Doug Bates and I have exchanged ideas on the issue of singularities in nonlinear models a number of times over the years. Both perspectives are "right", and though I will characterize them as adversarial, they are really complementary. These views can be overly simplified as
- if there's a singularity, something's wrong (DB)
- if you can minimize the objective you should (JN)
Thesse attitudes result in somewhat different output, and the JN attitude can
often have multiple solutions (even an infinity of solutions in some cases),
akin to collinearity in linear models. It is a minimization attitude rather
than a statistical usefulness viewpoint.
Sometimes in some problems, the singularity is local in the parameter space and
a suitable solution can be found by different starting point(s). I've found
crude minimizers, like the Nelder-Mead approach, often work better for these
problems, but prepare to go have a coffee while it chugs along. However, NM
only gives you a set of parameters, with no variability measures like nls. You
may be able to use the results as initial info to nls to get more info, but if
the singularity is at the solution, you need to think how to explain your
results.
John Nash
From: "Douglas Bates" <[EMAIL PROTECTED]>
Subject: Re: [R] error in function: nls (urgent)
To: tedzzx <[EMAIL PROTECTED]>
Cc: r-help@r-project.org
Message-ID:
<[EMAIL PROTECTED]>
Content-Type: text/plain; charset=ISO-8859-1
On Tue, Nov 18, 2008 at 6:19 AM, tedzzx <[EMAIL PROTECTED]> wrote:
> Hi,all:
> I am running a nonlinear regression and there is a problem.
Yes. The problem is that there is a singular gradient matrix at the
initial parameter estimates. You will need to modify your function or
your initial parameter estimates.
> There is a data frame: data
> p s x t
> 1 875.0 12392.5 11600 0.06967213
> 2 615.0 12332.5 12000 0.06967213
> 3 595.0 12332.5 12000 0.06967213
> 4 592.5 12337.0 12000 0.06967213
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