Introduction to Regression Procedures

Thin Plate Smoothing Splines: The TPSPLINE Procedure

PROC TPSPLINE decomposes the regressor contributions to the mean function into parametric components and into smooth functional components. Suppose that the regressor variables are collected into the vector bold x and that this vector is partitioned as bold x equals left-bracket bold x prime 1 bold x prime 2 right-bracket prime. The relationship between Y and bold x 2 is linear (parametric), and the relationship between Y and bold x 1 is nonparametric. PROC TPSPLINE fits models of the form

normal upper E left-bracket upper Y right-bracket equals g left-parenthesis bold x 1 right-parenthesis plus bold x prime 2 bold-italic beta

The function g left-parenthesis dot right-parenthesis can be represented as a sequence of spline basis functions.

The parameters are estimated by a penalized least squares method. The penalty is applied to the usual least squares criterion to obtain a regression estimate that fits the data well and to prevent the fit from attempting to interpolate the data (fit the data too closely).

Last updated: December 09, 2022