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

From: Murray Jorgensen <maj_at_stats.waikato.ac.nz>
Date: Fri 17 Feb 2006 - 18:23:15 EST

Hi Spencer,

you were the only one to reply. Yes I am aware of the intrinsic / parameter effects distinction and the advantages of LR tests and profiling over Wald tests based on the local curvature of the loglikelihood surface at the larger of two models being compared. My situation is that I am comparing two nested models both of which have uncomfortably many parameters for the amount of data available. I am able to fit the smaller of the two models but not the larger. In this situation neither the the Wald nor the LR test is available to me but the score test (a.k.a. the Lagrange Multiplier test) is available to me because it is based on the loglikelihood gradient at the smaller model.

I have been able to carry out the test by extracting

X <- smaller.nls$m$gradient()

and obtaining the extra columns of X for the parameters in larger but not in smaller by numerical differentiation. It seems that there should be some way of obtaining the extra columns without recourse to numerical differentiation, though.

Cheers, Murray Jorgensen

Spencer Graves wrote:
> 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

-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj@waikato.ac.nz                                Fax 7 838 4155
Phone +64 7 838 4773 wk Home +64 7 825 0441 Mobile 021 1395 862

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