Methodology (stat.ME)

Abstract: This work introduces a novel framework for dynamic factor model-based data integration of multiple subjects, called GRoup Integrative DYnamic factor models (GRIDY). The framework facilitates the determination of inter-subject differences between two pre-labeled groups by considering a combination of group spatial information and individual temporal dependence. Furthermore, it enables the identification of intra-subject differences over time by employing different model configurations for each subject. Methodologically, the framework combines a novel principal angle-based rank selection algorithm and a non-iterative integrative analysis framework. Inspired by simultaneous component analysis, this approach also reconstructs identifiable latent factor series with flexible covariance structures. The performance of the framework is evaluated through simulations conducted under various scenarios and the analysis of resting-state functional MRI data collected from multiple subjects in both the Autism Spectrum Disorder group and the control group.

Abstract: This paper investigates a general family of models that stratifies the space of covariance matrices by eigenvalue multiplicity. This family, coined Stratified Principal Component Analysis (SPCA), includes in particular Probabilistic PCA (PPCA) models, where the noise component is assumed to be isotropic. We provide an explicit maximum likelihood and a geometric characterization relying on flag manifolds. A key outcome of this analysis is that PPCA's parsimony (with respect to the full covariance model) is due to the eigenvalue-equality constraint in the noise space and the subsequent inference of a multidimensional eigenspace. The sequential nature of flag manifolds enables to extend this constraint to the signal space and bring more parsimonious models. Moreover, the stratification and the induced partial order on SPCA yield efficient model selection heuristics. Experiments on simulated and real datasets substantiate the interest of equalising adjacent sample eigenvalues when the gaps are small and the number of samples is limited. They notably demonstrate that SPCA models achieve a better complexity/goodness-of-fit tradeoff than PPCA.

Abstract: Intensive longitudinal data (ILD) collected in mobile health (mHealth) studies contain rich information on multiple outcomes measured frequently over time that have the potential to capture short-term and long-term dynamics. Motivated by an mHealth study of smoking cessation in which participants self-report the intensity of many emotions multiple times per day, we propose a dynamic factor model that summarizes the ILD as a low-dimensional, interpretable latent process. This model consists of two submodels: (i) a measurement submodel -- a factor model -- that summarizes the multivariate longitudinal outcome as lower-dimensional latent variables and (ii) a structural submodel -- an Ornstein-Uhlenbeck (OU) stochastic process -- that captures the temporal dynamics of the multivariate latent process in continuous time. We derive a closed-form likelihood for the marginal distribution of the outcome and the computationally-simpler sparse precision matrix for the OU process. We propose a block coordinate descent algorithm for estimation. Finally, we apply our method to the mHealth data to summarize the dynamics of 18 different emotions as two latent processes. These latent processes are interpreted by behavioral scientists as the psychological constructs of positive and negative affect and are key in understanding vulnerability to lapsing back to tobacco use among smokers attempting to quit.