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A structural after measurement approach to structural equation modeling.

Yves Rosseel1, Wen Wei Loh1

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The structural-after-measurement (SAM) approach to structural equation modeling (SEM) offers advantages over simultaneous estimation. SAM provides more robust estimates, improved convergence, and reduced bias, particularly in smaller samples.

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Structural equation modeling (SEM) typically estimates measurement and structural components concurrently.
  • A revisited approach, structural-after-measurement (SAM), proposes sequential estimation of these components.

Purpose of the Study:

  • To introduce a formal framework for the SAM approach in SEM with continuous latent variables and indicators.
  • To demonstrate the advantages of decoupled estimation over simultaneous estimation in SEM.

Main Methods:

  • Developed a formal framework for the SAM approach.
  • Reviewed and integrated earlier SAM methods within the new framework.
  • Proposed two variants: "Local" SAM and "Global" SAM.

Main Results:

  • SAM offers three key advantages: robustness to local misspecifications, better convergence in small samples, and reduced finite sample bias.
  • The framework supports two-step corrected standard errors and local/global fit measures.

Conclusions:

  • The SAM approach is a valuable estimation strategy for structural equation modeling.
  • It enhances robustness, convergence, and accuracy compared to standard simultaneous estimation methods.