Generalized Linear Additive Smooth Structures

• Activity Number: 254
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Brian Marx*+ and Paul Eilers
• Affiliation(s): Louisana State University and Leiden University
• Keywords: general additive models ; P-splines ; signal regression ; varing-coefficient models

Abstract

We propose a practical modeling approach that can accommodate a rich variety of predictors, united in a generalized linear model (GLM) setting. In addition to the usual ANOVA-type or covariate linear (L) predictors, we consider modeling any combination of smooth additive (G) components, varying coefficient} (V) components, and discrete representations of) signal (S) components. We assume that G is, and the coefficients of V and S are, inherently smooth--projecting each of these onto B-spline bases using a modest number of equally spaced knots. Enough knots are used to ensure more flexibility than needed; further smoothness is achieved through a difference penalty on adjacent B-spline coefficients (P-splines). This linear re-expression allows all of the parameters associated with these components to be estimated simultaneously in one large GLM through penalized likelihood. Thus, we have the advantage of avoiding both the backfitting algorithm and complex knot selection schemes. We regulate the flexibility of each component through a separate penalty parameter that is optimally chosen based on cross-validation or an information criterion.