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Area of Science:

  • Educational Psychology
  • Quantitative Psychology
  • Statistical Modeling

Background:

  • Observational units in educational psychology are often nested within hierarchical structures.
  • Multilevel modeling is essential for analyzing nested data, particularly in three-level longitudinal designs.
  • Determining appropriate sample sizes for reliable parameter estimation in these complex models remains a challenge.

Purpose of the Study:

  • To investigate the necessary sample size for accurate parameter estimation in three-level longitudinal multilevel models.
  • To provide evidence-based sample size recommendations for educational psychology research.
  • To evaluate the impact of sample size and missing data on estimation reliability.

Main Methods:

  • A population dataset was generated simulating a three-level longitudinal study (classrooms, students, occasions).
  • 1000 random samples were drawn under various sample size and missing data conditions.
  • Analysis results were compared against true population parameters to assess estimation bias and variance.

Main Results:

  • Unbiased fixed effects estimates were achieved with at least 15 level-2 units (students) within 35 level-3 units (classrooms).
  • Higher-level random effects variance estimates necessitate larger sample sizes.
  • Increasing the level-2 sample size demonstrated the most significant improvement in estimation soundness.

Conclusions:

  • Specific sample size recommendations are provided for three-level longitudinal multilevel models in educational psychology.
  • The findings highlight the critical role of level-2 sample size in achieving reliable parameter estimates.
  • Understanding data characteristics is key to optimizing sample size for robust multilevel analyses.