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We examined multi-level factors related to the longitudinal physical activity trajectories of adolescent girls to determine the important predictors for physical activity. The Trial of Activity in Adolescent Girls (TAAG) Maryland site recruited participants at age 14 ( n = 566) and followed up with these girls at age 17 ( n = 553) and age 23 ( n = 442). Individual, social factors and perceived environmental factors were assessed by questionnaire; body mass index was measured at age 14 and age 17, and self-reported at age 23. Neighborhood factors were assessed by geographic information systems. The outcome, moderate-to-vigorous physical activity (MVPA) minutes in a day, was assessed from accelerometers. A mixture of linear mixed-effects models with double penalization on fixed effects and random effects was used to identify the intrinsic grouping of participants with similar physical activity trajectory patterns and the most relevant predictors within the groups simultaneously. Three clusters of participants were identified. Two hundred and forty participants were clustered as “maintainers” and had consistently low MVPA over time; 289 participants were clustered as “decreasers” who had decreasing MVPA over time; 39 participants were grouped as “increasers” and had increasing MVPA over time. Each of the three clusters has its own cluster-specific factors identified using the clustering method, indicating that each cluster has unique characteristics. 

Abstract We propose a model-based clustering method for high-dimensional longitudinal data via regularization in this paper. This study was motivated by the Trial of Activity in Adolescent Girls (TAAG), which aimed to examine multilevel factors related to the change of physical activity by following up a cohort of 783 girls over 10 years from adolescence to early adulthood. Our goal is to identify the intrinsic grouping of subjects with similar patterns of physical activity trajectories and the most relevant predictors within each group. The previous analyses conducted clustering and variable selection in two steps, while our new method can perform the tasks simultaneously. Within each cluster, a linear mixed-effects model (LMM) is fitted with a doubly penalized likelihood to induce sparsity for parameter estimation and effect selection. The large-sample joint properties are established, allowing the dimensions of both fixed and random effects to increase at an exponential rate of the sample size, with a general class of penalty functions. Assuming subjects are drawn from a Gaussian mixture distribution, model effects and cluster labels are estimated via a coordinate descent algorithm nested inside the Expectation-Maximization (EM) algorithm. Bayesian Information Criterion (BIC) is used to determine the optimal number of clusters and the values of tuning parameters. Our numerical studies show that the new method has satisfactory performance and is able to accommodate complex data with multilevel and/or longitudinal effects.