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The Sampling Ratio in Multilevel Structural Equation Models: Considerations to Inform Study Design.

Joseph M Kush1, Timothy R Konold1, Catherine P Bradshaw1

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Educational and Psychological Measurement
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PubMed
Summary

This study found that lower sampling ratios in multilevel structural equation modeling (MSEM) minimally impact Level 2 construct measurement. Doubly latent MSEM models remain robust even with varying sample proportions.

Keywords:
doubly latentinterchangeability and exchangeabilitymultilevelsampling and measurement errorsampling ratiostructural equation model

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Area of Science:

  • Multilevel modeling
  • Psychometrics
  • Educational statistics

Background:

  • Multilevel structural equation modeling (MSEM) analyzes nested data by separating within- and between-group variance.
  • The impact of sampling ratios on MSEM's Level 2 (L2) latent construct measurement is not well understood.
  • Understanding these effects is crucial for accurate multilevel data analysis.

Purpose of the Study:

  • To investigate how sampling ratios affect the measurement of L2 latent constructs in MSEM.
  • To assess the bias and variability in L2 construct estimation under different sampling ratios.
  • To evaluate the performance of doubly latent MSEM models with varying sampling ratios.

Main Methods:

  • A two-step Monte Carlo simulation study was employed.
  • Doubly latent MSEM models were utilized to examine Level 2 construct measurement.
  • The influence of varying sampling ratios on model parameters and fit was analyzed.

Main Results:

  • Lower sampling ratios were associated with increased bias and estimation errors (standard errors, RMSE).
  • However, the magnitude of these errors was found to be negligible across simulations.
  • The doubly latent MSEM approach demonstrated resilience to variations in sampling ratios.

Conclusions:

  • Doubly latent MSEM models are a robust choice for researchers, even with lower sampling ratios.
  • Researchers should consider sampling ratios during MSEM study design, particularly in educational research.
  • The findings support the use of MSEM for analyzing complex hierarchical data structures.