A0151
Title: Sparse pairwise likelihood estimation for multivariate longitudinal mixed models
Authors: Francis Hui - The Australian National University (Australia) [presenting]
Samuel Muller - University of Sydney (Australia)
Alan Welsh - the Australian National University (Australia)
Abstract: In most longitudinal studies, the question of interest often involves studying not one but multiple response variables. For instance, in the social sciences we may be interested in uncovering the personal and environmental factors affecting the mental health of individuals over time, where mental health is measured using a set of questionnaire items. To analyze such data, we can extend the standard univariate mixed model approach to handle multiple outcomes. Estimating such multivariate mixed models presents a considerable challenge however, let alone performing variable selection to uncover which covariates are important in driving each of the outcomes. Motivated by composite likelihood ideas, we propose a new method for fixed effects selection in multivariate mixed models called Approximate Pairwise Likelihood Estimation and Shrinkage (APLES). The approach works by constructing a quadratic approximation to each component of the pairwise likelihood function, and augmenting this with a penalty that encourages individual and group coefficient sparsity. We show how the full regularization path for the APLES estimator can be constructed efficiently, and present a data-driven approach to selecting the tuning parameter. Asymptotic properties of the APLES estimator are discussed, with simulations studies demonstrating it can outperform univariate approaches based on analyzing each outcome separately.
