[R] Estimate parameters differential equations system

[peter dalgaard]

If you can solve the system and the parameters are identifiable from the y component, then I would think that nls() can do it. However, beware unidentifiablity: If x stays constant at its equilibrium value of (er...) d1*c/(m+d1), then even knowing x won't allow you to tease out c, d1, and m; and not knowing x you can't separate m from x in the mx term in dy/dt. So it likely depends on the exact experiment, especially the initial conditions of the system whether you can estimate things or not.

-pd

> On 29 Aug 2018, at 15:19 , Fanny Gallais <gallais.fanny using gmail.com> wrote:
> 
> Dear R users,
> 
> 
> 
> I am working on a simple mathematical model made of two ordinary
> differential equations:
> 
> 
> 
> dx/dt=-mx-d1(x-c)
> 
> dy/dt=mx-d2y
> 
> 
> 
> I would like to fit this model to my data and estimate the corresponding
> parameters. The thing is I only have observed data for y, x is unknown. Is
> it possible to do this in R?
> 
> 
> 
> Thank you for your help
> 
> Fanny
> 
> 	[[alternative HTML version deleted]]
> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
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