Direct generalized additive modeling with penalized likelihood

Generalized additive models (GAMs) have become an elegant and practical option in model building. Estimation of a smooth GAM component traditionally requires an algorithm that cycles through and updates each smooth, while holding other components at their current estimated fit, until specified convergence. We aim to fit all the smooth components simultaneously. This can be achieved using penalized B-spline or P-spline smoothers for every smooth component, thus transforming GAMs into the generalized linear model framework. Using a large number of equally spaced knots, P-splines purposely overfit each B-spline component. To reduce flexibility, a difference penalty on adjacent B-spline coefficients is incorporated into a penalized version of the Fisher scoring algorithm. Each component has a separate smoothing parameter, and the penalty is optimally regulated through extensions of cross validation or information criterion. An example using logistic additive models provides illustrations of the developments. (C) 1998 Elsevier Science B.V. All rights reserved.