Re: [R] nonlinear model: pseudo-design matrix

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Fri 17 Feb 2006 - 15:25:56 EST

          There doubtless is a way to extract the gradient information you desire, but have you considered profiling instead? Are you familiar with the distinction between intrinsic and parameter effects curvature?   In brief, part of the nonlinearities involved in nonlinear least squares are intrinsic to the problem, and part are due to the how the problem is parameterized. If you change the parameterization, you change the parameter effects curvature, but the intrinsic curvature remains unchanged. Roughly 30 years ago, Doug Bates and Don Watts reanalized a few dozen published nonlinear regression fits, and found that in all but perhaps one or two, the parameter effects were dominant and the intrinsic curvature was negligible. See Bates and Watts (1988) Nonlinear Regression Analysis and Its Applications (Wiley) or Seber and Wild (1989) Nonlinear Regression (Wiley).

          Bottom line:

  1. You will always get more accurate answers from profiling than from the Wald "pseudodesign matrix" approach. Moreover, often the differences are dramatic.
  2. I just did RSiteSearch("profiling with nls"). The first hit was "http://finzi.psych.upenn.edu/R/library/stats/html/profile.nls.html". If this is not satisfactory, please explain why.
	  hope this helps.
	  spencer graves

Murray Jorgensen wrote:
> Given a nonlinear model formula and a set of values for all the
> parameters defining a point in parameter space, is there a neat way to
> extract the pseudodesign matrix of the model at the point? That is the
> matrix of partial derivatives of the fitted values w.r.t. the parameters
> evaluated at the point.
>
> (I have figured out how to extract the gradient information from an nls
> fitted model using the nlsModel part, but I wish to implement a score
> test, so I need to be able to extract the information at points other
> than the mle.)
>
> Thanks, Murray Jorgensen



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