R help - Nov 2012 - Logistic curve fitting with y values >1 (R version 2.15.2, OS is OS X 10.6.8)

Hello,

I'm trying to fit a logistic curve to data but I'm having a hard time
discovering how.  Every tutorial I've come across either assumes the
logistic curve has 0<y<1 or assumes I have multiple categories of data

I simply have two vectors, a and b, of equal length with no missing
data, and I suspect they follow a logistic curve.

The vectors are

a<-c(39609, 39643, 39700, 39829, 39889, 39926, 40008, 40084, 40183,
40276, 40297, 40336, 40422, 40471, 40565, 40700, 40731, 40820, 40971,
41071, 41205)

b<-c(0,10000000, 100000000, 500000000, 800000000, 1000000000,
1500000000, 2000000000, 3000000000, 4000000000, 4500000000,
5000000000, 6500000000, 7000000000, 10000000000, 14000000000,
15000000000, 18000000000, 25000000000, 30000000000, 35000000000)

How do I find the best-fit logistic curve for this data in R?

- J


PS:  The tutorials I mentioned are
http://www.apsnet.org/EDCENTER/ADVANCED/TOPICS/ECOLOGYANDEPIDEMIOLOGYINR/DISEASEPROGRESS/Pages/NonlinearRegression.aspx,
which assumes I have multiple categories of data, and
http://ww2.coastal.edu/kingw/statistics/R-tutorials/logistic.html
which only accepts y between 0 and 1.

On Nov 9, 2012, at 12:52 PM, Jacob B. <jdbowenusf at gmail.com> wrote:
> Hello,
> 
> I'm trying to fit a logistic curve to data but I'm having a hard
time
> discovering how.  Every tutorial I've come across either assumes the
> logistic curve has 0<y<1 or assumes I have multiple categories of
data
> 
> I simply have two vectors, a and b, of equal length with no missing
> data, and I suspect they follow a logistic curve.
> 
> The vectors are
> 
> a<-c(39609, 39643, 39700, 39829, 39889, 39926, 40008, 40084, 40183,
> 40276, 40297, 40336, 40422, 40471, 40565, 40700, 40731, 40820, 40971,
> 41071, 41205)
> 
> b<-c(0,10000000, 100000000, 500000000, 800000000, 1000000000,
> 1500000000, 2000000000, 3000000000, 4000000000, 4500000000,
> 5000000000, 6500000000, 7000000000, 10000000000, 14000000000,
> 15000000000, 18000000000, 25000000000, 30000000000, 35000000000)
> 
> How do I find the best-fit logistic curve for this data in R?
> 
> - J

You might want to look at John Fox' appendix on non-linear models for some
additional insights:

 
http://socserv.mcmaster.ca/jfox/Books/Companion/appendix/Appendix-Nonlinear-Regression.pdf

Regards,

Marc Schwartz