Model Browser User's Guide

Local Model Class: Polynomials and Polynomial Splines

Polynomials

At the local level, if you have one input factor, you can choose Polynomial directly from the list of local model classes. Here you can choose the order of polynomials used, and you can define a datum model for this kind of local model (see below).

If there is more than one input factor, you can only choose Linear Models or Transient Models from the Local Model Class list. Under Linear Models you can choose Polynomial or Hybrid Spline. This is a different polynomial model where you can change more settings such as Stepwise, the Term Editor (where you can remove any model terms) and you can choose different orders for different factors (as with the global level polynomial models). See Local Model Class: Linear Models.

Different response features are available for this polynomial model and the Linear Models: Polynomial choice. You can view these by clicking the Response Features tab on the Local Model Setup dialog. Single input polynomials can have a datum model, and you can define response features relative to the datum. See Datum Models

See Polynomials for a general description of polynomial models.

Polynomial Spline

A spline is a piecewise polynomial, where different sections of polynomial are fitted smoothly together. The location of each break is called a knot.

This model has only one knot. You can choose the orders of the polynomials above and below the knot. See also Hybrid Splines. These global models also use splines, but use the same order polynomial throughout.

Polynomial splines are only available for single input factors. The following example shows a typical torque/spark curve, which requires a spline to fit properly. The knot is shown as a red spot at the maximum, and the curvature above and below the knot is different. In this case there is a cubic basis function below the knot and a quadratic above.

See Polynomial Splines for statistical details.

Local Model Setup

Local Model Class: Truncated Power Series