[R] Quality of fit statistics for NLS?

[Bert Gunter]

Inline below.

-- Bert

On Thu, Jan 26, 2012 at 12:16 PM, Max Brondfield
<max.brondfield at gmail.com> wrote:
> Dear all,
> I am trying to analyze some non-linear data to which I have fit a curve of
> the following form:
>
> dum <- nls(y~(A + (B*x)/(C+x)), start = list(A=370,B=100,C=23000))
>
> I am wondering if there is any way to determine meaningful quality of fit
> statistics from the nls function?
>
> A summary yields highly significant p-values, but it is my impression that
> these are questionable at best given the iterative nature of the fit:
No. They are questionable primarily because there is no clear null
model. They are based on profile likelihoods (as ?confint tells you),
which may or may not be what you want for "goodness of fit."

One can always get "goodness of fit" statistics but the question in
nonlinear models is: goodness of fit with respect to what? So the
answer to your question is: if you know what you're doing, certainly.
Otherwise, find someone who does.




>
>> summary(dum)
>
> Formula: y ~ (A + (B * x)/(C + x))
>
> Parameters:
>   Estimate Std. Error t value Pr(>|t|)
> A   388.753      4.794  81.090  < 2e-16 ***
> B   115.215      5.006  23.015  < 2e-16 ***
> C 20843.832   4646.937   4.485 1.12e-05 ***
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Residual standard error: 18.25 on 245 degrees of freedom
>
> Number of iterations to convergence: 4
> Achieved convergence tolerance: 2.244e-06
>
>
> Is there any other means of determining the quality of the curve fit? I
> have tried applying confidence intervals using confint(dum), but these
> curves seem unrealistically narrow. Thanks so much for your help!
> -Max
>
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>
>
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>



-- 

Bert Gunter
Genentech Nonclinical Biostatistics

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