Analyzing extensive time-series data from digital educational assessments, utilizing Dynamic Structural Equation Models
In the realm of educational research, the goal is to improve substantive and practical conclusions that can be drawn from studies. One approach to achieving this is by performing Structural Equation Modeling (SEM) on intensive longitudinal data, particularly using multi-level SEM within a Bayesian framework.
Intensive longitudinal data involves repeated measures over time within individuals, forming a hierarchical structure—observations nested within persons. Multi-level SEM can model within-person (level 1) and between-person (level 2) processes simultaneously, which is essential for capturing dynamics in educational settings. Bayesian estimation is favoured for its flexibility with complex models, handling small samples, and incorporating prior knowledge for longitudinal SEM.
Before diving into the analysis, it's crucial to test for stationarity in the time series data. This can be done through visual inspection or statistical tests like the Augmented Dickey-Fuller (ADF) or KPSS tests in R. Stationarity is important when modeling temporal processes to ensure consistent parameter estimation.
Model and prior specification are key components of Bayesian multi-level SEM. This involves defining the measurement model, structural paths, temporal components if modeling dynamics, and random effects for intercepts/slopes per individual. Priors can be chosen based on prior research or theory, ranging from informative to non-informative.
In Bayesian SEM, MCMC algorithms such as Gibbs sampling or Hamiltonian Monte Carlo estimate posterior distributions. Model fit can be evaluated via posterior predictive checks, convergence diagnostics, and information criteria such as WAIC or LOO. Assessing parameter credibility can be done through credible intervals and posterior means.
Upon completion of the analysis, findings should be reported with credible intervals, visualized through latent trajectories and random effects, and discussed in the educational context, emphasizing within-person and between-person effects separately.
Example computer code is provided for both Mplus and R to illustrate the process. The Mplus syntax for Bayesian Multi-level SEM with Intensive Longitudinal Data, and a simplified example using the `brms` package in R, demonstrate starting points for this sophisticated analysis framework.
For full modeling, extend the syntax with longitudinal dynamics (e.g., autoregressive paths) and tailor priors to your context. Advanced seminars and workshops, such as the one mentioned by StatsCamp (2025), provide in-depth training on longitudinal SEM including Bayesian approaches.
The SEM includes testing for stationarity, model and prior specification, model evaluation, and presentation of findings. This method has potential implications for future research in modeling intensive longitudinal educational data. An example is provided to illustrate the approach, using observation and heart rate data obtained via electrocardiography (ECG). The analysis of the ECG data aims to improve substantive and practical conclusions that can be drawn from educational research, as the heart rate data serves as an indicator of cognitive stress from a deep-reading study.
Online education and learning can benefit greatly from employing Structural Equation Modeling (SEM) on intensive longitudinal data. This data, known for its repeated measures over time within individuals, is crucial for capturing dynamics in educational settings. Multi-level SEM, particularly within a Bayesian framework, can model within-person and between-person processes simultaneously, enhancing the understanding of learning patterns and outcomes.
