Detecting Changes in Correlation Networks with Application to Functional Connectivity of fMRI Data.

Research questions in the human sciences often seek to answer if and when a process changes across time. In functional MRI studies, for instance, researchers may seek to assess the onset of a shift in brain state. For daily diary studies, the researcher may seek to identify when a person's psychological process shifts following treatment. The timing and presence of such a change may be meaningful in terms of understanding state changes. Currently, dynamic processes are typically quantified as static networks where edges indicate temporal relations among nodes, which may be variables reflecting emotions, behaviors, or brain activity. Here we describe three methods for detecting changes in such correlation networks from a data-driven perspective. Networks here are quantified using the lag-0 pair-wise correlation (or covariance) estimates as the representation of the dynamic relations among variables. We present three methods for change point detection: dynamic connectivity regression, max-type method, and a PCA-based method. The change point detection methods each include different ways to test if two given correlation network patterns from different segments in time are significantly different. These tests can also be used outside of the change point detection approaches to test any two given blocks of data. We compare the three methods for change point detection as well as the complementary significance testing approaches on simulated and empirical functional connectivity fMRI data examples.

Penalized Estimation and Forecasting of Multiple Subject Intensive Longitudinal Data.

Intensive longitudinal data (ILD) is an increasingly common data type in the social and behavioral sciences. Despite the many benefits these data provide, little work has been dedicated to realize the potential such data hold for forecasting dynamic processes at the individual level. To address this gap in the literature, we present the multi-VAR framework, a novel methodological approach allowing for penalized estimation of ILD collected from multiple individuals. Importantly, our approach estimates models for all individuals simultaneously and is capable of adaptively adjusting to the amount of heterogeneity present across individual dynamic processes. To accomplish this, we propose a novel proximal gradient descent algorithm for solving the multi-VAR problem and prove the consistency of the recovered transition matrices. We evaluate the forecasting performance of our method in comparison with a number of benchmark methods and provide an illustrative example involving the day-to-day emotional experiences of 16 individuals over an 11-week period.

A Square-Root Second-Order Extended Kalman Filtering Approach for Estimating Smoothly Time-Varying Parameters.

Researchers collecting intensive longitudinal data (ILD) are increasingly looking to model psychological processes, such as emotional dynamics, that organize and adapt across time in complex and meaningful ways. This is also the case for researchers looking to characterize the impact of an intervention on individual behavior. To be useful, statistical models must be capable of characterizing these processes as complex, time-dependent phenomenon, otherwise only a fraction of the system dynamics will be recovered. In this paper we introduce a Square-Root Second-Order Extended Kalman Filtering approach for estimating smoothly time-varying parameters. This approach is capable of handling dynamic factor models where the relations between variables underlying the processes of interest change in a manner that may be difficult to specify in advance. We examine the performance of our approach in a Monte Carlo simulation and show the proposed algorithm accurately recovers the unobserved states in the case of a bivariate dynamic factor model with time-varying dynamics and treatment effects. Furthermore, we illustrate the utility of our approach in characterizing the time-varying effect of a meditation intervention on day-to-day emotional experiences.

CHARACTERIZING FREQUENCY-SELECTIVE NETWORK VULNERABILITY FOR ALZHEIMER'S DISEASE BY IDENTIFYING CRITICAL HARMONIC PATTERNS.

Alzheimer's disease (AD) is a multi-factor neurodegenerative disease that selectively affects certain regions of the brain while other areas remain unaffected. The underlying mechanisms of this selectivity, however, are still largely elusive. To address this challenge, we propose a novel longitudinal network analysis method employing sparse logistic regression to identify frequency-specific oscillation patterns which contribute to the selective network vulnerability for patients at risk of advancing to the more severe stage of dementia. We fit and apply our statistical method to more than 100 longitudinal brain networks, and validate it on synthetic data. A set of critical connectome pathways are identified that exhibit strong association to the progression of AD.