SSfpl

0th

Percentile

Self-Starting Nls Four-Parameter Logistic Model

This selfStart model evaluates the four-parameter logistic function and its gradient. It has an initial attribute that will evaluate initial estimates of the parameters A, B, xmid, and scal for a given set of data.

Keywords
models
Usage
SSfpl(input, A, B, xmid, scal)
Arguments
input
a numeric vector of values at which to evaluate the model.
A
a numeric parameter representing the horizontal asymptote on the left side (very small values of input).
B
a numeric parameter representing the horizontal asymptote on the right side (very large values of input).
xmid
a numeric parameter representing the input value at the inflection point of the curve. The value of SSfpl will be midway between A and B at xmid.
scal
a numeric scale parameter on the input axis.
Value

• a numeric vector of the same length as input. It is the value of the expression A+(B-A)/(1+exp((xmid-input)/scal)). If all of the arguments A, B, xmid, and scal are names of objects, the gradient matrix with respect to these names is attached as an attribute named gradient.

encoding

UTF-8

nls, selfStart
library(stats) Chick.1 <- ChickWeight[ChickWeight$Chick == 1, ] SSfpl(Chick.1$Time, 13, 368, 14, 6) # response only A <- 13; B <- 368; xmid <- 14; scal <- 6 SSfpl(Chick.1\$Time, A, B, xmid, scal) # response and gradient print(getInitial(weight ~ SSfpl(Time, A, B, xmid, scal), data = Chick.1), digits = 5) ## Initial values are in fact the converged values fm1 <- nls(weight ~ SSfpl(Time, A, B, xmid, scal), data = Chick.1) summary(fm1) require(graphics) xx <- seq(-0.5, 5, len = 101) yy <- 1 + 4 / ( 1 + exp((2-xx))) par(mar = c(0, 0, 3.5, 0)) plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,6), xlim = c(-1, 5), xlab = "", ylab = "", lwd = 2, main = "Parameters in the SSfpl 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)) abline(h = 1, lty = 2, lwd = 0) arrows(-0.3, 0.25, -0.3, 0, length = 0.07, angle = 25) arrows(-0.3, 0.75, -0.3, 1, length = 0.07, angle = 25) text(-0.3, 0.5, expression(phi[2]), adj = c(0.5, 0.5)) segments(2, 0, 2, 3.3, lty = 2, lwd = 0.75) text(2, 3.3, expression(phi[3]), adj = c(0.5, 0)) segments(3, 1+4/(1+exp(-1)) - 0.025, 3, 2.5, lty = 2, lwd = 0.75) arrows(2.3, 2.7, 2.0, 2.7, length = 0.08, angle = 25) arrows(2.7, 2.7, 3.0, 2.7, length = 0.08, angle = 25) text(2.5, 2.7, expression(phi[4]), adj = c(0.5, 0.5))