Analyzing Multiple Multivariate Time Series Data Using Multilevel Dynamic Factor Models

Abstract

Multivariate time series data offer researchers opportunities to study dynamics of various systems in social and behavioral sciences. Dynamic factor model (DFM), as an idiographic approach for studying intraindividual variability and dynamics, has typically been applied to time series data obtained from a single unit. When multivariate time series data are collected from multiple units, how to synchronize dynamical information becomes a silent issue. To address this issue, the current study presented a multilevel dynamic factor model (MDFM) that analyzes multiple multivariate time series in multilevel SEM frameworks. MDFM not only disentangles within- and between-person variability but also models dynamics of the intraindividual processes. To illustrate the uses of MDFMs, we applied lag0, lag1, and lag2 MDFMs to empirical data on affect collected from 205 dating couples who had at least 50 consecutive days of observations. We also considered a model extension where the dynamical coefficients were allowed to be randomly varying in the population. The empirical analysis yielded interesting findings regarding affect regulation and coregulation within couples, demonstrating promising uses of MDFMs in analyzing multiple multivariate time series. In the end, we discussed a number of methodological issues in the applications of MDFMs and pointed out possible directions for future research.

ACKNOWLEDGMENT

We thank Dr. Emilio Ferrer in the Department of Psychology at the University of California, Davis, for allowing us to use the data in this research.

Notes

In this study, we used the dynamic factor model with the specification referred to as Process Factor Analysis model (See Browne & Nesselroade, 2005; Nesselroade, McArdle, Aggen, & Meyers, 2002, for a description of the other specification).

Similar attempts have been made in other modeling contexts, such as differential structural equation models (Boker & Ghisletta, 2001; Butner, Amazeen, & Mulvey, 2005) and state-space models (Chow, Hamaker, Fujita, & Boker, 2009).