Simultaneous Coefficient Clustering and Sparsity for Multivariate Mixed Models

In many applications of multivariate longitudinal mixed models, it is reasonable to assume that each response is informed by only a subset of covariates. Moreover, one or more responses may exhibit the same relationship to a particular covariate for example, if they are capturing the same underlying aspect of an individual physical, mental, and emotional health. To address the above challenges, we propose a method for simultaneous clustering and variable selection of fixed effect coefficients in multivariate mixed models. We achieve this in a computationally scalable manner via a composite likelihood approach: separate mixed models are first fitted to each response, after which the model estimates are combined into a single quadratic form resembling a multivariate Wald statistic. We then augment this with fusion- and sparsity-inducing penalties based on broken adaptive ridge regression. Simulation studies demonstrate that the proposed composite quadratic estimator is similar to or better than several existing techniques for fixed effects selection in (univariate) mixed models while being computationally much more efficient. We apply the proposed method to longitudinal panel data from Australia to quantify how an individual's overall health, assessed via a set of eight composite scores, evolves as a function of various demographic and lifestyle variables.