vm}{a numeric parameter representing the maximum value of the response.} |
| \item{K}{a numeric parameter representing the \code{input} value at |
| which half the maximum response is attained. In the field of enzyme |
| kinetics this is called the Michaelis parameter.} |
| } |
| \description{ |
| This \code{selfStart} model evaluates the Michaelis-Menten model and |
| its gradient. It has an \code{initial} attribute that |
| will evaluate initial estimates of the parameters \code{Vm} and \code{K} |
| } |
| \value{ |
| a numeric vector of the same length as \code{input}. It is the value of |
| the expression \code{Vm*input/(K+input)}. If both |
| the arguments \code{Vm} and \code{K} are |
| names of objects, the gradient matrix with respect to these names is |
| attached as an attribute named \code{gradient}. |
| } |
| \author{\enc{José}{Jose} Pinheiro and Douglas Bates} |
| \seealso{\code{\link{nls}}, \code{\link{selfStart}} |
| } |
| \examples{ |
| PurTrt <- Puromycin[ Puromycin$state == "treated", ] |
| SSmicmen(PurTrt$conc, 200, 0.05) # response only |
| local({ Vm <- 200; K <- 0.05 |
| SSmicmen(PurTrt$conc, Vm, K) # response _and_ gradient |
| }) |
| print(getInitial(rate ~ SSmicmen(conc, Vm, K), data = PurTrt), digits = 3) |
| ## Initial values are in fact the converged values |
| fm1 <- nls(rate ~ SSmicmen(conc, Vm, K), data = PurTrt) |
| summary(fm1) |
| ## Alternative call using the subset argument |
| fm2 <- nls(rate ~ SSmicmen(conc, Vm, K), data = Puromycin, |
| subset = state == "treated") |
| summary(fm2) # The same indeed: |
| stopifnot(all.equal(coef(summary(fm1)), coef(summary(fm2)))) |
| |
| ## Visualize the SSmicmen() Michaelis-Menton model parametrization : |
| |
| xx <- seq(0, 5, length.out = 101) |
| yy <- 5 * xx/(1+xx) |
| stopifnot(all.equal(yy, SSmicmen(xx, Vm = 5, K = 1))) |
| require(graphics) |
| op <- par(mar = c(0, 0, 3.5, 0)) |
| plot(xx, yy, type = "l", lwd = 2, ylim = c(-1/4,6), xlim = c(-1, 5), |
| ann = FALSE, axes = FALSE, main = "Parameters in the SSmicmen model") |
| mtext(quote(list(phi[1] == "Vm", phi[2] == "K"))) |
| usr <- par("usr") |
| arrows(usr[1], 0, usr[2], 0, length = 0.1, angle = 25) |
| arrows(0, usr[3], 0, usr[4], length = 0.1, angle = 25) |
| text(usr[2] - 0.2, 0.1, "x", adj = c(1, 0)) |
| text( -0.1, usr[4], "y", adj = c(1, 1)) |
| abline(h = 5, lty = 3) |
| arrows(-0.8, c(2.1, 2.9), |
| -0.8, c(0, 5 ), length = 0.1, angle = 25) |
| text( -0.8, 2.5, quote(phi[1])) |
| segments(1, 0, 1, 2.7, lty = 2, lwd = 0.75) |
| text(1, 2.7, quote(phi[2])) |
| par(op) |
| } |
| \keyword{models} |