Clustered data with small sample sizes: Comparing the performance of model-based and design-based approaches

Two classes of methods properly account for clustering of data: design-based methods and model-based methods. Estimates from both methods have been shown to be approximately equal with large samples. However, both classes are known to produce biased standard error estimates with small samples. This paper compares the bias of standard errors and statistical power of marginal effects for generalized estimating equations (a design-based method) and generalized/linear mixed effects models (model-based methods) with small sample sizes via a simulation study. Provided that the distributional assumptions are met, model-based methods produced the least-biased standard error estimates and greater relative statistical power.