Flexible approaches for estimating partial eta squared in mixed-effects models with crossed random factors

Area of Science:

• Statistics
• Quantitative Psychology
• Biostatistics

Background:

• Mixed-effects models are widely used for analyzing data with multiple sources of variation.
• Standardized effect sizes, such as eta-squared (η²), are crucial for interpreting model results.
• Existing methods for calculating η² in mixed-effects models have limitations, particularly with crossed random factors and random slopes.

Purpose of the Study:

• To develop and evaluate flexible approaches for estimating eta-squared (η²) in mixed-effects models.
• To address the limitations of current methods, especially for models with crossed random factors and random slopes.
• To provide practical recommendations for researchers using these complex models.

Main Methods:

• Introduction of novel, flexible methods for calculating eta-squared (η²) in mixed-effects models.
• Simulation study to compare the performance of new and existing methods.
• Assessment of strengths and weaknesses of various approaches.

Main Results:

• The proposed methods offer greater flexibility in estimating eta-squared (η²) for mixed-effects models with crossed random factors.
• Simulation results highlight the performance differences between various estimation techniques.
• Identification of a simple, recommended approach based on established statistical work.

Conclusions:

• New flexible methods for estimating eta-squared (η²) in mixed-effects models with crossed random factors are presented.
• The study provides valuable insights into the performance of different effect size estimation techniques.
• Recommendations are offered for a practical and robust approach to calculating eta-squared (η²) in complex statistical models.