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A practical guide and power analysis for GLMMs: detecting among treatment variation in random effects
Morgan P Kain1, Ben M Bolker2, Michael W McCoy1
1Department of Biology, East Carolina University , Greenville, NC , USA.
Peerj
|September 25, 2015
Summary
This study provides a blueprint for power analyses in generalized linear mixed models (GLMMs) to detect treatment differences in variance. Optimal sampling strategies depend on the target variance parameter and total sample size, with low overall power observed.
Area of Science:
- Ecology and Evolution
- Statistical Modeling
- Behavioral Ecology
Background:
- Generalized linear mixed models (GLMMs) are increasingly used in ecology and evolution to analyze hierarchical data.
- Detecting differences in variance by treatment at multiple hierarchical levels is crucial but optimal experimental designs remain unknown.
- Understanding variation is key to addressing emerging questions in behavioral ecology and evolutionary studies.
Purpose of the Study:
- To develop a blueprint for conducting power analyses for GLMMs, specifically focusing on detecting differences in variance by treatment.
- To determine optimal sampling schemes (ratios of individuals to repeated measures) that maximize the power to detect differences in random effects.
- To explore how total variation affects the power to detect differences in target variance parameters.
Main Methods:
- Developed parameterization and power analyses for random-intercepts and random-slopes GLMMs.
- Focused on hierarchically structured binomial data, with a framework generalizable to other error distributions.
- Determined optimal ratios of individuals to repeated measures and analyzed the impact of total variation on power.
Main Results:
- Power varied across different ratios of individuals to repeated measures, with an optimal ratio dependent on the target variance parameter and sample size.
- Overall power to detect variance differences was low, often requiring over 1,000 observations per treatment for 80% power.
- Power decreased with increasing variance in non-target random effects.
Conclusions:
- The developed power analyses are crucial for designing experiments aimed at detecting differences in variance in ecological and evolutionary studies.
- Results highlight the need for careful consideration of sampling schemes to maximize power in detecting treatment-related variance differences.
- This work aims to inspire novel experimental designs investigating the causes and implications of individual-level phenotypic variance.
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