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Adequate Sample Sizes for a Three-Level Growth Model.

Eunsoo Lee1, Sehee Hong1

  • 1Department of Education, Korea University, Seoul, South Korea.

Frontiers in Psychology
|July 19, 2021
PubMed
Summary

Researchers need adequate sample sizes for three-level growth models in longitudinal studies. Small sample sizes can lead to inaccurate variance component estimates, impacting multilevel modeling results.

Keywords:
Monte Carlo simulation studyintraclass correlationmultilevel (hierarchical) modelingsample sizethree-level growth model

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Multilevel models are essential for analyzing hierarchical data, particularly in longitudinal studies.
  • Three-level growth models are frequently employed to assess individual changes within group structures.
  • Existing sample size guidelines for three-level growth models are limited, risking unreliable research findings.

Purpose of the Study:

  • To determine appropriate sample sizes for three-level growth models under various realistic conditions.
  • To provide guidance for researchers using multilevel modeling with complex nested data structures.

Main Methods:

  • A Monte Carlo simulation study was conducted.
  • Investigated 12 conditions varying level-2 and level-3 sample sizes, and level-3 intraclass correlation.
  • Evaluated convergence rates, parameter bias, mean square error (MSE), coverage rates, and statistical power.

Main Results:

  • Regression coefficient estimates were found to be largely unbiased across conditions.
  • Variance component estimates demonstrated inaccuracy, particularly with smaller sample sizes.
  • Convergence rates and power were sensitive to sample size variations.

Conclusions:

  • Researchers must be cautious about potential inaccuracies in variance components when using small sample sizes in three-level growth models.
  • The study highlights the need for careful consideration of sample size adequacy in multilevel analyses.
  • Findings underscore the importance of robust sample sizes for reliable multilevel modeling outcomes.