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 level1 parameters such as the mean, variance, and autocorrelation are represented as random effects that are modeled on level 2 in a twolevel analysis.
Mplus Version 8, released April 20, 2017, offers twolevel, crossclassified, as well as singlelevel (N=1) time series analysis. In crossclassified analysis the random effects are allowed to vary not only across individuals but also across time to represent timevarying effects.
Mplus can estimate a variety of N=1, twolevel and crossclassified time series models. These include univariate autoregressive, regression, crosslagged, 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 and RDSEM Theory
The following papers discuss multilevel time series analysis modeling and estimation:
 Asparouhov, T. & Muthén, B. (2023). Residual Structural Equation Models. Structural Equation Modeling: A Multidisciplinary Journal, 30, 131. 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) 275297, DOI: 10.1080/10705511.2019.1626733 (Download scripts).
 Asparouhov, T. & Muthén, B. (2019). Latent variable centering of predictors and mediators in multilevel and timeseries models. Structural Equation Modeling: A
Multidisciplinary Journal, 26, 119142. 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, 359388, 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, 257269, DOI: 10.1080/10705511.2016.1253479
DSEM Applications
The following papers discuss multilevel time series analysis applications:
 Savord, A., McNeish, D., Iida, M., Quiroz, S. and Ha, T. (2023). Fitting the Longitudinal ActorPartner 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), 807822. DOI: 10.1080/10705511.2021.1915788
 Asparouhov, T. & Muthén, B. (2022). Practical aspects of Dynamic Structural Equation Models. Technical Report. Version 2. January 30, 2022.
 Hamaker, E.L., Asparouhov, T, & Muthén, B. (2021). Dynamic structural equation modeling as a combination of time series modeling, multilevel modeling, and structural equation modeling. To be published as Chapter 31 in: The Handbook of Structural Equation Modeling (2nd edition); Rick H. Hoyle (Ed.); Publisher: Guilford Press. (Download supplementary materials).
 McNeish, D. & Hamaker, E.L. (2020). A primer on twolevel dynamic structural equation models for intensive longitudinal data in Mplus. Psychological Methods, 25(5), 610–635. https://doi.org/10.1037/met0000250
 McNeish, D. (2019). TwoLevel dynamic structural equation models with small samples. Structural Equation Modeling: A Multidisciplinary Journal, 26(6), 948966. 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 selfcontrol 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, 885895. DOI: 10.1016/j.apenergy.2019.01.028
 Schultzberg, M. (2019). Using high frequency pretreatment outcomes to identify causal effects in nonexperimental 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), 275285. DOI: 10.1093/jpepsy/jsy089
 JolyBurra, 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, 495515, DOI:10.1080/10705511.2017.1392862. (Supplementary material).
DSEM Web Talks
DSEM Workshops
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:
DSEM Examples in the Mplus Version 8 User’s Guide
 N=1 time series analysis: User’s Guide ex 6.23 – 6.28
 Twolevel time series analysis: User’s Guide ex 9.30 – 9.37
 Crossclassified time series analysis: User’s Guide ex 9.38 – 9.40
RDSEM Examples in the Version 8.1 Mplus Language Addendum
These and other examples can be found in our User's Guide.
