[R] nls diagnostics?

[Spencer Graves]

Hi, All: 

      What tools exist for diagnosing singular gradient problems with 
'nls'?  Consider the following toy example:            

DF1 <- data.frame(y=1:9, one=rep(1,9))
nlsToyProblem <- nls(y~(a+2*b)*one, DF1, start=list(a=1, b=1),
                  control=nls.control(warnOnly=TRUE))
Error in nlsModel(formula, mf, start, wts) :
  singular gradient matrix at initial parameter estimates

      This example is obviously stupid, but other singular gradient 
problems are not so obvious. 

      If we transfer this problem to 'optim', we can get diagnostics 
from an eigen analysis of the hessian: 

dumfun <- function(x, y, one){
  d <- y-(x[1]+2*x[2])*one
  sum(d^2)
}
optimToyProblem <- optim(c(a=1, b=1), dumfun, hessian=TRUE,
                         y=DF1$y, one=DF1$one)
eigen(optimToyProblem$hessian, symmetric=TRUE)
$values
[1]  9.000000e+01 -7.105427e-10

$vectors
          [,1]       [,2]
[1,] 0.4472136 -0.8944272
[2,] 0.8944272  0.4472136

      The smallest eigenvalue is essentially numerically zero relative 
to the largest,confirming the 'singular gradient' message.  The 
corresponding eigenvector helps diagnose the problem:  Adding (-0.9, 
0.45)*z to any solution gives another equally good solution, for any z. 

      I've used this technique to diagnose many subtle convergence 
problems with 'optim'.  Are tools of this nature available for 'nls'? 

      Thanks,
      Spencer Graves