Enabling analytical power calculations for multilevel models with autocorrelated errors through deriving and...

Area of Science:

• Psychology
• Statistics
• Research Methodology

Background:

• Intensive longitudinal (IL) designs are increasingly used to study daily psychological fluctuations and individual differences.
• Multilevel models with autocorrelated errors are common for analyzing IL data.
• Determining optimal sample size and measurement frequency for sufficient statistical power is crucial for IL study design.

Purpose of the Study:

• To develop simple, analytical formulas for calculating statistical power in multilevel models with AR(1) within-person errors.
• To provide researchers with a computationally efficient method for power analysis in IL studies.
• To validate the accuracy of the derived analytical formulas against simulation-based methods.

Main Methods:

• Derivation of analytical formulas for statistical power using asymptotic approximations.
• Application of these formulas to multilevel models with AR(1) within-person errors.
• Comparison of the analytical approach with Monte Carlo simulation-based power computations.

Main Results:

• The study successfully derived simple-to-use analytical formulas for power calculations in specified IL models.
• The analytical approach demonstrated comparable performance to simulation-based methods.
• The analytical method offers significant time and resource savings for researchers.

Conclusions:

• The developed analytical formulas provide a practical and efficient tool for power analysis in intensive longitudinal studies.
• Researchers can utilize this method to optimize study design, ensuring sufficient statistical power.
• This approach facilitates more accessible and resource-conscious research in psychology and related fields.