Some questions about Curvefit, curve fitting and nonlinear regression

[Nick Cain]

Dear Stata-ites,

I've been working to fit some nonlinear functions to datasets I've put together and I've got questions about the theory behind the Curvefit module.

The data I'm using show the growth in renewable power capacity (y) by year (x) for various states. I've experimented with using both built-in Stata commands (such as fpfit and qfit) and with Wei's Curvefit module (http://fmwww.bc.edu/repec/bocode/c/curvefit.html). After testing a slew of models against my data, I've generated comparison R2 figures -- but I need some help finding resources to better understand the theory behind the various models contained in Curvefit. Although there are several presentations on nonlinear models (such as Dr. Williams' excellent tutorial: http://www3.nd.edu/~rwilliam/stats/StataHighlights.html) I'm still struggling to understand the right way to fit and test the various models -- especially the many models in Wei's Curvefit that aren't common in the social sciences (e.g., vapor pressure, rational, gompertz relational).

Do any list-goers know of a good textbook, article or web resource that clearly explains curve fitting? Do folks have a good source for capsule descriptions of the models contained in Curvefit?

Thanks!

-nick

[Nick Cox]

"curve fitting" is more a scientist's category than one in statistics, it seems to me. In practice it seems to mean fitting a nonlinear model by least squares; else one would call it something else, say linear regression. "nonlinear regression" is perhaps a better heading for you.

In my occasional forays into nonlinear modelling I seem to hit an assumption by statisticians or even scientists that the model is pre-defined as a standard in some field and the only real problem is how to fit it. That doesn't often match my scientific experience. In terms of what is closer to your needs, two books by Ratkowsky are a bit quirky but can be useful. As is often the case, you have to skip and skim past stuff that doesn't interest you, or period detail.

Ratkowsky, D.A. 1983. Nonlinear Regression Modeling. New York: Marcel Dekker.
Ratkowsky, D.A. 1990. Handbook of Nonlinear Regression Models. New York: Marcel Dekker.

Conversely, it would be expecting too much to encounter a complete catalogue of models. Even if attention is restricted to simple functions with a small number of parameters the menagerie is very large indeed.

I have not read it but based on their other work I would have high hopes of

Seber, G.A.F. and Wild, C.J. 1989. Nonlinear Regression. New York: John Wiley.

If I recall correctly,

Motulsky, H. and Christopoulos, A. 2004. Fitting models to biological data using linear and non-linear regression: a practical guide to curve fitting. New York: Oxford University Press.

is pitched at a friendly level but doesn't help much in conveying which models have which behaviour.

I wouldn't trust R-square to choose a model for me. Limiting behaviour and presence or absence of turning points within the support are what I would worry about as well as good fit in any quantitative sense.

I don't know curvefit (SSC) to comment.

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