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
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