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

From: paul v birke (nonlinear_at_rogers.com)
Date: 09/26/04 

Date: Sat, 25 Sep 2004 23:36:45 -0400
To: Frank Iannarilli <frankeye@cox.net>

Dear Frank and Clint

I have been trying to find more about Clint's suggestion re FIML

there are a number but does this look good Clint?

http://gsbwww.uchicago.edu/computing/research/SASManual/ets/chap14/sect1.htm

thanks

Paul

Frank Iannarilli wrote:
> Hi,
>
> Thanks, Paul and Clint, for responses thus far.
>
> 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).
>
>
> Clint, I considered the Box-Cox transformation (Y^a), but was
> underwhelmed by the suggested methods of estimating "a" (e.g.,
> iteratively, based on ML of presumed gaussian residuals).