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).

Mplus Web Talks

• Web Talk 6: Using Mplus To Do Dynamic Structural Equation Modeling, February 28, 2023.
  
  
• Web Talk 7: Using Mplus To Do DSEM with Cycles., May 2024.

DSEM and RDSEM Theory

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

• Asparouhov, T. & Muthén, B. (2024). Continuous Time Dynamic Structural Equation Models. Version 5. October 18, 2024.
  
  
• Asparouhov, T. & Muthén, B. (2023). Residual Structural Equation Models. Structural Equation Modeling: A Multidisciplinary Journal, 30, 1-31. DOI: 10.1080/10705511.2022.2074422
  
  
• Asparouhov, T. & Muthén, B. (2020). Comparison of models for the analysis of intensive longitudinal data. Structural Equation Modeling: A Multidisciplinary Journal, 27(2) 275-297, DOI: 10.1080/10705511.2019.1626733 (Download scripts).
  
  
• Asparouhov, T. & Muthén, B. (2019). Latent variable centering of predictors and mediators in multilevel and time-series models. Structural Equation Modeling: A Multidisciplinary Journal, 26, 119-142. DOI: 10.1080/10705511.2018.1511375 (Download scripts).
  
  
• Asparouhov, T., Hamaker, E.L. & Muthen, B. (2018). Dynamic structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 25:3, 359-388, DOI: 10.1080/10705511.2017.1406803 (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:

• McNeish, D. & MacKinnon, D.P. (2025). Intensive longitudinal mediation in Mplus. Psychological Methods, 30(2), 393–415. DOI: 10.1037/met0000536
  
  
• McNeish,D. (2025). Missing not at random intensive longitudinal data with dynamic structural equation models. Psychological Methods. Advance online publication. DOI: 10.1037/met0000742
  
  Muthén, B., Asparouhov, T. & Keijsers, L. (2025). Dynamic Structural Equation Modeling with Cycles. Structural Equation Modeling: A Multidisciplinary Journal, 32(2), 264-286. DOI: 10.1080/10705511.2024.2406510 (Download Supplementary Material). See also Mplus Web Talk 7.
  
  
• Muthén, B., Asparouhov, T. & Keijsers, L. (2025). Dynamic Structural Equation Modeling with Cycles. Structural Equation Modeling: A Multidisciplinary Journal, 32(2), 264-286. DOI: 10.1080/10705511.2024.2406510 (Download Supplementary Material). See also Mplus Web Talk 7.
  
  
• Asparouhov, T. & Muthén, B. (2024). Practical aspects of dynamic structural equation models. Technical Report. Version 4. December 2, 2024.
  
  
• Muthén, B., Asparouhov, T. & Shiffman, S. (2024). Dynamic Structural Equation Modeling with Floor Effects. Psychological Methods. Advance online publication. DOI: 10.1037/met0000720
  
  
• Hamaker, E.L., Asparouhov, T, & Muthén, B. (2023). Dynamic structural equation modeling as a combination of time series modeling, multilevel modeling, and structural equation modeling. Chapter 31, pp. 576-596 in: The Handbook of Structural Equation Modeling (2nd edition); Rick H. Hoyle (Ed.); Publisher: Guilford Press. (Download supplementary materials).
  
  
• Santangelo, P.S., Holtmann, J., Hosoya, G., Bohus, M., Kockler, T.D., Koudela-Hamila, S., Eid, M. & Ebner-Priemer, U.W. (2023). Within- and between-persons effects of self-esteem and affective state as antecedents and consequences of dysfunctional behaviors in the everyday lives of patients with borderline personality disorder. Clinical Psychological Science, 8(3), 428–449. DOI: 10.1177/2167702620901724
  
  
• Hasl, A., Voelkle, M., Kretschmann, J., Richter, D. & Brunner, M. (2023). A dynamic structural equation approach to modeling wage dynamics and cumulative advantage across the lifespan. Multivariate Behavioral Research, 58(3), 504-525, DOI: 10.1080/00273171.2022.2029339
  
  
• Savord, A., McNeish, D., Iida, M., Quiroz, S. & Ha, T. (2023). Fitting the longitudinal actor-partner interdependence model as a dynamic structural equation model in Mplus. Structural Equation Modeling: A Multidisciplinary Journal, 30(2), 296–314. DOI: 10.1080/10705511.2022.2065279
  
  
• McNeish, D., Mackinnon, D.P., Marsch, L.A. & Poldrack, R.A. (2021). Measurement in intensive longitudinal data. Structural Equation Modeling: A Multidisciplinary Journal, 28(5), 807-822. DOI: 10.1080/10705511.2021.1915788
  
  
• McNeish, D. & Hamaker, E.L. (2020). A primer on two-level dynamic structural equation models for intensive longitudinal data in Mplus. Psychological Methods, 25(5), 610–635. DOI: 10.1037/met0000250
  
  
• McNeish, D. (2019). Two-Level dynamic structural equation models with small samples. Structural Equation Modeling: A Multidisciplinary Journal, 26(6), 948-966. DOI: 10.1080/10705511.2019.1578657
  
  
• Mun, C.J., Suk, H.W., Davis, M.C., Karoly, P., Finan, P., Tennen, H., & Jensen, M.P. (2019). Investigating intraindividual pain variability: Methods, applications, issues, and directions. Pain. DOI: 10.1097/j.pain.0000000000001626
  
  
• Lundgren, B. & Schultzberg, M. (2019). Application of the economic theory of self-control to model energyconservation behavioral change in households. Energy. DOI: 10.1016/j.energy.2019.05.217
  
  
• Öhrlund, I., Schultzberg, M. & Bartusch, C. (2019). Identifying and estimating the effects of a mandatory billing demand charge. Applied Energy, 237, 885-895. DOI: 10.1016/j.apenergy.2019.01.028
  
  
• Schultzberg, M. (2019). Using high frequency pre-treatment outcomes to identify causal effects in non-experimental data. Doctoral Dissertation, Paper 1, Department of Statistics, Uppsala University.
  
  
• Armstrong, B., Covington, L.B., Unick, G.J., & Black, M.M. (2018). Bidirectional effects of sleep and sedentary behavior among toddlers: A dynamic multilevel modeling approach. Journal of Pediatric Psychology, 44(3), 275-285. DOI: 10.1093/jpepsy/jsy089
  
  
• Joly-Burra, E., Van der Linden, M. & Ghisletta, P. (2018). Intraindividual variability in inhibition and prospective memory in healthy older adults: Insights from response regularity and rapidity. Journal of Intelligence, 6(1), 13. DOI: 10.3390/jintelligence6010013
  
  
• 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 (Online supporting material).
  
  
• Schultzberg, M. & Muthén, B. (2018). Number of subjects and time points needed for multilevel time series analysis: A simulation study of dynamic structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 25:4, 495-515, DOI:10.1080/10705511.2017.1392862. (Supplementary material).
  
  

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

RDSEM Examples in the Version 8.1 Mplus Language Addendum

• Version 8.1 RDSEM examples