A simple Monte Carlo method for estimating power in multilevel designs.

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Estimating statistical power for multilevel models presents challenges due to complexity and multiple variation sources.
• Existing Monte Carlo simulation methods often focus on simpler models or require extensive parameter specification.

Purpose of the Study:

• To present a flexible Monte Carlo simulation approach for power analysis in a broad range of multilevel regression models with continuous outcomes.
• To introduce the R package mlmpower for automating complex power estimation procedures.

Main Methods:

• Developed a Monte Carlo simulation strategy accommodating numerous predictors, interactions, and random coefficients at multiple levels.
• Implemented a novel method for deriving population parameters using variance-explained effect sizes, eliminating the need for pilot data.
• Designed the mlmpower R package to automate data generation and analysis for power estimation.

Main Results:

• The approach supports complex models with non-orthogonal predictors and multiple interaction effects.
• The variance-explained effect size method provides an intuitive way to specify model parameters.
• The mlmpower package streamlines the power analysis process for multilevel models.

Conclusions:

• This flexible Monte Carlo approach significantly advances power estimation for complex multilevel models.
• The mlmpower R package offers a practical tool for researchers conducting power analyses.
• The method facilitates more accurate and efficient statistical power estimation in multilevel research.