Modeling Clustered Data with Very Few Clusters.

Area of Science:

• Statistics
• Methodology
• Educational Psychology

Background:

• Small-sample inference for clustered data is increasingly studied.
• Previous research often examines single method classes and lacks realistic predictor models.
• Limited understanding exists on differential performance of methods with very few clusters.

Purpose of the Study:

• To evaluate the performance of 12 statistical methods for clustered data under extreme small-sample conditions.
• To compare estimation bias, Type I error rates, and relative power across methods.
• To inform method selection in educational psychology research with few clusters.

Main Methods:

• A simulation study was conducted using a realistic data-generation model with multiple predictors.
• Twelve distinct methods for handling clustered data were implemented and compared.
• The motivating data from an educational psychology cluster randomized trial were analyzed using each method.

Main Results:

• Generalized estimating equations demonstrated poor performance.
• The selection of Bayesian prior distributions significantly impacted method performance.
• Fixed effect models exhibited strong performance across key metrics.

Conclusions:

• Fixed effect models are recommended for small-sample clustered data analysis when applicable.
• Careful consideration of Bayesian prior distributions is crucial for optimal performance.
• Method selection should account for the number of clusters and model complexity.