Improved Insight into and Prediction of Network Dynamics by Combining VAR and Dimension Reduction

Abstract

To understand within-person psychological processes, one may fit VAR(1) models (or continuous-time variants thereof) to multivariate time series and display the VAR(1) coefficients as a network. This approach has two major problems. First, the contemporaneous correlations between the variables will frequently be substantial, yielding multicollinearity issues. Moreover, the shared effects of the variables are not included in the network. Consequently, VAR(1) networks can be hard to interpret. Second, cross-validation results show that the highly parametrized VAR(1) model is prone to overfitting. In this paper we compare the pros and cons of two potential solutions to both problems. The first is to impose a lasso penalty on the VAR(1) coefficients, setting some of them to zero. The second, which has not yet been pursued in psychological network analysis, uses principal component VAR(1) (termed PC-VAR(1)). In this approach, the variables are first reduced to a few principal components, which are rotated towards simple structure; then VAR(1) analysis (or a continuous-time analog) is applied to the rotated components. Reanalyzing the data of a single participant of the COGITO study, we show that PC-VAR(1) has the better predictive performance and that networks based on PC-VAR(1) clearly represent both the lagged and contemporaneous variable relations.

Understanding personalized dynamics to inform precision medicine: a dynamic time warp analysis of 255 depressed inpatients

“…Overall, the study of intra-individual temporal dynamics of depression symptoms is rare in the literature. A growing field of research has focused on the development of individual dynamic networks of symptoms in which time-series or experience sampling methods (ESM) data are used to study the within-patient dynamical structure of symptoms [43][44][45][46][47]. These networks are mostly estimated using vector autoregression (VAR) which estimates both lagged (i.e., time minus one temporal) and contemporaneous (i.e., simultaneous) relationships among multiple symptoms [45].…”

The network approach to psychopathology: a review of the literature 2008–2018 and an agenda for future research

“…in real time)’ they are posited to operate (Hamaker & Wichers, 2017). Researchers have thus developed (Beltz & Gates, 2017; Bringmann, Ferrer, Hamaker, Borsboom, & Tuerlinckx, 2018; Bringmann et al, 2013; Bulteel, Tuerlinckx, Brose, & Ceulemans, 2018; Epskamp et al, 2018c) and evaluated (Bulteel, Tuerlinckx, Brose, & Ceulemans, 2016b; de Haan-Rietdijk, Voelkle, Keijsers, & Hamaker, 2017; Kuiper & Ryan, 2018; Schuurman, Ferrer, de Boer-Sonnenschein, & Hamaker, 2016; Schuurman, Houtveen, & Hamaker, 2015) methods for estimating within-subject network structure. These methods, especially vector autoregressive models, are growing in popularity and promise to substantially inform our understanding of the relationships among symptoms (see Fig.…”

Collinearity issues in autoregressive models with time-varying serially dependent covariates

“…While the sources and consequences of predictor collinearity have received ample attention for crosssectional methods (some refs), we studied the issue in the context of time series analysis, where it has been investigated far less (but see Bulteel et al, 2016, Bulteel et al, 2018. Specifically, this paper examined whether predictor collinearity in AR(1) models with a time-varying covariate can emerge as a function of the serial dependence within the variables involved.…”