SSbiexp Self-Starting Nls Biexponential model

Description

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.

Usage

SSbiexp(input, A1, lrc1, A2, lrc2)

Arguments

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.

Value

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.

Author(s)

José Pinheiro and Douglas Bates

See Also

nls, selfStart

Examples

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, length.out = 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))

## Show a no-noise example
datN <- data.frame(time = (0:600)/64)
datN$conc <- predict(fm1, newdata=datN)
plot(conc ~ time, data=datN) # perfect, no noise
## IGNORE_RDIFF_BEGIN
## Fails by default (scaleOffset=0):
## Not run: 
        nls(conc ~ SSbiexp(time, A1, lrc1, A2, lrc2), data = datN, trace=TRUE)
## End(Not run)

fmX1 <- nls(conc ~ SSbiexp(time, A1, lrc1, A2, lrc2), data = datN, control = list(scaleOffset=1))
fmX  <- nls(conc ~ SSbiexp(time, A1, lrc1, A2, lrc2), data = datN,
           control = list(scaleOffset=1, printEval=TRUE, tol=1e-11, nDcentral=TRUE), trace=TRUE)
all.equal(coef(fm1), coef(fmX1), tolerance=0) # ... rel.diff.: 1.57e-6
all.equal(coef(fm1), coef(fmX),  tolerance=0) # ... rel.diff.: 1.03e-12
## IGNORE_RDIFF_END
stopifnot(all.equal(coef(fm1), coef(fmX1), tolerance = 6e-6),
          all.equal(coef(fm1), coef(fmX ), tolerance = 1e-11))