EVOLUTION-MANAGER
Edit File: SSfpl.html
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Self-Starting Nls Four-Parameter Logistic Model</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link rel="stylesheet" type="text/css" href="R.css" /> </head><body> <table width="100%" summary="page for SSfpl {stats}"><tr><td>SSfpl {stats}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Self-Starting Nls Four-Parameter Logistic Model</h2> <h3>Description</h3> <p>This <code>selfStart</code> model evaluates the four-parameter logistic function and its gradient. It has an <code>initial</code> attribute computing initial estimates of the parameters <code>A</code>, <code>B</code>, <code>xmid</code>, and <code>scal</code> for a given set of data. </p> <h3>Usage</h3> <pre> SSfpl(input, A, B, xmid, scal) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>input</code></td> <td> <p>a numeric vector of values at which to evaluate the model.</p> </td></tr> <tr valign="top"><td><code>A</code></td> <td> <p>a numeric parameter representing the horizontal asymptote on the left side (very small values of <code>input</code>).</p> </td></tr> <tr valign="top"><td><code>B</code></td> <td> <p>a numeric parameter representing the horizontal asymptote on the right side (very large values of <code>input</code>).</p> </td></tr> <tr valign="top"><td><code>xmid</code></td> <td> <p>a numeric parameter representing the <code>input</code> value at the inflection point of the curve. The value of <code>SSfpl</code> will be midway between <code>A</code> and <code>B</code> at <code>xmid</code>.</p> </td></tr> <tr valign="top"><td><code>scal</code></td> <td> <p>a numeric scale parameter on the <code>input</code> axis.</p> </td></tr> </table> <h3>Value</h3> <p>a numeric vector of the same length as <code>input</code>. It is the value of the expression <code>A+(B-A)/(1+exp((xmid-input)/scal))</code>. If all of the arguments <code>A</code>, <code>B</code>, <code>xmid</code>, and <code>scal</code> are names of objects, the gradient matrix with respect to these names is attached as an attribute named <code>gradient</code>. </p> <h3>Author(s)</h3> <p>José Pinheiro and Douglas Bates</p> <h3>See Also</h3> <p><code><a href="nls.html">nls</a></code>, <code><a href="selfStart.html">selfStart</a></code> </p> <h3>Examples</h3> <pre> 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) </pre> <hr /><div style="text-align: center;">[Package <em>stats</em> version 3.6.0 <a href="00Index.html">Index</a>]</div> </body></html>