Multilevel Structural Equation Modeling (MSEM) is an advanced statistical framework that combines the strengths of traditional Multilevel Modeling (MLM) and Structural Equation Modeling (SEM) allowing for both latent variables and hierarchically clustered data. The most common estimator for MSEMs is Maximum Likelihood (ML) applied to the entire model simultaneously. ML offers desirable asymptotic properties (e.g., consistency, asymptotic efficiency) for valid models. However, ML requires strong

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... assumptions such as correct model specification and no excessive multivariate kurtosis (Browne, 1984). If these assumptions are violated, there is no guarantee about the usual statistical properties. Despite ML's properties and flexibility there may be circumstances when alternative estimators would be beneficial. The current study develops a limited information estimator for random intercept MSEMs. This estimator is based on the Model Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) estimator, which has been shown to be an excellent alternative to ML in single level SEMs (Bollen, 1996). After adapting the usual MIIV-2SLS procedure for the MSEM model, the current study examines the finite sample properties via two Monte Carlo Simulations. In the first simulation, both ML and MIIV-2SLS are used to estimate MSEMs with and without structural misspecification. Results suggest that MIIV-2SLS is robust to the spread of misspecification within levels and between levels. Further, MIIV-2SLS has accurate standard errors and the ability to test individual equations for misspecification based on the Sargan Test. The second simulation examines model fit testing by comparing the Sargan Test to ML based chi-square fit statistics. Results show that the Sargan test is sensitive to misspecification at both levels of the model with traditional fit statistics are only sensitive to misspecification in level 1. The power of the Sargan test is depends on the type of misspecification and the sample size. Finally, this s [...]