Five Parameter Logistics
Joerg Steinhilper
I'm looking for a formula to fit a set of data to a so called "five
parameter logistic" curve. I've already done this using a four
parameter logistic using
the following formula:
A - D
y = ( ------------- ) + D
1 + (x/C)^B
...And now I'm urgently looking for the 5 param. version.
Thanks,
Joerg
Peter Spellucci
In article <4ac97ddd.04020...@posting.google.com>,
ng.20....@spamgourmet.com (Joerg Steinhilper) writes:
so what is the fundamental difference?
you will use a nonlinear least squares estimator anyway.
see
http://plato.la.asu.edu/topics/problems/nlolsq.html
hth
peter
beli...@aol.com
If you expect your data to follow the functional form exactly, it
seems you have a set of nonlinear equations to solve. If your data has
noise, you have a nonlinear least squares problem. There exists
software for both types of problems.
Joerg Steinhilper
Peter,
many thanks for the link :-)
I will look through the sw to find an appropriate fit. I guess the
Levenberg Marq. 'method' would be the best to go for.
Thanks, Joerg
Jerry W. Lewis
a way to fit the coefficients given the five parameter model. Since you
posted in the numerical analysis newsgroups, the previous replies
presume that you know the model and just need to know how to fit it.
Since you only give the four paramter model, I presume that you are
farther back and don't know the five parameter model.
The only five parameter logistic that I have seen raises the entire
denominator to a power to give an asymmetric sigmoidal curve. When that
power is one, then it reduces to the four parameter model.
As far as I know, it is a pragmatic way to remove symmetry from the
curve that has no physical interpretation.
Jerry
Joerg Steinhilper
The desired 5PL (required in my special case) is:
A - D
y = D + -------------------------------------
[ 1 + ( x / C )^B ]^E
and I'm using the Levenberg-Marquardt algoritem/method to
evaluate the parameters to fit the set of data points.
Many thanks for giving direction to the appropriate solution ;)
Joerg
"Jerry W. Lewis" <post_a_reply@no_e-mail.com> wrote in message news:<402368E1.5000609@no_e-mail.com>...
beli...@aol.com
> I would like to state my final findings:
>
> The desired 5PL (required in my special case) is:
>
> A - D
> y = D + -------------------------------------
> [ 1 + ( x / C )^B ]^E
>
> and I'm using the Levenberg-Marquardt algoritem/method to
> evaluate the parameters to fit the set of data points.
>
> Many thanks for giving direction to the appropriate solution ;)
>
> Joerg
Your function is linear in A and D but nonlinear in B, C, and E.
Therefore you could reformulate your problem as a nonlinear least
squares fit in B, C, and E -- for any set of values of these
parameters, A and D can be computed using linear least squares.