Title: Varying-coefficient additive models: Two birds with one stone?
Authors: Jane-Ling Wang - University of California Davis (United States) [presenting]
Xiaoke Zhang - George Washington University (United States)
Abstract: Both varying-coefficient and additive models have been widely adopted as non-parametric modeling approaches that enjoy flexibility and parsimony. An intriguing question is how to choose between these two models in practice. Recently, it was shown that this dichotomy can be altogether bypassed by embedding both models into a larger model, the varying-coefficient additive model (VCAM), which includes both models as special cases. However, that work was specifically designed for densely observed functional response with vector covariates. We show how to extend the VCAM model to more general settings that allow for sparsely observed functional responses, a.k.a. longitudinal data, and longitudinal covariates, in addition to vector covariates. A new algorithm is proposed and its performance is demonstrated through simulations and data applications. The algorithm involves non-convex maximization so the choice of the initial estimates plays a crucial role. We discuss several options and their empirical performance. Theoretical results are established for the nonparametric component functions of the model, including rates of convergence, and future directions will be discussed.