Smoothing Splines

Select menu: Stats | Regression Analysis | Linear Models

The Smoothing spline option can be selected from the Linear Regression dialog dropdown list.

Smoothing splines are complicated functions, constructed from segments of cubic polynomials between the distinct values of a variate, and constrained to be “smooth” at the junctions. Models that contain splines are no longer linear, but are described as additive models because the effects of separate explanatory variates are still combined additively. The main use of smoothed terms in regression are to investigate the shape relationship with a view to later, parametric fitting, and to remove the effect of nuisance variables so as to concentrate on the variables of interest.

Response variate

Specifies the name of the response (or y-) variate.

Explanatory variate

Specifies the name of the explanatory (or x-) variate.

Degrees of freedom

Specifies the degrees of freedom to control the smoothness. This is effectively increasing or relaxing the constraints.

Groups

If the data values are classified into groups you can supply a factor defining the different categories. When a grouping factor is supplied a series of models are fitted.

The first model fitted (Common curve) is a spline regression, ignoring the groups. The second model (Parallel curves) is extended to include a different constant (or intercept) for each group, giving a set of parallel curves one for each group. The third model (Separate slopes) fits a common spline component to all groups, but allows each group to have a separate constant and linear slope term. The final model (Separate curves) has different constants, slopes and spline regressions for each group. The Final model list below the Groups field lets you select between the types of regression model that you want to fit.

Final model

This option is disabled until Run has been used, so that it fits all models and then lets you select the most appropriate model after reviewing the fits. If the analysis shows that different intercepts or slopes or spline terms are needed, you can use this option to select the final model and re-run the analysis to remove the interaction between the locally weighted regression and the groups factor. Similarly, if different intercepts or slopes are not needed this option can be used to fit just a common spline regression.