Parsimonious additive models

We present a new method for function estimation and variable selection, specifically designed for additive models fitted by cubic splines. Our method involves regularizing additive models using the l1–norm, which generalizes Tibshirani’s lasso to the nonparametric setting. As in the linear case, it shrinks coefficients, some of them reducing exactly to zero. It gives parsimonious models, select significant variables, and reveal nonlinearities in the effects of predictors. Two strategies for finding a parsimonious additive model solutions are proposed. Both algorithms are based on a fixed point algorithm, combined with a singular value decomposition that considerably reduces computation. The empirical behavior of parsimonious additive models is compared to the adaptive backfitting BRUTO algorithm. The results allow us to characterise the domains in which our approach is effective: it performs significantly better than BRUTO when model estimation is challenging. An implementation of this method is illustrated using real data from the Cophar 1 ANRS 102 trial. Parsimonious additive models are applied to predict the indinavir plasma concentration in HIV patients. Results suggest that our method is a promising technique for the research and application areas.