Fixed and random effects selection in nonparametric additive mixed models

Abstract

This paper considers the problem of model selection in a nonparametric additive mixed modeling framework. The fixed effects are modeled nonparametrically using truncated series expansions with B-spline basis. Estimation and selection of such nonparametric fixed effects are simultaneously achieved by using the adaptive group lasso methodology, while the random effects are selected by a traditional backward selection mechanism. To facilitate the automatic selection of model dimension, computable expressions for the degrees of freedom for both the fixed and random effects components are derived, and the Bayesian Information criterion (BIC) is used to select the final model choice. Theoretically it is shown that this BIC model selection method is consistent, while computationally a practical algorithm is developed for solving the optimization problem involved. Simulation results show that the proposed methodology is often capable of selecting the correct significant fixed and random effects components, especially when the sample size and/or signal to noise ratio are not too small. The new method is also applied to two real data sets.