Common Nonlinear Models

Here are several nonlinear models that come with the distribution of Splus and its open source sister, "R". I am approaching these models from a usability standpoint and looking for ways to simplify the analysis of data. The figures here were all generated using bezier curves from an applet. The figures are all examples of SVG, which is a W3C vector graphics specification .

Asymptotic Regression Model

The classic model for asymptotic regression is growth of the Loblolly pine.

Biexponential model

The classic model for a nonlinear fit of biexponential data is the pharmacokinetics of indomethacin.

First-order Compartment Model

This model arises from pharmakinetics, which is the dynamics of drug absorbtion, distribution and elimination. The factors in the model are rate of absorbtion and rate of elimination, which give rise to a stiff ODE system that decays exponentially. Since there are biological considerations, a nonlinear fit method is often more useful than the ODE solution.  In the function, d0 is the initial does, Ke is the elimination rate constant, Ka is the absorbtion rate constant, and Cl is the measure of the body's ability to eliminate the drug or clearance.

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References

The R Project

Classic equations

Winter: An Ecological Handbook


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