# 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 computing 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.

##### See Also

nls, selfStart

• SSfpl
##### Examples
library(stats) # NOT RUN { Chick.1 <- ChickWeight[ChickWeight$Chick == 1, ] SSfpl(Chick.1$Time, 13, 368, 14, 6) # response only local({ 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) ## Visualizing the SSfpl() parametrization xx <- seq(-0.5, 5, len = 101) yy <- 1 + 4 / (1 + exp((2-xx))) # == SSfpl(xx, *) : stopifnot( all.equal(yy, SSfpl(xx, A = 1, B = 5, xmid = 2, scal = 1)) ) require(graphics) op <- 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") mtext(quote(list(phi[1] == "A", phi[2] == "B", phi[3] == "xmid", phi[4] == "scal"))) 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 = c(1, 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])) arrows(-0.3, c(1/4, 3/4), -0.3, c(0, 1 ), length = 0.07, angle = 25) text (-0.3, 0.5, quote(phi[2])) text(2, -.1, quote(phi[3])) segments(c(2,3,3), c(0,3,4), # SSfpl(x = xmid = 2) = 3 c(2,3,2), c(3,4,3), lty = 2, lwd = 0.75) arrows(c(2.3, 2.7), 3, c(2.0, 3 ), 3, length = 0.08, angle = 25) text( 2.5, 3, quote(phi[4])); text(3.1, 3.5, "1") par(op) # } 
Documentation reproduced from package stats, version 3.6.2, License: Part of R 3.6.2

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