# SSasympOff

0th

Percentile

##### Self-Starting Nls Asymptotic Regression Model with an Offset

This selfStart model evaluates an alternative parametrization of the asymptotic regression function and the gradient with respect to those parameters. It has an initial attribute that creates initial estimates of the parameters Asym, lrc, and c0.

Keywords
models
##### Usage
SSasympOff(input, Asym, lrc, c0)
##### Arguments
input
a numeric vector of values at which to evaluate the model.
Asym
a numeric parameter representing the horizontal asymptote on the right side (very large values of input).
lrc
a numeric parameter representing the natural logarithm of the rate constant.
c0
a numeric parameter representing the input for which the response is zero.
##### Value

• a numeric vector of the same length as input. It is the value of the expression Asym*(1 - exp(-exp(lrc)*(input - c0))). If all of the arguments Asym, lrc, and c0 are names of objects, the gradient matrix with respect to these names is attached as an attribute named gradient.

##### encoding

UTF-8

nls, selfStart; example(SSasympOff) gives graph showing the SSasympOff parametrization, where $\phi_1$ is Asymp, $\phi_3$ is c0.
library(stats) CO2.Qn1 <- CO2[CO2$Plant == "Qn1", ] SSasympOff(CO2.Qn1$conc, 32, -4, 43) # response only 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) require(graphics) xx <- seq(0.5, 5, len = 101) yy <- 5 * (1 - exp(-(xx - 0.5)/(2*log(2)))) par(mar = c(0, 0, 4.0, 0)) plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,6), xlim = c(-1, 5), xlab = "", ylab = "", lwd = 2, main = "Parameters in the SSasympOff model") 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 = 2, lwd = 0) arrows(-0.8, 2.1, -0.8, 0, length = 0.1, angle = 25) arrows(-0.8, 2.9, -0.8, 5, length = 0.1, angle = 25) text(-0.8, 2.5, expression(phi[1]), adj = c(0.5, 0.5)) segments(0.5, 0, 0.5, 3, lty = 2, lwd = 0.75) text(0.5, 3.1, expression(phi[3]), adj = c(0.5, 0)) segments(1.5, 2.525, 1.5, 3, lty = 2, lwd = 0.75) arrows(0.7, 2.65, 0.5, 2.65, length = 0.08, angle = 25) arrows(1.3, 2.65, 1.5, 2.65, length = 0.08, angle = 25) text(1.0, 2.65, expression(t[0.5]), adj = c(0.5, 0.5))