1. Introduction  
2. Bayesian Mixed Effects Estimation  
3. Consistency of Bayesian Estimators  
3.1. Preliminaries  
3.2. Model Specifications  
3.3. Assumptions  
3.4. Weighted Sum of Random Effects  
3.5. Main Results for $\pmb{\theta}$  
3.6. Integrated Likelihood  
4. Simulation Study 1: Strongly Informative Balanced Design for $\sigma_{\epsilon}$ and $\sigma_{a}$  
4.1. Model  
4.2. Sampling and Estimation  
4.3. Results  
5. Simulation Study 2: Exploring Consistency Requirements  
5.1. Sample Design and Estimation  
5.2. Results  
6. Application: The PISA 2000  
7. Discussion