[R] question about nls

[Gabor Grothendieck]

On Fri, Mar 15, 2013 at 9:45 AM, Prof J C Nash (U30A) <nashjc at uottawa.ca> wrote:
> Actually, it likely won't matter where you start. The Gauss-Newton direction
> is nearly always close to 90 degrees from the gradient, as seen by turning
> trace=TRUE in the package nlmrt function nlxb(), which does a safeguarded
> Marquardt calculation. This can be used in place of nls(), except you need
> to put your data in a data frame. It finds a solution pretty
> straightforwardly, though with quite a few iterations and function
> evaluations.
>

Interesting observation but it does converge in 5 iterations with the
improved starting value whereas it fails due to a singular gradient
with the original starting value.

> Lines <- "
+ x    y
+ 60 0.8
+ 80 6.5
+ 100 20.5
+ 120 45.9
+ "
> DF <- read.table(text = Lines, header = TRUE)
>
> # original starting value - singular gradient
> nls(y ~ exp(a + b*x)+d,DF,start=list(a=0,b=0,d=1))
Error in nlsModel(formula, mf, start, wts) :
  singular gradient matrix at initial parameter estimates
>
> # better starting value - converges in 5 iterations
> lm1 <- lm(log(y) ~ x, DF)
> st <- setNames(c(coef(lm1), 0), c("a", "b", "d"))
> nls(y ~ exp(a + b*x)+d, DF, start=st)
Nonlinear regression model
  model:  y ~ exp(a + b * x) + d
   data:  DF
      a       b       d
-0.1492  0.0342 -6.1966
 residual sum-of-squares: 0.5743

Number of iterations to convergence: 5
Achieved convergence tolerance: 6.458e-07
>