If you add a print(p), you will find that after a few iterations
u is negative which leads to problems with the power. It sometimes help write
u=exp(p), and compute the log later. From a statistical point of view, I am not
always happy with that solution, but even Pinheiro/Bates use it in the nlme
samples.
f <- function (x,p) {
print(p)
u <- exp(p[1])
v <- p[2]
w <- p[3]
(x*u)^v+w # You don't need the I(( here.
}
Nonlinear regression model
model: y ~ f(x, c(a, b, d))
data: parent.frame()
a b d
-2.125873 12.781581 5.577249
residual sum-of-squares: 21.12331
Dieter