Measurement Model Misspecification in Dynamic Structural Equation Models: Power, Reliability, and Other Considerations

Dynamic Structural Equation Models (DSEMs) integrate multilevel modeling, time series analysis, and structural equation modeling within a Bayesian estimation framework, offering a versatile tool for analyzing intensive longitudinal data (ILD). However, the impact of measurement structure misspecification in DSEMs, especially under varying reliability conditions and model complexities, remains underexplored. Our Monte Carlo simulation revealed that omitting measurement errors when present led to severe biases in dynamic parameters regardless of reliability conditions, though power remained high. Increasing the number of participants and time points ameliorated but did not eliminate all biases. A single-indicator DSEMs with a measurement structure using composite scores showed similar performance to multiple indicators DSEMs. Empirical applications showed discrepancies in dynamic parameters based on the number of indicators and measurement structures used. Leveraging these findings, we provide design recommendations, functions for extending reliability indices from single-indicator to multiple-indicator models, and guidelines for power evaluations under different reliability conditions.