Overview | The estimand and g-computation | Fix #1 — estimand (v0.1.0.9000) | Differential misclassification | Mediator identification: two $2\times2$ systems | Fix #2 — mediator solve (v0.1.0.9000) | Exact-population recovery (runnable) | Exposure identification: closed-form $2\times2$ inverse | Convergence of the bound to the truth | Finite-sample coverage and inference | This is the Imbens–Manski problem, not estimator bias | Cost | Practical implication: grid resolution | References

A worked example | 1. Specify the mediation model | 2. Fit each imputation | 3. Pool with Rubin's rules | 4. Inference on the indirect effect | Migrating from the S4 API

Why MBCO does not commute with Rubin's rules | In practice | References

1. Architecture (S7, four verbs, three classes) | 2. Ecosystem contracts | 2.1 medfit::MediationData (the fitting contract) | 2.2 RMediation (the inference contract) | 2.3 Dependency direction (no cycle) | 3. The MI estimator and Rubin's rules | 4. MBCO under MI: D4-stacking (and why it is hosted here) | 4.1 Why MBCO does not commute with Rubin's rules | 4.2 D4 combination | 4.3 Hosting decision | 5. The IPW estimator | 5.1 Pipeline | 5.2 Weight estimation | 5.3 Variance: sandwich vs model | 6. Cross-package engineering decisions | 7. Design-choice summary | 8. References

Introduction | Installation | Quick Start | Step 1: Define Your Method | Step 2: Configure the Simulation | Step 3: Select Scenarios | Step 4: Run the Simulation | Step 5: Analyze Results | Execution Modes | Custom Scenarios | HPC Cluster Support | Next Steps

Overview | The joint estimand | A worked example | Plugin (point estimate) | Parametric bootstrap | Nonparametric bootstrap | MBCO (deterministic) | Scope and limitations

Overview | What is $P_{med}$? | Installation | Basic Example: Linear Mediation | 1. Simulate Data | 2. Estimate $P_{med}$ | 3. Interpret Results | MBCO intervals (deterministic) | Advanced Example: Binary Outcome (GLM) | 1. Simulate Binary Data | 2. Estimate with GLM | Conclusion

Overview | Setup | Step 1: Simulate Data | Step 2: Fit Mediation Models | Step 3: Extract Mediation Structure | Step 4: Confidence Intervals (RMediation) | Distribution of Product Method | Monte Carlo Method | Compare Methods | Step 5: Probabilistic Effect Size (probmed) | Step 6: Sensitivity Analysis (medrobust) | Step 7: Bootstrap Inference (medfit) | Complete Results Summary | Interpretation | Using SEM with lavaan | Session Information | References

Introduction | Installation | Loading the Ecosystem | Package Management | Check Installed Versions | Update Packages | Check for Conflicts | Core Workflow | 1. Fit Models | 2. Extract Mediation Structure | 3. Choose Your Analysis | Confidence Intervals (RMediation) | Probabilistic Effect Size (probmed) | Sensitivity Analysis (medrobust) | Bootstrap Inference (medfit) | Ecosystem Design | Foundation Package | Specialized Packages | Type Safety | Next Steps | Session Info

Introduction | Overview of Methods | Method Comparison | Performance and Accuracy Comparison | When to Use Each Method | Distribution of Product (DOP) | Monte Carlo (MC) | Asymptotic Normal | Working with S7 Classes | Practical Recommendations | Conclusion

Introduction | Basic Usage | Single Mediator Analysis | Multiple Mediators | Using S7 Classes | Available Methods | Integration with Structural Equation Modeling | Validation and Error Handling | Conclusion

Feature Comparison | Workflow 1: Base R (lm/glm) | Workflow 2: lavaan | Workflow 3: mediation | Conclusion

Overview | Data Logic and Sources | Variable Dictionary | R Code for Data Generation | Verifying the Bias | Descriptive Statistics | Using with medrobust | Saving the Dataset

Introduction | What is Differential Misclassification? | The Problem | The Solution: Partial Identification | Installation | Key Concepts | Natural Direct and Indirect Effects | Misclassification Parameters | Basic Workflow | Example 1: Exposure Misclassification | Step 1: Generate Synthetic Data | Step 2: Define Sensitivity Region | Step 3: Compute Bounds | Step 4: Visualize Results | Step 5: Test Specific Hypotheses | Step 6: Bootstrap Inference | Step 7: Using Generic Methods | Step 8: Sensitivity Plots | Power Analysis | Planning a Study | Understanding Power Results | Visualizing Power Curves | Interpreting Power Analysis Results | Example 2: Mediator Misclassification | Example 3: Non-Differential Misclassification | Understanding the Output | Bound Interpretation | Compatibility Testing | Falsification Analysis | Advanced Features | Extracting Results | Comparing Different Scenarios | Falsification Summary | Practical Recommendations | Choosing the Sensitivity Region | Grid Resolution | Bootstrap Replications | Parallel Processing | Interpreting Results | When Bounds are Tight | When Bounds are Wide | When Most Parameters Are Falsified | Common Use Cases | 1. Recall Bias in Epidemiology | 2. Social Desirability Bias | 3. Instrument Quality | Computational Performance | Grid Resolution Trade-offs | Grid Search Algorithms | Caching Results | Computational Complexity | Limitations and Assumptions | Next Steps | Getting Help | References | Session Information

Introduction | Causal Framework | Partial Identification under Differential Misclassification | Testable Implications | References

Introduction | UML Class Diagram | Class Documentation | medrobust_bounds | sensitivity_region | compatibility_test | Method Documentation | print() | summary() | plot() | as.data.frame()

Overview | The Computational Challenge | Exponential Complexity | The Solution: Smart Sampling | Available Grid Methods | 1. Latin Hypercube Sampling ("lhs") ⭐ DEFAULT | 2. Regular Grid ("regular") | 3. Sobol Sequences ("sobol") | 4. Adaptive Grid ("adaptive") | 5. Binary Search on Bounds ("binary") | 6. Auto-Selection ("auto") | Performance Comparison | Test Case: Exposure Misclassification | Large Grid Performance (n_grid=50) | Recommended Workflow | Three-Stage Analysis | Stage 1: Quick Exploration | Stage 2: Refinement | Stage 3: Publication-Quality Results | Accuracy vs. Speed Trade-offs | Bound Width Differences | When is approximation acceptable? | Combining with Parallel Processing | Selection Guide | Algorithm Implementation Details | Reproducibility | Memory Efficiency | Computational Complexity | Practical Examples | Example 1: Quick sensitivity check | Example 2: Publication-ready analysis | Example 3: Comparing methods | Future Enhancements | References | Session Information