% File src/library/stats/man/SSbiexp.Rd % Part of the R package, http://www.R-project.org % Copyright 1995-2014 R Core Team % Distributed under GPL 2 or later \name{SSbiexp} \encoding{UTF-8} \title{Self-Starting Nls Biexponential model} \usage{ SSbiexp(input, A1, lrc1, A2, lrc2) } \alias{SSbiexp} \arguments{ \item{input}{a numeric vector of values at which to evaluate the model.} \item{A1}{a numeric parameter representing the multiplier of the first exponential.} \item{lrc1}{a numeric parameter representing the natural logarithm of the rate constant of the first exponential.} \item{A2}{a numeric parameter representing the multiplier of the second exponential.} \item{lrc2}{a numeric parameter representing the natural logarithm of the rate constant of the second exponential.} } \description{ This \code{selfStart} model evaluates the biexponential model function and its gradient. It has an \code{initial} attribute that creates initial estimates of the parameters \code{A1}, \code{lrc1}, \code{A2}, and \code{lrc2}. } \value{ a numeric vector of the same length as \code{input}. It is the value of the expression \code{A1*exp(-exp(lrc1)*input)+A2*exp(-exp(lrc2)*input)}. If all of the arguments \code{A1}, \code{lrc1}, \code{A2}, and \code{lrc2} 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{ Indo.1 <- Indometh[Indometh$Subject == 1, ] SSbiexp( Indo.1$time, 3, 1, 0.6, -1.3 ) # response only A1 <- 3; lrc1 <- 1; A2 <- 0.6; lrc2 <- -1.3 SSbiexp( Indo.1$time, A1, lrc1, A2, lrc2 ) # response and gradient print(getInitial(conc ~ SSbiexp(time, A1, lrc1, A2, lrc2), data = Indo.1), digits = 5) ## Initial values are in fact the converged values fm1 <- nls(conc ~ SSbiexp(time, A1, lrc1, A2, lrc2), data = Indo.1) summary(fm1) ## Show the model components visually require(graphics) xx <- seq(0, 5, len = 101) y1 <- 3.5 * exp(-4*xx) y2 <- 1.5 * exp(-xx) plot(xx, y1 + y2, type = "l", lwd=2, ylim = c(-0.2,6), xlim = c(0, 5), main = "Components of the SSbiexp model") lines(xx, y1, lty = 2, col="tomato"); abline(v=0, h=0, col="gray40") lines(xx, y2, lty = 3, col="blue2" ) legend("topright", c("y1+y2", "y1 = 3.5 * exp(-4*x)", "y2 = 1.5 * exp(-x)"), lty=1:3, col=c("black","tomato","blue2"), bty="n") axis(2, pos=0, at = c(3.5, 1.5), labels = c("A1","A2"), las=2) ## and how you could have got their sum via SSbiexp(): ySS <- SSbiexp(xx, 3.5, log(4), 1.5, log(1)) ## --- --- stopifnot(all.equal(y1+y2, ySS, tolerance = 1e-15)) } \keyword{models}