Re: Multiple Regression w/ Polynomial-in-Y?

From: Phil Sherrod (phil.sherrod_at_REMOVETHISsandh.com)
Date: 09/30/04 

Date: Thu, 30 Sep 2004 16:29:58 GMT

On 25-Sep-2004, frankeye@cox.net (Frank Iannarilli) wrote:

> Paul, my motivation was a chemometric application, where I wanted to
> use PLS to estimate a regression between spectral intensity
> measurements (x) and chemical concentration (y). At higher
> concentrations, we have reason to believe there is self-absorption,
> thus a pragmatic way to model the emitted intensities versus
> concentration is:
> x.w = y - c*y^2 (c positive)
> that is, intensities will tend to be "compressed" at higher
> concentrations.
>
> I could have tried doing PLS using polynomial terms of x on the LHS,
> but my proposed approach seemed a more parsimonious model.
>
>
> Clint, I'm not sure I follow your point. I looked up FIML estimation,
> and discovered that two-stage least squares is related to that. But I
> don't really see the connection of either of these to what I'm
> showing. Thanks, nonetheless.
>
>
> Paul, indeed I hope others chime in. For what I was trying to do, the
> non-linear PLS (NLPLS), kernelized-PLS, etc seemed overkill, when I
> really simply needed to estimate the coefficient of my RHS quadratic
> term in Y (as well as w).

I am the author of a nonlinear regression program called NLREG
(http://www.nlreg.com). NLREG has the ability to fit pretty much any
function to data, but you have to specify the form of the function with
parameters whose values are to be computed. In addition to normal function
fitting of the form:

 y = f(x1,x2,...)

NLREG also can handle general fitting of functions that don't have a simple
variable on the left of the equal sign. This is done by minimizing a
general function:

 f(y1, x2, x3, ...)

An example of this type of fit can be seen at
http://www.nlreg.com/circular.htm

If you want to send me your data and function definition, I will be happy to
try to run it through NLREG. Or you can download a free, demonstration copy
of NLREG from http://www.nlreg.com/DownloadDemo.htm and try it yourself. 

-- 
Phil Sherrod
(phil.sherrod 'at' sandh.com)
http://www.dtreg.com  (decision tree modeling)
http://www.nlreg.com  (nonlinear regression)
http://www.NewsRover.com (Usenet newsreader)
http://www.LogRover.com (Web statistics analysis)

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