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Jieru Chen1, Audrey J Leroux1

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Multiple membership random effects models (MMrem) are robust to non-normal residuals for fixed effects and level-one variance. However, the level-two variance component and credible intervals are sensitive to non-normality, impacting statistical performance.

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Monte Carlo simulationMultiple membershipmultilevel modelingresidual normality

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Area of Science:

  • Statistics
  • Quantitative Psychology
  • Educational Measurement

Background:

  • Conventional hierarchical linear modeling (HLM) assumes purely nested data structures.
  • Multiple membership random effects models (MMrem) accommodate non-purely nested data where units belong to multiple higher-level groups.
  • Prior research explored residual non-normality in HLM, but its impact on MMrem remains unexamined.

Purpose of the Study:

  • To investigate the statistical performance of two-level multiple membership random effects models (MMrem) under conditions of level-two residual non-normality.
  • To extend previous findings on residual non-normality from purely nested to multiple membership data structures.
  • To assess parameter estimate biases and inferential errors in MMrem with non-normal residuals.

Main Methods:

  • A Monte Carlo simulation study was employed to evaluate two-level MMrem.
  • Simulation factors included level-two residual distribution (normal vs. non-normal), sample sizes, intracluster correlation coefficient, and mobility rate.
  • Bias and coverage rates of credible intervals were analyzed.

Main Results:

  • Fixed effect parameter estimates and the level-one variance component were robust to level-two residual non-normality.
  • The level-two variance component estimate was sensitive to both level-two residual non-normality and sample size.
  • Coverage rates of 95% credible intervals significantly deviated from nominal levels when level-two residuals were non-normal.

Conclusions:

  • MMrem fixed effects and level-one variance are reliable even with non-normal residuals.
  • Caution is advised when interpreting the level-two variance component and credible intervals in MMrem under residual non-normality, especially with smaller sample sizes.
  • Findings inform the application of MMrem for analyzing complex data with multiple group memberships and potential residual non-normality.