| % File src/library/stats/man/SSgompertz.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2017 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{SSgompertz} |
| \title{Self-Starting Nls Gompertz Growth Model} |
| \usage{ |
| SSgompertz(x, Asym, b2, b3) |
| } |
| \alias{SSgompertz} |
| \arguments{ |
| \item{x}{a numeric vector of values at which to evaluate the model.} |
| \item{Asym}{a numeric parameter representing the asymptote.} |
| \item{b2}{a numeric parameter related to the value of the function at |
| \code{x = 0}} |
| \item{b3}{a numeric parameter related to the scale the \code{x} axis.} |
| } |
| \description{ |
| This \code{selfStart} model evaluates the Gompertz growth model |
| and its gradient. It has an \code{initial} attribute that |
| creates initial estimates of the parameters \code{Asym}, |
| \code{b2}, and \code{b3}. |
| } |
| \value{ |
| a numeric vector of the same length as \code{input}. It is the value of |
| the expression \code{Asym*exp(-b2*b3^x)}. If all of |
| the arguments \code{Asym}, \code{b2}, and \code{b3} are |
| names of objects the gradient matrix with respect to these names is attached as |
| an attribute named \code{gradient}. |
| } |
| \author{Douglas Bates} |
| \seealso{\code{\link{nls}}, \code{\link{selfStart}} |
| } |
| \examples{ |
| DNase.1 <- subset(DNase, Run == 1) |
| SSgompertz(log(DNase.1$conc), 4.5, 2.3, 0.7) # response only |
| local({ Asym <- 4.5; b2 <- 2.3; b3 <- 0.7 |
| SSgompertz(log(DNase.1$conc), Asym, b2, b3) # response _and_ gradient |
| }) |
| print(getInitial(density ~ SSgompertz(log(conc), Asym, b2, b3), |
| data = DNase.1), digits = 5) |
| ## Initial values are in fact the converged values |
| fm1 <- nls(density ~ SSgompertz(log(conc), Asym, b2, b3), |
| data = DNase.1) |
| summary(fm1) |
| plot(density ~ log(conc), DNase.1, # xlim = c(0, 21), |
| main = "SSgompertz() fit to DNase.1") |
| ux <- par("usr")[1:2]; x <- seq(ux[1], ux[2], length.out=250) |
| lines(x, do.call(SSgompertz, c(list(x=x), coef(fm1))), col = "red", lwd=2) |
| As <- coef(fm1)[["Asym"]]; abline(v = 0, h = 0, lty = 3) |
| axis(2, at= exp(-coef(fm1)[["b2"]]), quote(e^{-b[2]}), las=1, pos=0) |
| } |
| \keyword{models} |