Only yesterday, I was got essentially that error message. I solved it by setting "trace=TRUE" and studying which paramters were moving. With that information, I looked at the function and thought of ways to reparameterize it to make things more stable. That helped but did not solve the problem. Ultimately, I fixed two of the most volatile parameters to sensible values. Then nls gave me answers very quickly.
An excellent reference on nonlinear regression is Bates and Watts (1988) Nonlinear regression and its applications (Wiley). They talk some about reparameterizations. A major contribution of this book is distinguishing between the intrinsic nonlinearity of the problem, which cannot be fixed without changing the model, and "parameter effect curvature", which can be fixed by just writing the model in a different but equivalent way. Pages 256-259 summarize some 67 different examples from published literature. In each case, parameter effects curvature was more than the intrinsic curvature, with the median being a factor of 16 larger.
For my problem yesterday, I did not just restrict myself to reparameterizations: I also considered alternative models with similar but formally different behavior.
Also, have you considered using "optim" first, then feeding the answers to "nls"? McCullough found a few years ago that it was easier for him to get answers if he did it that way, because the S-Plus versions of "nls" seems to get lost and quit prematurely, while "optim" will at least produce an answer. If I'm not mistaken, this issue is discussed in either McCullough, B. D. (1999) Assessing the reliability of statistical software: Part II The American Statistician, 53, 149-159 or McCullough, B. D. (1998) Assessing the reliability of statistical software: Part I The American Statistician, 52, 358-366. I don't remember now which paper had this, but I believe one of them did; I think I'd look at the second first. (McCullough discussed "nlminb" instead of "optim". The former has been replaced by the latter in R.)
hope this helps. spencer graves
giovanni caggiano wrote:
Dear All, A couple of questions about the nls package.
1. I'm trying to run a nonlinear least squares regression but the routine gives me the following error message:
step factor 0.000488281 reduced below `minFactor' of 0.000976563
even though I previously wrote the following command: nls.control(minFactor = 1/4096), which should set the
minFactor to a lower level than the default one,
1/1024=0.000976563. Is there any way of setting the new minfactor to a
lower level?
2. Is it possible to set some constraints upon the parameters to be estimated in a nls regression?
Thanks, Giovanni
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