Modeling and Multivariate Methods - SAS

46 Introduction to the Fit Model Platform Chapter 2
Construct Model Effects
Table 2.4 Descriptions of the Attributes Options (Continued)
Excluded Effect
Knotted Spline Effect
Use the Excluded Effect attribute when you want to estimate least squares
means of an interaction, or include it in lack of fit calculations, but do not
want it in the model.
Assigns the Knotted attribute to an effect. Choose the number of knots.
When you run the model, JMP fits a segmentation of smooth polynomials
to the specified effect. When you select this attribute, a dialog box appears
where you can specify the number of knot points.
Note: Knotted splines are implemented only for main-effect continuous
terms.
See “Knotted Spline Effect” on page 46.
Knotted Spline Effect
Note: Knotted splines are implemented only for main-effect continuous terms.
Use the Knotted Spline Effect option to have JMP fit a segmentation of smooth polynomials to the
specified effect. When you select this attribute, a window appears, enabling you to specify the number of
knot points.
JMP follows the advice in the literature in positioning the points. The knotted spline is also referred to as a
Stone spline or a Stone-Koo spline. See Stone and Koo (1986). If there are 100 or fewer points, the first and
last knot is the fifth point inside the minimum and maximum, respectively. Otherwise, the first and last
knot is placed at the 0.05 and 0.95 quantile if there are 5 or fewer knots, or the 0.025 and 0.975 quantile for
more than 5 knots. The default number of knots is 5 unless there are less than or equal to 30 points. In that
case, the default is 3 knots.
Knotted splines have the following properties in contrast to smoothing splines:
• Knotted splines work inside of general models with many terms, where smoothing splines are for
bivariate regressions.
• The regression basis is not a function of the response.
• Knotted splines are parsimonious, adding only k – 2 terms for curvature for k knot points.
• Knotted splines are conservative compared to pure polynomials in the sense that the extrapolation
outside the range of the data is a straight line, rather than a (curvy) polynomial.
• There is an easy test for curvature.
Example Using the Knotted Spline Effect to Test for Curvature
To test for curvature, follow these steps:
1. Open the Growth.jmp sample data table.
2. Select Analyze > Fit Model.