Talk:Nonlinear regression

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Questions

I'm moving some questions from the article page to the talk page.

--is there a rigorous theory of when analytic solutions are possible?

--are there some models that have no analytic solutions, but have iterative solutions that are guarenteed to converge to the global optimal?

These can be addressed in the article text at some point. Wile E. Heresiarch 15:15, 13 Oct 2004 (UTC)

The clever graphic showing polynomial regression is inappropriate, since polynomial regression is a special case of linear regression, not nonlinear regression. A model is linear if the unknowns are a linear function of the knowns. In this case the Xs and Y are the knowns and the betas are the unknowns, so having powers of X in the predictors makes no difference. It is still linear. Blaise 10:19, 26 March 2006 (UTC)[reply]

Good lord, what an unfortunate term then. It really shouldn't be called "linear" if it isn't simply meant to imply a linear relationship between x and y. If I hadn't chanced upon these Wikipedia articles, I'd continue to have no idea about these peculiar term usages, which I had thought I knew for 25 years. 207.189.230.42 (talk) 08:05, 25 May 2009 (UTC)[reply]

Some Problems with the Material added, on Monte Carlo

The use of Monte Carlo deserves consideration. However, as it seems to me, the material just added has several problems. In essence, this is kind of jumping the gun on full development of the article.

1. There is not yet, and needs to be, a section on inference for nonlinear regression. Statistical inference is what distinguishes nonlinear regression from curve fitting. Most procedures from linear regression have analogues in nonlinear regression. The mention of Monte Carlo would belong in that section. 2. I think you are talking about parametric bootstrap. Why not mention nonparametric bootstrap (ordinarily, resampling). 3. You have put in an unusual procedure when as yet there is no mention of the standard errors available in standard nonlinear regression software. 4. The title is not correct. The material suggested is about evaluating error, not about parameter estimation. I don't think Monte Carlo is used for parameter estimation. 5. The use of Monte Carlo simulation as described could be considered for many statistical models. The material is not specific to nonlinear regression. 6. Use of Monte Carlo to evaluate sampling error is an important procedure in practice. I would say we do need to review other articles to see that this is covered. For example, since such materials may be used by government statisticians, it is a service to the public to provide some material.

If these points are not addressed, I will most likely take a shot at them at some point. Dfarrar 21:34, 20 March 2007 (UTC)[reply]

Major revision

This article has been subject to a major revision which brings it into line with regression analysis and linear regression. The section on Monte Carlo has been removed, as it is wholly inappropriate; it has been replaced by a section on parameter statistics. Petergans (talk) 16:48, 23 February 2008 (UTC)[reply]

Linear Transformation vs. Linearization

The proper term for moving a function to a domain where it is linear is a linear transformation. Linearization almost always refers to approximating a function as linear for some bounded range. This is presented in the note:

"Linearization" as used here is not to be confused with the local linearization involved in standard algorithms such as the Gauss-Newton algorithm. Similarly, the methodology of generalized linear models does not involve linearization for parameter estimation.

I'm removing the note as it is no longer needed after the correction. I agree the note was very relevant and important when the term linearization was used.

Linear regression via Linear transform vs. non-linear regression

Someone had suggested that shifting a problem into a linear domain is unnecessary and not recommended. I would ask the author of that section to provide some basis for his assertion beyond referring to the linear transformation section which indicates that its fair as long as proper consideration is given to errors. Certain problems, where in datasets are very large or where time intervals are very short, such as in a feedback control system, can only be practically solved by linear regression. Proper weighting of data points can compensate for the transform and yield theoretically optimal results. —Preceding unsigned comment added by 198.123.51.205 (talk) 22:58, 13 June 2008 (UTC)[reply]

It is not necessary because there are so many nonlinear programs available, including the use of SOLVER in EXCEL. Once the system has been set up the nonlinear refinement is just as easy as the linear one. The size of the dataset is immaterial. The time required is hardly an issue with modern computers.

It is not reccommended because transforming the weights is subject to error as a linear transformation has to be assumed. The Lineweaver-Burk example cited later shows how dangerous the transformation can be. That example is not just of academic interest: enzyme kinetics are used in hospital path labs on samples from real patients. Petergans (talk) 07:49, 16 June 2008 (UTC)[reply]

I disagree that modern computers are fast enough or have large enough memories for the use of linear transformations to be deprecated. This makes the assumption that the user has no time limit for computation or that the user is working on a data set that can fit in the memory of a computer. When working with very large data sets, as often done in physics experiments and simulations, data can exceed several terabytes. Also keep in mind the Fourier and Laplace transforms are also linear transformation. In engineering, applying these linear transform before curve fitting is the rule rather than the exception. —Preceding unsigned comment added by 63.201.67.93 (talk) 09:50, 3 August 2008 (UTC)[reply]