R help - Apr 2009 - How to compare parameters of non linear fitting curves

Hi,

I'm using a non linear model to fit experimental survival curves.

This model describes the fraction of "still active" experiments as a  
function of time t as follows:
f(t)=(1+exp(-etaD*cD)) / (1+exp(etaD(t-cD)))

Moreover, when experiments are still active, they may change of state  
(from 0 to 1). But they may fall inactive before changing their state  
(their state still equals 0). The survival curve of state may also be  
fitted with the following model:
f(A)=(1+exp(-eta1*c1)) / (1+exp(eta1(t-c1))) * (1+exp(-etaD*cD)) /  
(1+exp(etaD(t-cD)))

I estimate with nlm 1?) values of etaD and cD parameters and 2?)  
inject them as constant in the function to be minimized by nlm to  
estimate values of eta1 and c1.

I perform these estimations for two different experimental conditions  
that both have their values of etaD,eta1, cD and c1.

I would like to know if there is any statistical method to compare the  
estimated values of parameters of the two distributions ? And wether  
it's the case, how to perform it in R ?

Hope I'm clear enough for getting help,

Etienne

-------------------------------------------------------------------
Etienne Toffin, PhD Student
Unit of Social Ecology
Universit? Libre de Bruxelles, CP 231
Boulevard du Triomphe
B-1050 Brussels
Belgium

Tel: +32(0)2/650.55.30
Fax: +32(0)2/650.57.67
http://www.ulb.ac.be/sciences/use/toffin.html

Is your first model a special case of the second with eta1 = 0?  
If yes, what about using 2*log(likelihood ratio) being approximately 
chi-square? 


      Can you recast the problem to use "nls"?  If yes, might the
'nls'
methods for 'anova' or 'profile' give you what you want? 


      Hope this helps,
      Spencer

Etienne Toffin wrote:
> Hi,
>
> I'm using a non linear model to fit experimental survival curves.
>
> This model describes the fraction of "still active" experiments
as a
> function of time t as follows:
> f(t)=(1+exp(-etaD*cD)) / (1+exp(etaD(t-cD)))
>
> Moreover, when experiments are still active, they may change of state 
> (from 0 to 1). But they may fall inactive before changing their state 
> (their state still equals 0). The survival curve of state may also be 
> fitted with the following model:
> f(A)=(1+exp(-eta1*c1)) / (1+exp(eta1(t-c1))) * (1+exp(-etaD*cD)) / 
> (1+exp(etaD(t-cD)))
>
> I estimate with nlm 1?) values of etaD and cD parameters and 2?) 
> inject them as constant in the function to be minimized by nlm to 
> estimate values of eta1 and c1.
>
> I perform these estimations for two different experimental conditions 
> that both have their values of etaD,eta1, cD and c1.
>
> I would like to know if there is any statistical method to compare the 
> estimated values of parameters of the two distributions ? And wether 
> it's the case, how to perform it in R ?
>
> Hope I'm clear enough for getting help,
>
> Etienne
>
> -------------------------------------------------------------------
> Etienne Toffin, PhD Student
> Unit of Social Ecology
> Universit? Libre de Bruxelles, CP 231
> Boulevard du Triomphe
> B-1050 Brussels
> Belgium
>
> Tel: +32(0)2/650.55.30
> Fax: +32(0)2/650.57.67
> http://www.ulb.ac.be/sciences/use/toffin.html
>
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