SSasymp | R Documentation |
This selfStart
model evaluates the asymptotic regression
function and its gradient. It has an initial
attribute that
will evaluate initial estimates of the parameters Asym
, R0
,
and lrc
for a given set of data.
Note that SSweibull()
generalizes this asymptotic model
with an extra parameter.
SSasymp(input, Asym, R0, lrc)
input |
a numeric vector of values at which to evaluate the model. |
Asym |
a numeric parameter representing the horizontal asymptote on
the right side (very large values of |
R0 |
a numeric parameter representing the response when
|
lrc |
a numeric parameter representing the natural logarithm of the rate constant. |
a numeric vector of the same length as input
. It is the value of
the expression Asym (R0-Asym)*exp(-exp(lrc)*input)
. If all of
the arguments Asym
, R0
, and lrc
are
names of objects, the gradient matrix with respect to these names is
attached as an attribute named gradient
.
José Pinheiro and Douglas Bates
nls
, selfStart
Lob.329 <- Loblolly[ Loblolly$Seed == "329", ] SSasymp( Lob.329$age, 100, -8.5, -3.2 ) # response only local({ Asym <- 100 ; resp0 <- -8.5 ; lrc <- -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 <- nls(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329) summary(fm1) ## Visualize the SSasymp() model parametrization : xx <- seq(-.3, 5, length.out = 101) ## Asym (R0-Asym) * exp(-exp(lrc)* x) : yy <- 5 - 4 * exp(-xx / exp(3/4)) stopifnot( all.equal(yy, SSasymp(xx, Asym = 5, R0 = 1, lrc = -3/4)) ) require(graphics) op <- 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 <- 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 <- 1 4*exp(-3/4) ; t.5 <- log(2) / exp(-3/4) ; AR2 <- 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)}~{} %=>% {}~~ {t[0.5] == frac(log(2), e^{phi[3]})}), adj = c(0, 0.5)) par(op)
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