[R] Help with nonlinear least squares regression curve fitting

[Andrew Robinson]

Finding starting values is a bit of a dark art.  That said, there are steps
you can take, but it may take time.

First, I would scale Year so that it's not in the thousands! Experiment
with subtracting 1980 or so.  For specific advice, see inline.

On Thu, Feb 26, 2015 at 3:03 AM, Corey Callaghan <ccallaghan2013 at fau.edu>
wrote:

> The curves' functions that I want to test are in the code here (hopefully
> correctly):
>
> Inverse Quadratic Curve:
> fitmodel <- nls(Area ~ (-a*Year)*(Year + b), data = df, start=list(a=??,
> b=??, c=??))
>

I would plot the data and a smooth spline, differentiate the curve
function, identify some parameter values somewhere stable, and estimate
some values by eye, or even predict them from the first derivative of the
spline - spline.smooth will do this.

Sigmodial Curve:
> fitmodel <- nls(Area~a/(1+exp(-(b+c*Year))), data=df, start=list(a=???,
> b=???, c=??))
>

I'd use the highest value as a, fit spline as above then invert area at two
times to get b and c.

Double sigmoidal Curve:
> fitmodel <- nls(Area~a+2b(1/(1+exp(-abs(-c*Year+d)))-1/2)*sign(-c*Year+d),
> data=df, start=list(a=???, b=???, c=???)
>

 I'd use min(Area) as a, figure out b from the maximum (I guess 2b+a is the
asymptote), and experiment with two values for year to retrieve c and d
.... uniroot might help?

Cheers

Andrew

-- 
Andrew Robinson
Deputy Director, CEBRA, School of Biosciences
Reader & Associate Professor in Applied Statistics  Tel: (+61) 0403 138 955
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4599
University of Melbourne, VIC 3010 Australia
Email: a.robinson at ms.unimelb.edu.au
Website: http://www.ms.unimelb.edu.au/~andrewpr

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