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Description: Traditionally, researchers have used time series and multilevel models to analyze intensive longitudinal data. However, these models do not directly address traits and states which conceptualize the stability and variability implicit in longitudinal research, and they do not explicitly take into account measurement error. An alternative to overcome these drawbacks is to consider structural equation models (state-trait SEMs) for longitudinal data that represent traits and states as latent variables. Most of these models are encompassed in the Latent State-Trait (LST) theory. These state-trait SEMs can be problematic when the number of measurement occasions increases. As they require the data to be in wide format, these models quickly become overparameterized and lead to non-convergence issues. For these reasons, multilevel versions of state-trait SEMs have been proposed, which require the data in long format. To study how suitable state-trait SEMs are for intensive longitudinal data, we carried out a simulation study. We compared the traditional single level to the multilevel version of three state-trait SEMs. The selected models were the multistate-singletrait (MSST) model, the common and unique trait-state (CUTS) model, and the trait-state-occasion (TSO) model. Furthermore, we also included an empirical application. Our results indicated that the TSO model performed best in both the simulated and the empirical data. To conclude, we highlight the usefulness of state-trait SEMs to study the psychometric properties of the questionnaires used in intensive longitudinal data. Yet, these models still have multiple limitations, some of which might be overcome by extending them to more general frameworks. Code for this project is availabe at https://github.com/secastroal/LST_Analyses