From: Spencer Graves <spencer.graves_at_pdf.com>

Date: Sat 18 Feb 2006 - 09:32:19 EST

Hi Spencer,

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sat Feb 18 09:34:54 2006

Date: Sat 18 Feb 2006 - 09:32:19 EST

Hi, Murray:

I just got 54 hits from RSiteSearch("numerical differentiation"), the first of which mentioned a function "numericDeriv" WITH a warning (http://finzi.psych.upenn.edu/R/Rhelp02a/archive/55462.html).

hope this helps. spencer graves ###################

Hi Spencer,

I will try some of the ways you suggest and thank you for the suggestions. I still think that performing a score test is a sensible thing to do in my situation, though.

Murray

Spencer Graves wrote:

> Hi, Murray:

*>
**> When I have problems with nonconvergence of nls, I often
**> move the problem to "optim(..., hessian=TRUE)". Even if the larger
**> model is overparameterized and the hessian is singular, I optim usually
**> returns an answer from which I can then compute 2*log(likelihood ratio).
**> Moreover, the hessian will help me diagnose the problem. If it were my
**> problem today, I'd try the following:
**>
**> (1) If there are substantial differences in the diagonal elements
**> of the hessian, it suggests the scaling should be adjusted. Not too
**> long ago, someone else suggested that this could be done within optim
**> via the argument control = list(parscale=...). I have yet to try that,
**> but I think it should work fine.
**>
**> (2) If the diagonal elements of the hessian do not differ by more
**> than a couple orders of magnitude, then I'd try eigen(fit$hessian,
**> symmetric=TRUE). The relative magnitudes of the eigenvalues will expose
**> the effective numer of paramaters that can be estimated, and the
**> eigenvectors associated with the smallest eigenvalues can help one
**> diagnose the problem.
**>
**> hope this helps.
**> spencer graves
**>
**> Murray Jorgensen wrote:
**>
*

>> 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 >> >> >> > ______________________________________________R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sat Feb 18 09:34:54 2006

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