## Dynamic structural equation modeling of intensive longitudinal data using Mplus version 8 (Part 4)

### Tihomir Asparouhov

**ABSTRACT:**

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Mplus Version 8 features new methods for analyzing intensive longitudinal data such as that obtained with ecological momentary assessments, experience sampling methods, daily diary methods, and ambulatory assessments. Typically, such data have a large number of time points, T = 20-150, and may come from a single case (e.g., person or dyad), or multiple cases.In this first of a series of three talks, we will begin by explaining how intensive longitudinal data differs from other forms of data, such as cross-sectional and traditional panel data. We will argue that a particularly valuable feature of intensive longitudinal data is that they allows us to study the dynamics of processes over time. This can be done by using time series analysis, a class of statistical techniques that is very popular in fields like econometrics. However, time series analysis is typically restricted to single case data.Dynamic structural equation modeling (DSEM) as it is now developed and implemented in Mplus version 8 allows for the analysis of time series data from a single case, but also allows for multilevel extensions of these models, such that quantitative differences in the dynamics of different cases can be accounted for by the inclusion of random effects. We will present two empirical applications to illustrate the modeling opportunities that DSEM offers.

Part 2 on DSEM in Mplus Version 8 builds on Ellen Hamaker’s Part 1 introduction and describes further DSEM analysis possibilities. Advantages of the Bayesian analysis used for DSEM over ML are briefly discussed. To put the new modeling features in a familiar context, the shortcomings of conventional growth modeling approaches using wide and long format for intensive longitudinal data applications are contrasted with the flexibility of multilevel time series modeling for these data. A series of increasingly more general models are explored using data from a smoking cessation study with N=200 and T=100 (five random measurement occasions per day for 20 days). The starting point is a two-level model with random effects as in Hamaker’s presentation. Cross-classified time series analysis is then introduced where subject and time are crossed resulting in more flexible modeling than possible with two-level analysis in that the random effects are allowed to vary across not only subjects but also time. The cross-classified analysis is used to identify which random effects vary across time and to get an idea of time trends. Trend analysis is then added to the two-level time series modeling in a general time series version of the conventional two-level, long format approach. The advantages of the cross-classified analysis as compared to Time-Varying Effect Modeling (TVEM) are discussed. Throughout the presentation, new time series plots are shown. The modeling part of the talk concludes with a brief overview of two-level and cross-classified DSEM factor analysis with random measurement intercepts and random loadings.

In closing, new non-time series features in Mplus Version 8 are mentioned, including two-level modeling with random variances; two-level random autocorrelation modeling for short longitudinal data; standardization for two-level models with random slopes and random variances; random slopes for covariates with missing data; new within/between scatter plots and histograms for two-level models, including sample and model-estimated cluster-specific means and variances; new Posterior Predictive P-values for BSEM; and output in HTML format.