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Estimating and Testing Random Intercept Multilevel Structural Equation Models with Model Implied Instrumental

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A new limited information estimator, Model Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS), is developed for Multilevel Structural Equation Models (MSEM). This MIIV-2SLS estimator shows robustness to misspecification and performs well with fewer than 100 clusters.

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Area of Science:

  • Multilevel Structural Equation Models (MSEM)
  • Econometrics
  • Statistical Modeling

Background:

  • Maximum Likelihood (ML) is a common estimation method for SEMs.
  • Limited information estimators offer an alternative or supplement to ML.
  • Multilevel SEMs require specialized estimation techniques.

Purpose of the Study:

  • Develop a novel limited information estimator for random intercept Multilevel Structural Equation Models (MSEM).
  • Introduce a multilevel overidentification test statistic for within and between levels.
  • Evaluate the performance and robustness of the new estimator and test statistic.

Main Methods:

  • Model Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) estimator.
  • Development of a multilevel overidentification test statistic.
  • Monte Carlo simulation analysis to assess estimator performance.

Main Results:

  • MIIV-2SLS demonstrates greater robustness than ML to misspecification in MSEM.
  • The MIIV-2SLS estimator performs well with fewer than 100 clusters.
  • The multilevel overidentification test statistic performs effectively at both within and between levels.

Conclusions:

  • The proposed MIIV-2SLS estimator is a viable and robust alternative for MSEM.
  • The developed overidentification test aids in model evaluation for multilevel data.
  • This research contributes to advanced statistical methods for complex hierarchical data structures.