| % File src/library/stats/man/SSasympOff.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2017 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{SSasympOff} |
| \encoding{UTF-8} |
| \title{Self-Starting Nls Asymptotic Regression Model with an Offset} |
| \usage{ |
| SSasympOff(input, Asym, lrc, c0) |
| } |
| \alias{SSasympOff} |
| \arguments{ |
| \item{input}{a numeric vector of values at which to evaluate the model.} |
| \item{Asym}{a numeric parameter representing the horizontal asymptote on |
| the right side (very large values of \code{input}).} |
| \item{lrc}{a numeric parameter representing the natural logarithm of |
| the rate constant.} |
| \item{c0}{a numeric parameter representing the \code{input} for which the |
| response is zero.} |
| } |
| \description{ |
| This \code{selfStart} model evaluates an alternative parametrization |
| of the asymptotic |
| regression function and the gradient with respect to those parameters. |
| It has an \code{initial} |
| attribute that creates initial estimates of the parameters |
| \code{Asym}, \code{lrc}, and \code{c0}. |
| } |
| \value{ |
| a numeric vector of the same length as \code{input}. It is the value of |
| the expression \code{Asym*(1 - exp(-exp(lrc)*(input - c0)))}. If all of |
| the arguments \code{Asym}, \code{lrc}, and \code{c0} 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}}; |
| \code{example(SSasympOff)} gives graph showing the \code{SSasympOff} |
| parametrization. |
| } |
| \examples{ |
| CO2.Qn1 <- CO2[CO2$Plant == "Qn1", ] |
| SSasympOff(CO2.Qn1$conc, 32, -4, 43) # response only |
| local({ Asym <- 32; lrc <- -4; c0 <- 43 |
| SSasympOff(CO2.Qn1$conc, Asym, lrc, c0) # response and gradient |
| }) |
| getInitial(uptake ~ SSasympOff(conc, Asym, lrc, c0), data = CO2.Qn1) |
| ## Initial values are in fact the converged values |
| fm1 <- nls(uptake ~ SSasympOff(conc, Asym, lrc, c0), data = CO2.Qn1) |
| summary(fm1) |
| |
| ## Visualize the SSasympOff() model parametrization : |
| |
| xx <- seq(0.25, 8, by=1/16) |
| yy <- 5 * (1 - exp(-(xx - 3/4)*0.4)) |
| stopifnot( all.equal(yy, SSasympOff(xx, Asym = 5, lrc = log(0.4), c0 = 3/4)) ) |
| require(graphics) |
| op <- par(mar = c(0, 0, 4.0, 0)) |
| plot(xx, yy, type = "l", axes = FALSE, ylim = c(-.5,6), xlim = c(-1, 8), |
| xlab = "", ylab = "", lwd = 2, |
| main = "Parameters in the SSasympOff model") |
| mtext(quote(list(phi[1] == "Asym", phi[2] == "lrc", phi[3] == "c0"))) |
| 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(3/4, -.2, 3/4, 1.6, lty = 2) |
| text (3/4, c(-.3, 1.7), quote(phi[3])) |
| arrows(c(1.1, 1.4), -.15, |
| c(3/4, 7/4), -.15, length = 0.07, angle = 25) |
| text (3/4 + 1/2, -.15, quote(1)) |
| segments(c(3/4, 7/4, 7/4), c(0, 0, 2), # 5 * exp(log(0.4)) = 2 |
| c(7/4, 7/4, 3/4), c(0, 2, 0), lty = 2, lwd = 2) |
| text( 7/4 +.1, 2./2, quote(phi[1]*e^phi[2]), adj = c(0, .5)) |
| par(op) |
| } |
| \keyword{models} |