Sparse Pairwise Likelihood Estimation for Multivariate Longitudinal Mixed Models

ABSTRACTIt is becoming increasingly common in longitudinal studies to collect and analyze data on multiple responses. For example, in the social sciences we may be interested in uncovering the factors driving mental health of individuals over time, where mental health is measured using a set of questionnaire items. One approach to analyzing such multi-dimensional data is multivariate mixed models, an extension of the standard univariate mixed model to handle multiple responses. Estimating multivariate mixed models presents a considerable challenge however, let alone performing variable selection to uncover which covariates are important in driving each response. Motivated by composite likelihood ideas, we propose a new approach for estimation and fixed effects selection in multivariate mixed models, called approximate pairwise likelihood estimation and shrinkage (APLES). The method works by constructing a quadratic approximation to each term in the pairwise likelihood function, and then augmenting this ap...