Overview | The Problem | Quick Start Example | Three Analysis Functions | 1. bmvb(): Basic Comparison | 2. bglm(): Subgroup analysis | 3. bglmm(): With Clustering | Decision Rules | All Rule (Conjunctive) | Any Rule (Disjunctive) | Compensatory Rule (Weighted) | Test Directions | Right-sided Test | Left-sided Test | Understanding the Output | Key Output Elements | Posterior Samples | Practical Considerations | Sample Size | MCMC Settings | Missing Data | Comparison with Frequentist Approaches | Traditional approach | Bayesian approach | Advantages of Bayesian approach | Next Steps | References

Introduction | When to Use Subgroup Analysis | Example: Clinical Trial with Age Effects | Generate Data | Full sample analysis | Subgroup Analysis | Three Methods for Population Definition | 1. Value Method: Specific Covariate Level | 2. Empirical Method: Observed Covariate Range | 3. Analytical Method: Theoretical Covariate Distribution | Choosing a Method | Comparing Results Across Methods | Understanding Regression Coefficients | Decision Rules | All Rule | Any Rule | Compensatory Rule | Practical Example: Subgroup Analysis | Discrete Covariates | Sample Size Considerations | Specifying Prior Distributions | Default Priors | Custom Fixed Effects Priors | Prior Sensitivity Analysis | Further Reading | MCMC Diagnostics | Comparison: bmvb() and bglm() | Advanced: Extracting Predictions | Summary | References

Introduction | When to Use Multilevel Models | Example: Educational Intervention Study | Generate Example Data | Fit Multilevel Model | Interpretation | Specifying Population of Interest | Specific Ability Level | Ability Range (Empirical) | Ability Range (Analytical) | Decision Rules with Multilevel Data | All Rule (Conjunctive) | Any Rule (Disjunctive) | Compensatory Rule | Specifying Prior Distributions | Fixed Effects Priors (bglm and bglmm) | Default Priors | Custom Fixed Effects Priors | Random Effects Priors | Population-Level Random Effects | Random Effects Covariance | Prior Sensitivity Analysis | Guidelines for Choosing Priors | Common Mistakes to Avoid | Further Reading | MCMC Diagnostics | Extracting Posterior Samples | Data Requirements | Common Issues and Solutions | Warning: "Very few clusters (J < 5)" | Warning: "MCMC chains may not have converged" | Slow computation | Summary | References