Time Series Analysis: Dynamic Structural Equation Modeling (DSEM)

Time series analysis is used to analyze intensive longitudinal data such as those obtained with ecological momentary assessments, experience sampling methods, daily diary methods, and ambulatory assessments. Such data typically have a large number of time points, for example, twenty to two hundred. The measurements are typically closely spaced in time.

Multilevel time series analysis of intensive longitudinal data typically considers time points nested within individuals. Individual differences in level-1 parameters such as the mean, variance, and autocorrelation are represented as random effects that are modeled on level 2 in a two-level analysis.

Mplus Version 8, released April 20, 2017, offers two-level, cross-classified, as well as single-level (N=1) time series analysis. In cross-classified analysis the random effects are allowed to vary not only across individuals but also across time to represent time-varying effects.

Mplus can estimate a variety of N=1, two-level and cross-classified time series models. These include univariate autoregressive, regression, cross-lagged, confirmatory factor analysis, Item Response Theory, and structural equation models for continuous, binary, ordered categorical (ordinal), or combinations of these variable types. Bayesian analysis is used in the estimation using a flexible latent variable modeling framework referred to as dynamic structural equation modeling (DSEM).

DSEM Theory

The following papers discuss multilevel time series analysis modeling and estimation:

• Asparouhov, T., Hamaker, E.L. & Muthen, B. (2017). Dynamic structural equation models. Structural Equation Modeling: A Multidisciplinary Journal. DOI: 10.1080/10705511.2017.140680 (Download Mplus analyses)
  
  
• Asparouhov, T., Hamaker, E.L. & Muthén, B. (2017). Dynamic Latent Class Analysis, Structural Equation Modeling: A Multidisciplinary Journal, 24:2, 257-269, DOI: 10.1080/10705511.2016.1253479
  
  

DSEM Applications

The following papers discuss multilevel time series analysis applications:

• Hamaker, E.L., Asparouhov, T., Brose, A., Schmiedek, F. & Muthén, B. (2018). At the frontiers of modeling intensive longitudinal data: Dynamic structural equation models for the affective measurements from the COGITO study. Multivariate Behavioral Research, DOI: 10.1080/00273171.2018.1446819
  
  
• Schultzberg, M. & Muthén, B. (2017). Number of subjects and time points needed for multilevel time series analysis: A simulation study of dynamic structural equation modeling. Revised version. Accepted for publication in Structural Equation Modeling. Supplementary material is found here.
  
  

DSEM Workshops

• Videos from the July 2017 Mplus Users’ Meeting on DSEM in Utrecht. Next meeting is Fall 2018.
• August 17-18, 2017 Johns Hopkins workshop slides and videos.

DSEM Webinars

DSEM in Mplus Version 8 was presented to the Prevention Science Methodology Group (PSMG) in March and April 2017. Following are links to videos and handouts from these occasions:

• Part 1, March 14: Ellen Hamaker (3.14.2017) (handout)
• Part 2, March 21: Bengt Muthén (3.21.2017) (handout)
• Part 3, March 28: Bengt Muthén (3.28.2017)(handout)
• Part 4, April 11: Tihomir Asparouhov (4.11.2017) (handout)

DSEM Examples in the Mplus Version 8 User’s Guide

• N=1 time series analysis: User’s Guide ex 6.23 – 6.28
• Two-level time series analysis: User’s Guide ex 9.30 – 9.37
• Cross-classified time series analysis: User’s Guide ex 9.38 – 9.40