EVOLUTION-MANAGER

Edit File: SSasymp.html

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<table width="100%" summary="page for SSasymp {stats}"><tr><td>SSasymp {stats}</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>Self-Starting Nls Asymptotic Regression Model</h2>

<h3>Description</h3>

<p>This <code>selfStart</code> model evaluates the asymptotic regression
function and its gradient.  It has an <code>initial</code> attribute that
will evaluate initial estimates of the parameters <code>Asym</code>, <code>R0</code>,
and <code>lrc</code> for a given set of data.
</p>
<p>Note that <code><a href="SSweibull.html">SSweibull</a>()</code> generalizes this asymptotic model
with an extra parameter.
</p>

<h3>Usage</h3>

<pre>
SSasymp(input, Asym, R0, lrc)
</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>Asym</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>R0</code></td>
<td>
<p>a numeric parameter representing the response when
<code>input</code> is zero.</p>
</td></tr>
<tr valign="top"><td><code>lrc</code></td>
<td>
<p>a numeric parameter representing the natural logarithm of
the rate constant.</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>Asym+(R0-Asym)*exp(-exp(lrc)*input)</code>.  If all of
the arguments <code>Asym</code>, <code>R0</code>, and <code>lrc</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>

<p><code><a href="nls.html">nls</a></code>, <code><a href="selfStart.html">selfStart</a></code>
</p>

<h3>Examples</h3>

<pre>

Lob.329 &lt;- Loblolly[ Loblolly$Seed == "329", ]
SSasymp( Lob.329$age, 100, -8.5, -3.2 )   # response only
local({
  Asym &lt;- 100 ; resp0 &lt;- -8.5 ; lrc &lt;- -3.2
  SSasymp( Lob.329$age, Asym, resp0, lrc) # response _and_ gradient
})
getInitial(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329)
## Initial values are in fact the converged values
fm1 &lt;- nls(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329)
summary(fm1)

## Visualize the SSasymp()  model  parametrization :

xx &lt;- seq(-.3, 5, len = 101)
  ##  Asym + (R0-Asym) * exp(-exp(lrc)* x) :
  yy &lt;- 5 - 4 * exp(-xx / exp(3/4))
  stopifnot( all.equal(yy, SSasymp(xx, Asym = 5, R0 = 1, lrc = -3/4)) )
  require(graphics)
  op &lt;- par(mar = c(0, .2, 4.1, 0))
  plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,5.2), xlim = c(-.3, 5),
       xlab = "", ylab = "", lwd = 2,
       main = quote("Parameters in the SSasymp model " ~
                    {f[phi](x) == phi[1] + (phi[2]-phi[1])*~e^{-e^{phi[3]}*~x}}))
  mtext(quote(list(phi[1] == "Asym", phi[2] == "R0", phi[3] == "lrc")))
  usr &lt;- 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 = 3)
  arrows(c(0.35, 0.65), 1,
         c(0  ,  1   ), 1, length = 0.08, angle = 25); text(0.5, 1, quote(1))
  y0 &lt;- 1 + 4*exp(-3/4) ; t.5 &lt;- log(2) / exp(-3/4) ; AR2 &lt;- 3 # (Asym + R0)/2
  segments(c(1, 1), c( 1, y0),
           c(1, 0), c(y0,  1),  lty = 2, lwd = 0.75)
  text(1.1, 1/2+y0/2, quote((phi[1]-phi[2])*e^phi[3]), adj = c(0,.5))
  axis(2, at = c(1,AR2,5), labels= expression(phi[2], frac(phi[1]+phi[2],2), phi[1]),
       pos=0, las=1)
  arrows(c(.6,t.5-.6), AR2,
         c(0, t.5   ), AR2, length = 0.08, angle = 25)
  text(   t.5/2,   AR2, quote(t[0.5]))
  text(   t.5 +.4, AR2,
       quote({f(t[0.5]) == frac(phi[1]+phi[2],2)}~{} %=&gt;% {}~~
                {t[0.5] == frac(log(2), e^{phi[3]})}), adj = c(0, 0.5))
  par(op)
</pre>

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