What is global nonlinear regression?

The idea of global nonlinear regression

A global model defines a family of curves, rather than just a single curve and some parameters are shared between data sets. For each shared parameter, fit one (global) best-fit value that applies to all the data sets. For each non-shared parameter, fit a separate (local) best-fit value for each data set.

Nonlinear regression finds parameters of a model that make the curve come as close as possible to the data. This is done by minimizing the sum of the squares of the vertical distances between the data points and curve. Global nonlinear regression extends this idea to fitting several data sets at once and minimizes the sum (of all data sets) of sum (of all data points) of squares.

The uses of global nonlinear regression

Prism makes it easy to share a parameter across several data sets in order to enable global curve fitting. There are three uses for this.

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Test whether a parameter differs significantly between data sets. Prism tests this by comparing the goodness-of-fit when the parameter is shared, with the goodness-of-fit when the parameter is fit individually to each dataset. You set up this kind of comparison in the Compare tab, not the Constrain tab.

•	Fit families of data where each dataset is incomplete, but the entire family of datasets defines the parameters. See an example.

•	Fit models where the parameter(s) you care about cannot be determined from any one dataset, but only from the relationship between several data sets.

The first two uses of global fitting do not require writing special models. The third use requires that you write a model for this purpose.

Global nonlinear regression with Prism

Prism makes it very easy to perform global nonlinear regression. Enter your data on one data table, click analyze, choose nonlinear regression and choose a model. On the Constrain tab of the Nonlinear regression dialog, choose which parameter(s) to share among data sets.