# SSgompertz

0th

Percentile

##### Self-Starting Nls Gompertz Growth Model

This selfStart model evaluates the Gompertz growth model and its gradient. It has an initial attribute that creates initial estimates of the parameters Asym, b2, and b3.

Keywords
models
##### Usage
SSgompertz(x, Asym, b2, b3)
##### Arguments
x

a numeric vector of values at which to evaluate the model.

Asym

a numeric parameter representing the asymptote.

b2

a numeric parameter related to the value of the function at x = 0

b3

a numeric parameter related to the scale the x axis.

##### Value

a numeric vector of the same length as input. It is the value of the expression Asym*exp(-b2*b3^x). If all of the arguments Asym, b2, and b3 are names of objects the gradient matrix with respect to these names is attached as an attribute named gradient.

nls, selfStart
library(stats) # NOT RUN { 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) # }