Accounting for Data-Dependent Degrees of Freedom Selection When Testing the Effect of a Continuous Covariate in Generalized Additive Models

摘要

Often in generalized additive models (GAMs), the amount of smoothing is chosen to optimize some data-dependent criterion (e.g., AIC). Through simulations, we estimated the type I error of the GAM-based tests of (i) no association and (ii) linearity while using this approach. Overall, type I error rates were much higher than nominal levels. We proposed new critical values, which resulted in correct Overall type I error. We also compared power to detect nonlinearities of GAMs with several df-selection strategies with conventional parametric models. To illustrate our approach, we re-analyzed the association between body mass index and coronary heart disease mortality.