# [R] Assessing the fit of a nonlinear model to a new dataset

Rebecca Lester rebecca.lester at deakin.edu.au
Fri Apr 12 09:06:24 CEST 2013

```Thank you all for your useful suggestions.

Jean, I had already tried to use the maxiter command in that way, but it simply told me that the model had not converged.

Based on Profs Ripley and Nash's comments, I have opted to use an alternative approach, and am creating a distribution of plausible models, and comparing my sum of squared residuals to those arising from that distribution. This seems to work.

Thanks again.

Cheers,

Rebecca

-----
Rebecca Lester
Lecturer, Freshwater Ecology
School of Life & Environmental Sciences
Deakin University
PO Box 423, Warrnambool, 3280

Ph: +61 3 5563 3330
Fax: +61 3 5563 3462

-----Original Message-----
From: Prof J C Nash (U30A) [mailto:nashjc at uottawa.ca]
Sent: Saturday, 6 April 2013 7:42 AM
To: r-help at r-project.org; Rebecca Lester
Subject: Re: Assessing the fit of a nonlinear model to a new dataset

Given nls has a lot of C code (and is pretty complicated), I doubt you'll find much joy doing that.

nlxb from my nlmrt package is all in R, but you'll need to do quite a bit of work at each stage. I don't form the J' J matrix, and do a Marquardt approximation by adding appropriate rows to the J matrix then do a qr decomposition on that.

In any event, the Hessian (which  J' J is only a rather poor appriximation to) is what you want, and it may not be positive definite at the iterates, so you have infinite standard errors. Well, if the curvature was 0, they'd be infinite. Since the curvature is negative, maybe the SEs are more than infinite, if that has any meaning.

I have one problem for which I generated 1000 starting points and >75% had the Hessian indefinite. That is a simple logistic nonlinear regression, albeit with nasty data.

JN

> Message: 90 Date: Fri, 5 Apr 2013 05:06:57 +0000 From: Rebecca Lester
> <rebecca.lester at deakin.edu.au> To: "r-help at r-project.org"
> <r-help at r-project.org> Subject: [R] Assessing the fit of a nonlinear
> model to a new dataset Message-ID:
> <5A72FAA65583BC45A816A698A960E92788612C8A at mbox-f-3.du.deakin.edu.au>
> Content-Type: text/plain Hi all, I am attempting to apply a nonlinear
> model developed using nls to a new dataset and assess the fit of that
> model. At the moment, I am using the fitted model from my fit dataset
> as the starting point for an nls fit for my test dataset (see below).
> I would like to be able to view the t-statistic and p-values for each
> of the iterations using the trace function, but have not yet worked
> out how to do this. Any other suggestions are also welcome. Many
> thanks, Rebecca
>> model.wa <- nls(y ~ A*(x^B), start=list(A=107614,B=-0.415)) # create
>> nls() power model for WA data
>> summary(model.wa) # model summary
>
> Formula: y ~ A * (x^B)
>
> Parameters:
>     Estimate Std. Error t value Pr(>|t|)
> A  7.644e+04  1.240e+04   6.165 4.08e-06 ***
> B -3.111e-01  4.618e-02  -6.736 1.15e-06 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Residual standard error: 5605 on 21 degrees of freedom
>
> Number of iterations to convergence: 6 Achieved convergence tolerance:
> 7.184e-06
>   (6 observations deleted due to missingness)
>
>
>> model.vic <- nls(y.vic ~ A*(x.vic^B), start = list(A = 7.644e+04, B =
>> -3.111e-01), trace = T)
> 3430193778 :  76440.0000    -0.3111
> 2634092902 :  48251.9235397    -0.2552481
> 2614516166 :  27912.1921354    -0.1772322
> 2521588892 :  32718.3764594    -0.1862611
> 2521233646 :  32476.4536126    -0.1836836
> 2521230904 :  32553.0767231    -0.1841362
> 2521230824 :  32540.063480    -0.184059
> 2521230822 :  32542.2970040    -0.1840721
>
>
>
>
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