Hi everyone. This is my first post to this forum and I'm hoping someone can
help.

I'm trying to finish up some analysis for my thesis and this is the last
problem I have. I have calculated data for 15 different species of birds;
below is an example of one species and what the data might look like.

I have three a priori nonlinear curves that I want to test each data set
against in order to see which of the three curves has the best fit. (I
suspect the fit won't be that great for any of them in some instances.)

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=??))

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

My problem is I can't really figure out how to choose the correct starting
values to avoid getting the singular matrix error. Any help as to how to go
about this would be appreciated! Does everything look right? My method is
okay?

If I can get the fits to run I plan on using AIC to select the best curve
for each of the 15 species.

I thank you in advance for your consideration and help on this!
Cheers,
Corey Callaghan


df:
Area                     Year
104.7181283     1984
32.88026974     1985
56.07395863     1986
191.3422143     1987
233.4661392     1988
57.28317116     1989
201.1273404     1990
34.42570796     1991
165.8962342     1992
58.21905274     1993
114.6643724     1994
342.3461986     1995
184.8877994     1996
94.90509356     1997
45.2026941      1998
68.6196393      1999
575.2440229     2000
519.7557581     2001
904.157509      2002
1107.357517     2003
1682.876061     2004
40.55667824     2005
740.5032604     2006
885.7243469     2007
395.4190968     2008
1031.314519     2009
2597.544987     2010
1316.968695     2011
848.7093901     2012
5076.675075     2013
6132.975491     2014



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