| SSbiexp {stats} | R Documentation |
This selfStart model evaluates the biexponential model function
and its gradient. It has an initial attribute that
creates initial estimates of the parameters A1, lrc1,
A2, and lrc2.
SSbiexp(input, A1, lrc1, A2, lrc2)
input |
a numeric vector of values at which to evaluate the model. |
A1 |
a numeric parameter representing the multiplier of the first exponential. |
lrc1 |
a numeric parameter representing the natural logarithm of the rate constant of the first exponential. |
A2 |
a numeric parameter representing the multiplier of the second exponential. |
lrc2 |
a numeric parameter representing the natural logarithm of the rate constant of the second exponential. |
a numeric vector of the same length as input. It is the value of
the expression
A1*exp(-exp(lrc1)*input)+A2*exp(-exp(lrc2)*input).
If all of the arguments A1, lrc1, A2, and
lrc2 are names of objects, the gradient matrix with respect to
these names is attached as an attribute named gradient.
José Pinheiro and Douglas Bates
Indo.1 <- Indometh[Indometh$Subject == 1, ]
SSbiexp( Indo.1$time, 3, 1, 0.6, -1.3 ) # response only
A1 <- 3; lrc1 <- 1; A2 <- 0.6; lrc2 <- -1.3
SSbiexp( Indo.1$time, A1, lrc1, A2, lrc2 ) # response and gradient
print(getInitial(conc ~ SSbiexp(time, A1, lrc1, A2, lrc2), data = Indo.1),
digits = 5)
## Initial values are in fact the converged values
fm1 <- nls(conc ~ SSbiexp(time, A1, lrc1, A2, lrc2), data = Indo.1)
summary(fm1)
## Show the model components visually
require(graphics)
xx <- seq(0, 5, len = 101)
y1 <- 3.5 * exp(-4*xx)
y2 <- 1.5 * exp(-xx)
plot(xx, y1 + y2, type = "l", lwd=2, ylim = c(-0.2,6), xlim = c(0, 5),
main = "Components of the SSbiexp model")
lines(xx, y1, lty = 2, col="tomato"); abline(v=0, h=0, col="gray40")
lines(xx, y2, lty = 3, col="blue2" )
legend("topright", c("y1+y2", "y1 = 3.5 * exp(-4*x)", "y2 = 1.5 * exp(-x)"),
lty=1:3, col=c("black","tomato","blue2"), bty="n")
axis(2, pos=0, at = c(3.5, 1.5), labels = c("A1","A2"), las=2)
## and how you could have got their sum via SSbiexp():
ySS <- SSbiexp(xx, 3.5, log(4), 1.5, log(1))
## --- ---
stopifnot(all.equal(y1+y2, ySS, tolerance = 1e-15))