[Paper Review] Discovering Psychological Dynamics in Time-Series Data

Sacha Epskamp, Lourens Waldorp+2 more|arXiv (Cornell University)|Sep 14, 2016

Mental Health Research Topics9 citations

TL;DR

This paper introduces a novel multilevel vector autoregression (mlVAR) framework that extends Gaussian graphical models (GGMs) to time-series psychological data by simultaneously estimating within-subject temporal networks and between-subject contemporaneous networks. It demonstrates that multilevel VAR models can disentangle within- and between-subject effects, revealing causal-like pathways through both time-lagged and contemporaneous relationships, and implements the method in an R package for empirical use.

ABSTRACT

This paper provides a methodological overview of statistical network models in cross-sectional and time-series data. The increasing trend of modeling psychological data through networks attempts to highlight potential causal relationships between observed variables. When data are cross-sectional, it is becoming increasingly popular to estimate a Gaussian graphical model (GGM; a network of partial correlation coefficients). In a time-series analysis, networks are typically constructed through the use of (multilevel) vector autoregression (VAR). VAR estimates a directed network that encodes temporal predictive effects - the temporal network. We show that GGM and VAR models are closely related: VAR generalizes the GGM by taking violations of independence between consecutive cases into account. VAR analyses can also return a GGM that encodes relationships within the same window of measurement - the contemporaneous network, which has not yet been extensively utilized in the literature. When multiple subjects are measured, multilevel VAR estimates fixed and random temporal networks. Proper centering can disentangle within- and between-subject variance in such processes. We show, for the first time, that the between-subject effects can be summarized in a GGM network - the between-subjects network. We argue that such between-subjects effects can also indicate causal pathways. Furthermore, we propose a novel two-step, multilevel estimation procedure to obtain fixed and random effects for contemporaneous network structures. We have implemented this procedure in the R package mlVAR. We present a simulation study to show the performance of mlVAR and to showcase the method in an empirical example on personality inventory items and physical exercise.

Motivation & Objective

• To address the gap in modeling both temporal and contemporaneous relationships in longitudinal psychological data.
• To develop a method that disentangles within-subject dynamics from between-subject differences in network structures.
• To show that between-subject networks—previously underutilized—can reflect meaningful causal pathways.
• To propose a two-step multileleve estimation procedure for estimating fixed and random effects in contemporaneous (GGM-like) networks.
• To implement and validate the method via simulation and empirical application to personality and physical exercise data.

Proposed method

• The method uses multilevel vector autoregression (VAR) to model time-lagged predictive effects between variables across time points.
• It estimates fixed and random effects for temporal networks, capturing individual differences in dynamic relationships.
• Proper centering of variables is applied to separate within- and between-subject variance components.
• The method extracts a contemporaneous network from the residual covariance matrix, representing relationships within the same measurement window.
• A two-step estimation procedure is proposed to separately estimate fixed and random effects for the contemporaneous network structure.
• The approach is implemented in the R package mlVAR, enabling scalable and reproducible analysis of multilevel time-series data.

Experimental results

Research questions

• RQ1 Can multilevel VAR models effectively disentangle within- and between-subject variance in psychological time-series data?
• RQ2 Do between-subject networks derived from multilevel VAR models reflect meaningful, potentially causal, relationships among variables?
• RQ3 How well can the proposed two-step estimation procedure recover fixed and random effects in contemporaneous network structures?
• RQ4 What is the performance of mlVAR in detecting true network structures under varying levels of measurement error and sample size?
• RQ5 Can the method uncover distinct psychological dynamics in personality traits and physical exercise behaviors over time?

Key findings

• The multilevel VAR framework successfully separates within- and between-subject effects, enabling the estimation of both temporal and contemporaneous network structures.
• Between-subject networks derived from residual covariance matrices capture stable, potentially causal, relationships across individuals.
• The two-step estimation procedure for contemporaneous networks improves accuracy in estimating fixed and random effects compared to standard approaches.
• Simulation results show that mlVAR maintains good statistical power and low Type I error rates under realistic conditions.
• Empirical analysis of personality and exercise data revealed distinct within-person dynamic patterns and meaningful between-person network structures.