## SPLINE, BSPLINE, and PSPLINE Comparisons

SPLINE is a transformation. It takes a variable as input and produces a
transformed variable as output. Internally, with SPLINE, a B-spline
basis is used to find the transformation, which is a linear combination
of the columns of the B-spline basis. However, with SPLINE, the basis is
not made available in any output.
BSPLINE is an expansion. It takes a variable as input and produces more
than one variable as output. The output variables comprise the B-spline
basis that is used internally by SPLINE.

PSPLINE is an expansion. It takes a variable as input and produces more
than one variable as output. The difference between PSPLINE and BSPLINE
is that PSPLINE produces a piecewise polynomial, whereas BSPLINE
produces a B-spline. A matrix consisting of a piecewise polynomial
basis and an intercept spans the same space as the B-spline matrix, but
the basis vectors are quite different. The numbers in the piecewise
polynomials can get quite large; the numbers in the B-spline basis range
between 0 and 1. There are many more zeros in the B-spline basis.

Interchanging SPLINE, BSPLINE, and PSPLINE should have no effect on the
fit of the overall model except for the fact that PSPLINE is much more
prone to numerical problems. Similarly, interchanging a CLASS
expansion and an OPSCORE
transformation should have no effect on the fit of the overall model.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.