The TPSPLINE procedure uses the penalized least squares method to fit a nonparametric regression model. It computes thin-plate smoothing splines to approximate smooth multivariate functions observed with noise. The TPSPLINE procedure allows great flexibility in the possible form of the regression surface. In particular, PROC TPSPLINE makes no assumptions of a parametric form for the model. The generalized cross validation (GCV) function can be used to select the amount of smoothing.

The TPSPLINE procedure complements the methods provided by the standard SAS regression procedures such as the GLM, REG, and NLIN procedures. These procedures can handle most situations in which you specify the regression model and the model is known up to a fixed number of parameters. However, when you have no prior knowledge about the model, or when you know that the data cannot be represented by a model with a fixed number of parameters, you can use the TPSPLINE procedure to model the data.

The TPSPLINE procedure uses the penalized least squares method to fit the data with a flexible model in which the number of effective parameters can be as large as the number of unique design points. Hence, as the sample size increases, the model space also increases, enabling the thin-plate smoothing spline to fit more complicated situations.

The main features of the TPSPLINE procedure are as follows:

provides penalized least squares estimates

supports the use of multidimensional data

supports multiple SCORE statements

fits both semiparametric models and nonparametric models

provides options for handling large data sets

supports multiple dependent variables

enables you to choose a particular model by specifying the model degrees of freedom or smoothing parameter

supports graphical displays produced through ODS Graphics