A comparison of observation-level random effect and Beta-Binomial models for modelling overdispersion in Binomial...

Area of Science:

• Ecology
• Biostatistics
• Statistical Modeling

Background:

• Overdispersion, excess variation beyond expected, is common in biological data.
• Failure to model overdispersion leads to biased parameter estimates and standard errors.
• Observation-level random effects (OLRE) and Beta-Binomial models are methods to address overdispersion in binomial data.

Purpose of the Study:

• Investigate the performance of OLRE and Beta-Binomial models for binomial data with overdispersion.
• Assess model performance under varying degrees of overdispersion and low random effect sample sizes (<5 levels).
• Compare the ability of OLRE and Beta-Binomial models to recover unbiased parameter estimates.

Main Methods:

• Simulation study using mixed-effects models for binomial data.
• Introduced varying degrees of overdispersion generated by different processes.
• Evaluated OLRE and Beta-Binomial models under different random effect sample sizes.

Main Results:

• OLRE efficacy depends on the overdispersion source; they failed with Beta-Binomial generated overdispersion but succeeded with added noise.
• Comparing OLRE and Beta-Binomial model estimates identified OLRE performance issues.
• Beta-Binomial models performed well generally but underestimated effects for non-Beta-Binomial data.
• Both models performed poorly with <5 random intercept levels, especially for variance components.

Conclusions:

• OLRE are useful for binomial overdispersion but require careful validation due to context-dependent performance.
• Beta-Binomial models offer a robust alternative, though potential underestimation should be considered.
• Low random effect sample sizes (<5 levels) severely impact both models' ability to estimate variance components.