  Generalized additive models (GAMs) play an important role in modeling and
understanding complex relationships in modern applied statistics. They allow
for flexible, data-driven estimation of covariate effects. Yet researchers
often have a priori knowledge of certain effects, which might be monotonic or
periodic (cyclic) or should fulfill boundary conditions. We propose a unified
framework to incorporate these constraints for both univariate and bivariate
effect estimates and for varying coefficients. As the framework is based on
component-wise boosting methods, variables can be selected intrinsically, and
effects can be estimated for a wide range of different distributional
assumptions. Bootstrap confidence intervals for the effect estimates are
derived to assess the models. We present three case studies from environmental
sciences to illustrate the proposed seamless modeling framework. All discussed
constrained effect estimates are implemented in the comprehensive R package
mboost for model-based boosting.
