[R] nls, reach limit bounds

[UyenThao Nguyen]

Hi Ravi and Spencer,

Thank you very much for your help.

I did plot the data, and saw that the data didn't seem to have an inflection point. Yes, the data contained 6 points of duplicates, which the 4 P logistic regression is appropriate to use. 

I tried the dose response model (drm in drc package), this model works without any problem. Do you know if the drm has different tolerance in convergent or something else? Let's say if I choose drm to fit the data, Can I get the parameters in the same way nls gives me? I tested a converged data set on both drm and nls, and I can't see any relationship between their parameters although the fits were similar.

Thank you.
Uyen

-----Original Message-----
From: Ravi Varadhan [mailto:RVaradhan at jhmi.edu] 
Sent: Monday, July 13, 2009 3:32 PM
To: 'spencerg'; UyenThao Nguyen
Cc: r-help at r-project.org
Subject: RE: [R] nls, reach limit bounds

Hi Uyen, 

You do not have enough information to estimate 4 parameters in your
nonlinear model.  Even though you have 12 data points, only 6 are
contributing independent information (you essentially have 6 replicate
points).  If you plot the fittted function you will see that it fits your
data really well.  However, you will also see that the fitted curve is far
from reaching the asymptote.  An implication of this is that you cannot
reliably estimate b0 and b1 separately.  So, you need more data, especially
for larger x values in the asymptotic region.

Ravi.

----------------------------------------------------------------------------
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Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:
http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadhan.h
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-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of spencerg
Sent: Saturday, July 11, 2009 9:50 PM
To: UyenThao Nguyen
Cc: r-help at r-project.org
Subject: Re: [R] nls, reach limit bounds

      Have you plotted the data?  There are two standard sources of
non-convergence problems like this:  First, there may not be enough
information in your data to estimate all four parameters.  Second, if that's
not the case, then  your starting values are not appropriate. 


      I routinely use "optim" or "nlminb" to find a sensible solution,
because these general purpose optimizers are more likely to converge than
"nls".  To do this, I write a function with a name like "SSElogistic" to
compute the sum of squares of residuals for your model.  I like to use
"optim" with "hessian=TRUE".  Then I compute "eigen(fit$hessian,
symmetric=TRUE)", with "fit" = the object returned by "optim".  If the
smallest eigenvalue is negative, it says that optim found a saddle point.
If the smallest eigenvalue is less than, e.g.,
1e-8 times the largest, it says that the smallest eigenvector is very poorly
estimated.  Round those numbers off grossly to 1 significant digit, and they
will likely suggest which parameter you can fix and drop from the model. 


      Hope this helps. 
      Spencer Graves


UyenThao Nguyen wrote:
> Hi,
>
> I am trying to fit a 4p logistic to this data, using nls function. The
function didn't freely converge; however, it converged if I put a lower and
an upper bound (in algorithm port). Also, the b1.A parameter always takes
value of the upper bound, which is very strange. Has anyone experienced
about non-convergent of nls and how to deal with this kind of problem?
>
> Thank you very much.
>
>
>
> ########################################################################3
>            y           x
> 1  0.8924619 -0.31875876
> 2  1.1814749 -0.21467016
> 3  1.6148266  0.06069784
> 4  2.2091363  0.54032947
> 5  2.7019079  1.04921802
> 6  3.0679585  1.60745502
> 9  0.9436973 -0.31875876
> 10 1.2201133 -0.21467016
> 11 1.6470043  0.06069784
> 12 2.2090048  0.54032947
> 13 2.6864857  1.04921802
> 14 3.0673523  1.60745502
>
> new.cont=nls.control(maxiter = 10000, tol = 1e-05, minFactor = 1e-08,
>             printEval = FALSE, warnOnly = FALSE)
>
>
> b0.A=.9*min(DAT$y)
> b1.A=1.1*max(DAT$y)-b0.A
> b2.A=-1*mean(DAT$x)
> b3.A=1
>
>
> b0.A
> b1.A
> b2.A
> b3.A
>
> nls.mdl.A=nls(y~b0 + b1/(1+exp(-b2-b3*x)),data=DAT,start = 
> list(b0=b0.A, b1=b1.A, b2=b2.A, b3=b3.A), lower=-10, upper=10, 
> algorithm="port",trace=T,control=new.cont)
>
> ##################################
>
>
>
> 	[[alternative HTML version deleted]]
>
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