Principal-Component-Based Functional Linear Mixed Models

• Activity Number: 20
• Type: Topic Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Sonja Greven* and Jona Cederbaum and Haochang Shou
• Companies: LMU and Ludwig Maximilians University Munich and University of Pennsylvania
• Keywords: functional data ; functional principal components ; functional additive mixed model ; Karhunen-Loeve-expansion ; sparse functional data

Abstract

We propose a general class of functional linear mixed models, where latent processes are expanded in truncated functional principal component (FPC) bases. FPCs, due to representing the main modes of variation in the data, typically allow for representations with few basis functions and thus can increase computational efficiency as well as often being of interest in their own right. We provide estimation approaches that allow for separate FPC expansions for each latent process. We extend the class of principal-component-based functional linear mixed models compared to previous approaches as well as allowing for sparsely observed functional data. In addition, we show how to embed our approach in a functional additive mixed model framework, which allows for approximate inference in addition to point estimation. We apply our methods to a phonetic study on sibilant assimilation.