SSbiexp {stats} R Documentation

## 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)

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

## Fails by default (scaleOffset=0) on most platforms {also after increasing maxiter !}
## 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

stopifnot(all.equal(coef(fm1), coef(fmX1), tolerance = 6e-6),
all.equal(coef(fm1), coef(fmX ), tolerance = 1e-11))


[Package stats version 4.4.0 Index]