Generalized boosted additive models

Abstract Additive nonparametric regression models have become widespread statistical tools. When multicollinearity is present in the data Generalized additive models present instability in the fitting process. This phenomenon, known as concurvity, can lead to poor parameter estimates. We provide a methodology to deal with data affected by collinearity and concurvity and an alternative class of models, the Generalized Boosted Additive Model (GBAM), that is not affected by concurvity. GBAMs are based on prediction components, obtained via regression with optimal scaling transformations, that are computed in a sequential way, using a forward stagewise boosting procedure, to predict the outcome variable with the aim to obtain an improvement in the predictive power of the model.