Tetrad Manual
  • About
    • 📚 Project Background
    • 👥 Contributors
    • 📄 Papers and Books
    • 📬 Questions or Suggestions?
  • Workflows
    • Causal Analysis Workflows
      • 🧭 What You’ll Learn
      • 📌 Why a Workflow Matters
      • 🗺️ How the Workflow Is Organized
      • 🧠 Practical Advice Before You Begin
      • 🙌 Where to Start
    • Data Exploration: Understanding Your Data Before Causal Discovery
      • 1. Load and Inspect Your Data
      • 2. Review Variable Types
      • 3. Examine Marginal Distributions with Histograms
      • 4. Explore Pairwise Relationships with the Plot Matrix
      • 5. Consider Linearity and Gaussianity (Informally)
      • 6. Reflect on Causal Sufficiency and Latent Variables
      • 7. Clarify Your Modeling Goals
      • 8. Moving Forward
      • Practical Notes
    • Algorithm Selection and Assumptions
      • What This Page Covers
      • 1. Which Assumptions Matter?
        • 1.1. Causal Sufficiency
        • 1.2. Functional Form and Distribution
        • 1.3. Modeling Goal
        • 1.4. Sample Size and Dimensionality
      • 2. Major Algorithm Families in Tetrad
        • 2.1. Constraint-Based Methods
        • 2.2. Score-Based Methods
        • 2.3. Hybrid Methods
        • 2.4 Time Series Data (Lagged Variables)
      • 3. Mapping Assumptions to Starting Choices
      • 4. Choosing Tests and Scores
        • 4.1. Independence Tests
        • 4.2. Scores
      • 5. What If You’re Unsure?
      • 6. Using Grid Search Effectively
      • 7. Summary
      • 🧭 Next Step
    • Manual Exploration: Try Searches Interactively
      • Why Use Manual Exploration?
      • When Manual Exploration Is Useful
      • Pipelines: The Interactive Workflow
      • Building a Simple Pipeline
      • Examples of Manual Exploration
        • A. Varying Test Sensitivity
        • B. Comparing Algorithms
        • C. Adding Background Knowledge
        • D. Exploring Nonlinearity or Non-Gaussianity
      • Inspecting Results
      • How Manual Exploration Leads to Grid Search
      • Tips for Effective Manual Exploration
      • Summary
      • 🧭 Next Step
    • Running Searches and Grid Search Tips
      • Why Use Grid Search?
      • From Single Runs to Systematic Search
      • Running a Basic Search
      • What to Sweep in Grid Search
        • 1. Significance Level (α) — Test-Based Methods
        • 2. Penalty or Discount — Score-Based Methods
        • 3. Algorithm Choice
        • 4. Tests and Scores
      • Interpreting Grid Search Results
        • 1. Markov Consistency
        • 2. Model Complexity
      • A Practical Starter Pattern
      • Reading Grid Search Output
      • Common Pitfalls to Avoid
        • Sweeping Too Many Parameters at Once
        • Changing Background Knowledge Too Early
        • Delaying Diagnostics
        • Not Recording What Was Tried
      • Where Grid Search Fits in the Workflow
      • 🧭 Next Step
    • Model Evaluation and Markov Checking
      • Why Model Evaluation Matters
      • What the Markov Checker Does
        • Intuition
      • Running the Markov Checker in Tetrad
      • Interpreting Markov Checker Output
        • Key Outputs
        • How to Read the Results
      • Minimal Markov-Consistent Models
      • Comparing Models from Grid Search
      • Important Caveats
        • Markov Checking Is Not a Proof
        • Test Choice Matters
        • Sampling Variability Exists
      • Beyond Markov Checking
      • Practical Tips
      • Summary
      • 🧭 Next Step
    • Interpreting Results
      • 1. What a Discovered Graph Represents
      • 2. Types of Output and Their Meaning
        • 2.1 Fully Directed Acyclic Graphs (DAGs)
        • 2.2 Completed Partially Directed Acyclic Graphs (CPDAGs)
        • 2.3 Partial Ancestral Graphs (PAGs)
      • 3. Interpreting Common Edge Marks
      • 4. Robustness and Stability
      • 5. What You Can Say (With Care)
      • 6. What You Should Avoid Saying Unqualified
      • 7. Using Background Knowledge
      • 8. Communicating Uncertainty Clearly
      • 9. Documenting Your Analysis
      • 10. Summary
      • 🧭 What’s Next
    • Example: Auto MPG Analysis with Grid Search
      • 1. The Auto MPG Dataset
        • Data Preparation
      • 2. Loading and Exploring the Data in Tetrad
        • Visual Exploration
      • 3. Algorithm Choice and Assumptions
        • Causal Sufficiency
        • Algorithm: BOSS
        • Score: Degenerate Gaussian BIC
      • 4. Setting Up the Grid Search
        • Step 1: Connect the Data
        • Step 2: Algorithms Tab
        • Step 3: Table Columns Tab
        • Step 4: Comparison Tab (Initial Setup)
        • Step 5: Set Parameter Ranges
      • 5. Running the Comparison
      • 6. Interpreting the Comparison Results
        • Choosing a Model
      • 7. Viewing the Selected Graph
      • 8. What This Example Illustrates
      • 9. Next Steps
  • Tetrad Interface
    • Overview
      • Main Window
        • Project tree
        • Work area and tabs
        • Menus and toolbar
        • Status bar, logging pane, and messages
      • Working with Data
        • Importing data
        • Viewing and editing data
        • Linking data and graphs
        • Saving and exporting data
      • Graph Editor
        • Opening and creating graphs
        • Basic editing operations
        • Layout and visualization
        • Background knowledge and tiers
        • Saving and exporting graphs
      • Running Algorithms
        • Launching a search
        • Choosing tests and scores
        • Setting parameters
        • Running and monitoring
        • Re-running with modified settings
      • Estimate model parameters
        • Basic workflow
        • Inspecting the fitted model
        • Relationship to graphs and search
        • Where to look next
      • Viewing and Exporting Results
        • Graph results
        • Tabular and numeric results
        • Exporting graphs and tables
        • Reusing results in pipelines
      • Simulation and Utilities
        • Simulating data on the workbench
        • Resampling and bootstrap workflows
        • Grid Search (overview)
        • Other utilities
    • Box by Box
      • Graph Box
        • Purpose
        • Typical workflow
        • Key controls
        • Common patterns & tips
        • Related pages
      • Compare Box
        • Purpose
        • Typical workflow
        • Types of comparisons
        • Key controls
        • Common patterns & tips
        • Related pages
      • Grid Search Box (Data)
        • Purpose of Data-Based Grid Search
        • When This Mode Is Used
        • Basic Setup
        • Algorithms Tab
        • Table Columns Tab
        • Comparison Tab
        • Interpreting Results
        • View Graphs Tab
        • Notes and Best Practices
        • Summary
      • Grid Search (Simulation)
        • When to Use Simulation-Based Grid Search
        • Key Difference from Data-Based Grid Search
        • Step 1: Select a Simulation
        • Step 2: Algorithms Tab
        • Step 3: Table Columns Tab
        • Step 4: Comparison Tab
        • Step 5: Run Counts and Randomness
        • Running the Comparison
        • Interpreting Simulation Results
        • Common Pitfalls
        • Summary
        • 🧭 Next Steps
      • Parametric Model Box
        • Purpose
        • Typical workflow
        • Key controls
        • Common patterns & tips
        • Related pages
      • Instantiated Model Box
        • Purpose
        • Typical workflow
        • Key controls
        • Common patterns & tips
        • Related pages
      • Estimator Box
        • Purpose
        • Typical workflow
        • Key controls
        • Common patterns & tips
        • Estimator types and detail pages
        • Related pages
      • Data Box
        • Purpose
        • Typical workflow
        • Key controls
        • Common patterns & tips
        • Related pages
      • Simulation Box
        • Purpose
        • Simulation setup
        • Running a simulation
        • Using simulated graphs and data in other boxes
        • Common patterns & tips
        • Related pages
      • Search Box
        • Purpose
        • Wizard workflow
        • Connecting data, knowledge, and outputs
        • Common patterns & tips
        • Related pages
      • Latent Clusters Box
        • Purpose
        • Typical workflow
        • Key controls
        • Common patterns & tips
        • Related pages
      • Latent Structure Box
        • Purpose
        • Wizard workflow
        • Connecting data, clusters, knowledge, and outputs
        • Common patterns & tips
        • Related pages
      • Knowledge Box
        • Purpose
        • Typical workflow
        • Key controls
        • Common patterns & tips
        • Related pages
      • Updater Box
        • Purpose
        • Typical workflow
        • Updater types and detail pages
        • Connecting the Updater with other boxes
        • Common patterns & tips
        • Related pages
      • Regression box
        • Multiple Linear Regression
        • Logistic Regression
        • Adjustment Total Effects
        • IDA Check
        • Interpretation and workflow notes
        • Summary
      • Note Box
        • Purpose
        • Typical workflow
        • Key controls
        • Common patterns & tips
        • Related pages
    • Data Preparation
      • Where data preparation happens in Tetrad
      • Typical data preparation workflow
      • What the rest of this section covers
    • Detail Callouts
      • Data subset / resample
        • Inputs and outputs
        • Variable selection
        • Rows and sampling
        • Typical use cases
      • Detail: Graph Menu (Graph Box)
        • Random Graph
        • Graph Properties
        • Underlinings
        • Paths
        • Highlight
        • Check Graph Type
        • Manipulate Graph
        • PAG Edge Specialization Markups
        • Summary
      • Detail: Display Subgraphs
        • Purpose
        • Basic workflow
        • Subgraph types
        • Summary
      • Detail: Markov Checker
        • Purpose
        • Basic workflow
        • Outputs
        • Interpreting results
      • Detail: Bootstrapping and Ensemble Graphs
        • What Bootstrapping Does
        • Enabling Bootstrapping
        • Running a Bootstrapped Search
        • The Edges Tab: Bootstrap Frequencies
        • Ensemble Graph Display Options
        • How to Use Bootstrapping Effectively
        • Important Caveats
        • Summary
      • Detail: Parametric & Instantiated Model Types
        • Model families
        • Interaction with Estimator and Simulation
      • Detail: Simulation types
        • Bayes net
        • Linear structural equation model
        • Linear Fisher model
        • Nonlinear additive SEM (CAM)
        • General noise SEM
        • Additive noise SEM
        • Lee and Hastie
        • Conditional Gaussian
        • Time series
        • Choosing a simulator
      • Detail: Bayes (Multinomial) Parametric Model
        • When to use Bayes models
        • Main panel layout
        • Typical workflow
        • Tips and caveats
      • Detail: Bayes (Multinomial) Instantiated Model
        • How Bayes instantiated models are created
        • Instantiated Model box layout (Bayes)
        • Typical uses
        • Tips
      • Detail: ML Bayes Estimator
        • Purpose
        • Inputs and requirements
        • How it works (conceptually)
        • Output
        • Tips and common issues
        • Related pages
      • Detail: Dirichlet Estimator
        • Purpose
        • Inputs and requirements
        • How it works (conceptually)
        • Output
        • Tips and common issues
        • Related pages
      • Detail: EM Bayes Estimator
        • Purpose
        • Inputs and requirements
        • How it works (conceptually)
        • Output
        • Tips and common issues
        • Related pages
      • Detail: SEM (Linear) Parametric Model
        • When to use SEM models
        • Main panel layout
        • Typical workflow
        • Tips and caveats
      • Detail: SEM (Linear) Instantiated Model
        • How SEM instantiated models are created
        • Instantiated Model box layout (SEM)
        • File menu options (SEM instantiated model)
      • Detail: SEM (Linear) Estimator
        • Purpose
        • Inputs and requirements
        • How it works (conceptually)
        • Output
        • File menu options (SEM Estimator)
      • Detail: Hybrid (Conditional Gaussian) Parametric Model
        • When to use Hybrid models
        • Main panel layout
        • Typical workflow
        • Tips and caveats
      • Detail: Hybrid (Conditional Gaussian) Instantiated Model
        • How Hybrid instantiated models are created
        • Instantiated Model box layout (Hybrid)
        • Typical uses
        • Tips
      • Detail: Hybrid CG Estimator
        • Purpose
        • Inputs and requirements
        • How it works (conceptually)
        • Output
        • Tips and common issues
        • Related pages
      • Detail: Generalized Parametric Model
        • When to use Generalized models
        • Main panel layout
        • Typical workflow
        • Tips and caveats
      • Detail: Generalized Instantiated Model
        • How Generalized instantiated models are created
        • Instantiated Model box layout (Generalized)
        • Typical uses
        • Tips
      • Detail: Generalized SEM Estimator
        • Purpose
        • Inputs and requirements
        • How it works (conceptually)
        • Output
        • Tips and common issues
        • Related pages
      • Detail: Junction Tree Updater
        • Purpose
        • Inputs and setup
        • How it works (conceptually)
        • Output
        • Tips
        • Related pages
      • Detail: Approximate Updater
        • Purpose
        • Inputs and setup
        • How it works (conceptually)
        • Output
        • Tips
        • Related pages
      • Detail: Row Summing Updater
        • Purpose
        • Inputs and setup
        • How it works (conceptually)
        • Output
        • Tips
        • Related pages
      • Detail: SEM Updater
        • Purpose
        • Inputs and setup
        • How it works (conceptually)
        • Output
        • Tips
        • Related pages
      • Detail: Adjustment and Total Effects: Amenability and Discrete Variables
        • What Is an Amenable Pair?
        • Amenability via Visible Edges
        • How Amenability Is Reported in the Tool
        • Discrete Variables and Regression Output
        • Amenability and Refining Equivalence Classes
        • Summary
      • Detail: IDA Check (Regression box)
        • Layout and controls
        • Table columns
        • Summary statistics (bottom)
        • Typical usage
        • Notes and references
      • Detail: N-tad Explorer
        • Basic workflow
        • Interpretation
        • Tips and notes
        • Using N-tad Explorer with SEMs
  • Python and R Bindings
    • py-tetrad (Python Binding)
    • rpy-tetrad (R Binding)
    • When to Use These Bindings
    • Related Python Ecosystem Tools
      • Relationship to Tetrad
      • Recommendation
  • Graphs and DataSets
    • Graph Types and Formats
      • 1. Core Graph Types in Tetrad
        • 1.1 DAG — Directed Acyclic Graph
        • 1.2 CPDAG — Completed Partially Directed Acyclic Graph
        • 1.3 MAG — Maximal Ancestral Graph
        • 1.4 PAG — Partial Ancestral Graph
      • 2. Endpoint Marking System
      • 3. PAG Edge-Specialization Markup (Optional GUI Feature)
        • 3.1 Two Independent Attributes
        • (A) Visibility
        • (B) Directness
        • 3.2 The Four Directed-Edge Types
        • 3.3 Undirected Edges Represent Selection Bias
      • 4. Saving and Loading Graphs
        • 4.1 Conceptual Plain-Text Format
      • 5. Graphs and Data: Name Matching
      • 6. Summary
    • Data Types and Formats
      • 1. Overview of Supported Formats
      • 2. Dataset Format (Tabular Data)
        • Notes
      • 3. Discrete Data
      • 4. Continuous Data
      • 5. Covariance and Correlation Matrices
        • 5.1 Required Structure
        • 5.2 Lower Triangle Covariance Matrix Example
        • 5.3 Full Square Covariance Matrix Example (Current Default)
        • 5.4 Correlation Matrices
        • 5.5 Common Parsing Errors for Covariance/Correlation Files
      • 6. Lower-Triangular Format
        • 6.1 Note on GUI Display
      • 7. Exporting Data from Tetrad
      • 8. Summary
  • Search Algorithms
    • Choosing an Algorithm
      • 🔍 Choosing an Algorithm
      • 🧭 Recommended Algorithms (At a Glance)
      • 🔍 DAG / CPDAG Methods (No Latent Confounders)
      • 🌀 PAG Methods (Hidden Confounders Allowed)
      • 🔧 Other Useful Algorithm Classes
      • 🎛 Choosing CI Tests & Scores (Quick Guide)
      • ⚠️ Common Pitfalls and Fixes
    • Search Algorithms — By Type
      • Legend — Algorithm Categories
        • Extra Structural Badges
      • 🔍 Constraint-Based Algorithms (CPDAG / PAG)
      • 📏 Score-Based Algorithms (CPDAG)
      • 🌀 Hybrid Algorithms (Score + FCI)
      • 🎨 Non-Gaussian, Moment-Based, and Orientation Algorithms
      • Nonlinear & Distribution-Shift Algorithms
      • 📦 Stability / Resampling / Ensemble Wrappers
      • 🧪 Specialized / Utility Algorithms
      • Latent Clustering (Measurement Block Discovery)
      • Latent Structure / Measurement-Model Construction
    • Search Algorithms — Alphabetical
      • 1. BOSS — Best Order Score Search
        • 1.1. Key idea
        • 1.2. When to use
        • 1.3. How it works (at a glance)
        • 1.4. Strengths
        • 1.5. Limitations
        • 1.6. How it relates to other Tetrad algorithms
        • 1.7. Prior knowledge support
        • 1.8. Parameters
        • 1.9. Reference
        • 1.10. Summary
      • 2. BOSS-FCI — Best-Order Score Search + FCI Refinement
        • 2.1. Key Idea
        • 2.2. When to Use
        • 2.3. Strengths
        • 2.4. Limitations
        • 2.5. How It Differs From Related Algorithms
        • 2.6. Prior Knowledge Support
        • 2.7. Key Parameters in Tetrad
        • 2.8. Reference
        • 2.9. Summary
      • 3. BPC — Build Pure Clusters
        • 3.1. Basic Assumptions
        • 3.2. High-Level Algorithm
        • 3.3. Output and Interpretation
        • 3.4. Parameters in Tetrad
        • 3.5. Strengths
        • 3.6. Limitations
        • 3.7. Reference
        • 3.8. Summary
      • 4. CAM — Causal Additive Model
        • 4.1. Key Idea
        • 4.2. When to Use CAM
        • 4.3. Prior Knowledge Support
        • 4.4. Strengths
        • 4.5. Limitations
        • 4.6. Key Parameters in Tetrad
        • 4.7. Reference
        • 4.8. Summary
      • 5. CCD — Cyclic Causal Discovery
        • 5.1. Key Idea
        • 5.2. When to Use
        • 5.3. Prior Knowledge Support
        • 5.4. Strengths
        • 5.5. Limitations
        • 5.6. Key Parameters in Tetrad
        • 5.7. Reference
        • 5.8. Summary
      • 6. CD-NOD — Causal Discovery from Nonstationary / Distribution-Shifted Data
        • 6.1. Key Idea
        • 6.2. When to Use
        • 6.3. Prior Knowledge Support
        • 6.4. Strengths
        • 6.5. Limitations
        • 6.6. Key Parameters in Tetrad / Scripting
        • 6.7. Reference
        • 6.8. Summary
      • 7. Conservative PC (CPC) — Conservative Collider Orientation
        • 7.1. Key Idea
        • 7.2. When to Use
        • 7.3. Prior Knowledge Support
        • 7.4. Strengths
        • 7.5. Limitations
        • 7.6. Key Parameters in Tetrad
        • 7.7. Reference
        • 7.8. Summary
      • 8. CStaR (Causal Stability Ranking)
        • 8.1. High-level idea
        • 8.2. Inputs
        • 8.3. Outputs
        • 8.4. Parameters
        • 8.5. When to use CStaR
        • 8.6. References
        • 8.7. Summary
      • 9. DAGMA — Learning DAGs via M-Matrices and Log-Determinant Acyclicity
        • 9.1. Key Idea
        • 9.2. When to Use
        • 9.3. Prior Knowledge Support
        • 9.4. Strengths
        • 9.5. Limitations
        • 9.6. Key Parameters in Tetrad
        • 9.7. Reference
        • 9.8. Summary
      • 10. DirectLiNGAM
        • 10.1. Key Idea
        • 10.2. When to Use
        • 10.3. Prior Knowledge Support
        • 10.4. Strengths
        • 10.5. Limitations
        • 10.6. Key Parameters in Tetrad
        • 10.7. Reference
        • 10.8. Summary
      • 11. DM (Detect–Mimic)
        • 11.1. DM-PC
        • 11.2. DM-FCIT
      • 12. Factor Analysis
        • 12.1. Purpose
        • 12.2. When to Use
        • 12.3. How It Works (Conceptual)
        • 12.4. Strengths
        • 12.5. Limitations
        • 12.6. Relation to Other Latent Tools
        • 12.7. References
        • 12.8. Summary
      • 13. FAS — Fast Adjacency Search
        • 13.1. Key Idea
        • 13.2. When to Use
        • 13.3. Case Study: High-dimensional fMRI Preprocessing
        • 13.4. Prior Knowledge Support
        • 13.5. Strengths
        • 13.6. Limitations
        • 13.7. Key Parameters in Tetrad
        • 13.8. Reference
        • 13.9. Summary
      • 14. FASK — Fast Adjacency Skewness
        • 14.1. Key Idea
        • 14.2. When to Use
        • 14.3. Prior Knowledge Support
        • 14.4. Strengths
        • 14.5. Limitations
        • 14.6. Key Parameters in Tetrad
        • 14.7. Reference
        • 14.8. Summary
      • 15. FASK-Vote — Multi-Dataset FASK Voting over IMaGES
        • 15.1. Key Idea
        • 15.2. When to Use
        • 15.3. Prior Knowledge Support
        • 15.4. Strengths
        • 15.5. Limitations
        • 15.6. ImagES Parameters
        • 15.7. FASK Parameters
        • 15.8. Reference
        • 15.9. Summary
      • 16. FCI — Fast Causal Inference
        • 16.1. Key idea
        • 16.2. When to use FCI
        • 16.3. Assumptions
        • 16.4. How it works (at a glance)
        • 16.5. How it relates to other Tetrad algorithms
        • 16.6. Strengths
        • 16.7. Limitations
        • 16.8. Prior knowledge
        • 16.9. Key parameters in Tetrad
        • 16.10. References
      • 17. FCI-IOD — FCI with Independent Overlapping Datasets
        • 17.1. Key Idea
        • 17.2. When to Use
        • 17.3. Prior Knowledge Support
        • 17.4. Strengths
        • 17.5. Limitations
        • 17.6. Key Parameters in Tetrad
        • 17.7. Reference
        • 17.8. Summary
      • 18. FCIT — FCI with Targeted Testing
        • 18.1. Key Idea
        • 18.2. When to Use
        • 18.3. Strengths
        • 18.4. Limitations
        • 18.5. How It Differs From Related Algorithms
        • 18.6. Prior Knowledge Support
        • 18.7. Key Parameters in Tetrad
        • 18.8. Reference
        • 18.9. Summary
      • 19. FGES — Fast Greedy Equivalence Search
        • 19.1. Key Idea
        • 19.2. A Nuanced View of Scalability and Sparsity
        • 19.3. When to Use FGES
        • 19.4. Prior Knowledge Support
        • 19.5. Strengths
        • 19.6. Limitations
        • 19.7. Key Parameters in Tetrad
        • 19.8. Reference
        • 19.9. Summary
      • 20. FGES-MB — FGES Markov Blanket Search
        • 20.1. Key idea
        • 20.2. When to use FgesMb
        • 20.3. Prior knowledge support
        • 20.4. Strengths
        • 20.5. Limitations
        • 20.6. Key parameters in Tetrad
        • 20.7. Reference
        • 20.8. Summary
      • 21. FOFC — Find One-Factor Clusters
        • 21.1. Key Idea
        • 21.2. When to Use
        • 21.3. Prior Knowledge Support
        • 21.4. Strengths
        • 21.5. Limitations
        • 21.6. Key Parameters in Tetrad
        • 21.7. Reference
        • 21.8. Summary
      • 22. FTFC — Find Two-Factor Clusters (Sextad-Based)
        • 22.1. Key Idea
        • 22.2. Relation to FOFC and GFFC
        • 22.3. When to Use FTFC
        • 22.4. Strengths
        • 22.5. Limitations
        • 22.6. Parameters in Tetrad
        • 22.7. Reference
        • 22.8. Summary
      • 23. GFCI — Greedy Fast Causal Inference
        • 23.1. 🔍 Key Idea
        • 23.2. 🎯 When to Use GFCI
        • 23.3. 🧠 Prior Knowledge
        • 23.4. ⭐ Strengths
        • 23.5. ⚠️ Limitations
        • 23.6. 🔧 Key Parameters (Tetrad)
        • 23.7. ⛓ Relation to Other Algorithms
        • 23.8. 📚 Reference
      • 24. GFFC — Generalized Find Factor Clusters
        • 24.1. Key Idea
        • 24.2. Algorithm Overview
        • 24.3. Why Use GFFC?
        • 24.4. Strengths
        • 24.5. Limitations
        • 24.6. Parameters in Tetrad
        • 24.7. Reference
        • 24.8. Summary
      • 25. GIN (Generalized Independent Noise)
        • 25.1. Overview
        • 25.2. Requirements
        • 25.3. Parameters
        • 25.4. How the Algorithm Works
        • 25.5. Output
        • 25.6. When to Use
        • 25.7. When Not to Use
        • 25.8. Notes
        • 25.9. References
      • 26. GRaSP — Greedy Relaxations of the Sparsest Permutation
        • 26.1. Key idea
        • 26.2. When to use
        • 26.3. How it works (at a glance)
        • 26.4. Strengths
        • 26.5. Limitations
        • 26.6. How it relates to other Tetrad algorithms
        • 26.7. Prior knowledge support
        • 26.8. Key parameters in Tetrad
        • 26.9. Reference
        • 26.10. Summary
      • 27. GRaSP-FCI — Greedy Relaxations of Sparsest Permutation + FCI Refinement
        • 27.1. Key Idea
        • 27.2. When to Use
        • 27.3. Strengths
        • 27.4. Limitations
        • 27.5. How It Differs From Related Algorithms
        • 27.6. Prior Knowledge Support
        • 27.7. Key Parameters in Tetrad
        • 27.8. Reference
        • 27.9. Summary
      • 28. ICA Lingam — ICA-Based LiNGAM
        • 28.1. Key Idea
        • 28.2. When to Use
        • 28.3. Prior Knowledge Support
        • 28.4. Strengths
        • 28.5. Limitations
        • 28.6. Key Parameters in Tetrad
        • 28.7. Reference
        • 28.8. Summary
      • 29. ICA LingD — Cyclic LiNGAM (Lacerda et al.)
        • 29.1. Key Idea
        • 29.2. When to Use
        • 29.3. Prior Knowledge Support
        • 29.4. Strengths
        • 29.5. Limitations
        • 29.6. Key Parameters in Tetrad
        • 29.7. Reference
        • 29.8. Summary
      • 30. IMaGES — Independent Multiple-sample Greedy Equivalence Search
        • 30.1. Key Idea
        • 30.2. Variants
        • 30.3. When to Use
        • 30.4. Prior Knowledge Support
        • 30.5. Strengths
        • 30.6. Limitations
        • 30.7. Key Parameters in Tetrad
        • 30.8. Reference
        • 30.9. Summary
      • 31. Latent Clusters
        • 31.1. Key Idea
        • 31.2. When to Use
        • 31.3. Prior Knowledge Support
        • 31.4. Strengths
        • 31.5. Limitations
        • 31.6. Latent Cluster Algorithms in Tetrad
        • 31.7. Relationship to Latent Structure Algorithms
        • 31.8. Summary
      • 32. LV-Heuristic — Heuristic Latent-Variable PAG from a Single DAG
        • 32.1. What LV-Heuristic Is (and Is Not)
        • 32.2. Key Idea
        • 32.3. When to Use LV-Heuristic
        • 32.4. Strengths
        • 32.5. Limitations
        • 32.6. How LV-Heuristic Differs From Other Mixed-Strategy Algorithms
        • 32.7. Prior Knowledge Support
        • 32.8. Key Parameters in Tetrad
        • 32.9. Reference
        • 32.10. Summary
      • 33. Mimbuild Bollen
        • 33.1. Purpose
        • 33.2. How It Works (Conceptual)
        • 33.3. Strengths
        • 33.4. Limitations
        • 33.5. Relation to Other Latent Tools
        • 33.6. References
        • 33.7. Summary
      • 34. Mimbuild PCA
        • 34.1. Purpose
        • 34.2. How It Works (Conceptual)
        • 34.3. Strengths
        • 34.4. Limitations
        • 34.5. Relation to Other Latent Tools
        • 34.6. References
        • 34.7. Summary
      • 35. PagSamplingRfci
        • 35.1. Key Idea
        • 35.2. When to Use
        • 35.3. Prior Knowledge Support
        • 35.4. Strengths
        • 35.5. Limitations
        • 35.6. Key Parameters in Tetrad
        • 35.7. Reference
        • 35.8. Summary
      • 36. Pairwise Orientation Methods — FaskPw & RSkew
        • 36.1. Overview
        • 36.2. FaskPw — FASK Pairwise Left–Right Orientation
        • 36.3. Key Idea
        • 36.4. When to Use
        • 36.5. Strengths
        • 36.6. Limitations
        • 36.7. Parameters in Tetrad
        • 36.8. RSkew — Robust Skewness Orientation (Hyvärinen & Smith, 2013)
        • 36.9. Key Idea (informal)
        • 36.10. When to Use
        • 36.11. Strengths
        • 36.12. Limitations
        • 36.13. Parameters in Tetrad
        • 36.14. Prior Knowledge Support
        • 36.15. Summary
      • 37. PC — Peter–Clark Algorithm
        • 37.1. Key Idea
        • 37.2. When to Use
        • 37.3. Prior Knowledge Support
        • 37.4. Strengths
        • 37.5. Limitations
        • 37.6. Key Parameters in Tetrad
        • 37.7. Historical Notes
        • 37.8. Additional Reference
        • 37.9. Summary
      • 38. PC-Max — PC with Maximum-p Collider Orientation
        • 38.1. Key Idea
        • 38.2. When to Use
        • 38.3. Relation to Standard PC
        • 38.4. Prior Knowledge Support
        • 38.5. Strengths
        • 38.6. Limitations
        • 38.7. Key Parameters in Tetrad
        • 38.8. Reference
        • 38.9. Summary
      • 39. PCD — PC for Deterministic Relations
        • 39.1. Key Idea
        • 39.2. When to Use
        • 39.3. Prior Knowledge Support
        • 39.4. Strengths
        • 39.5. Limitations
        • 39.6. Key Parameters in Tetrad
        • 39.7. Summary
      • 40. PC-MB — PC Markov Blanket Search
        • 40.1. Key Idea
        • 40.2. When to Use
        • 40.3. Prior Knowledge Support
        • 40.4. Strengths
        • 40.5. Limitations
        • 40.6. Key Parameters in Tetrad
        • 40.7. Reference
        • 40.8. Summary
      • 41. PCMCI — Time-Series Causal Discovery (Runge et al.)
        • 41.1. Key Idea
        • 41.2. When to Use
        • 41.3. Prior Knowledge Support
        • 41.4. Strengths
        • 41.5. Limitations
        • 41.6. Key Parameters in Tetrad
        • 41.7. Reference
        • 41.8. Summary
      • 42. Restricted BOSS — Target-Focused Best Order Score Search
        • 42.1. Key Idea
        • 42.2. When to Use
        • 42.3. Prior Knowledge Support
        • 42.4. Strengths
        • 42.5. Limitations
        • 42.6. Key Parameters in Tetrad
        • 42.7. Reference
        • 42.8. Summary
      • 43. RFCI — Really Fast Causal Inference
        • 43.1. Key Idea
        • 43.2. When to Use
        • 43.3. Prior Knowledge Support
        • 43.4. Strengths
        • 43.5. Limitations
        • 43.6. Key Parameters in Tetrad
        • 43.7. Reference
        • 43.8. Summary
      • 44. RFCI-BSC
        • 44.1. Key Idea
        • 44.2. When to Use
        • 44.3. Prior Knowledge Support
        • 44.4. Strengths
        • 44.5. Limitations
        • 44.6. Key Parameters in Tetrad
        • 44.7. Reference
        • 44.8. Summary
      • 45. SingleGraphAlg (Imported Graph Wrapper)
        • 45.1. What it does
        • 45.2. Typical workflow
        • 45.3. When to use (and when not to)
      • 46. SP — Sparsest Permutation
        • 46.1. Key idea
        • 46.2. When to use
        • 46.3. How it works (at a glance)
        • 46.4. Strengths
        • 46.5. Limitations
        • 46.6. How it relates to other Tetrad algorithms
        • 46.7. Prior knowledge support
        • 46.8. Reference
        • 46.9. Summary
      • 47. SP-FCI — Sparsest-Permutation FCI
        • 47.1. Key Idea
        • 47.2. When to Use
        • 47.3. Strengths
        • 47.4. Limitations
        • 47.5. Key Parameters in Tetrad
        • 47.6. Knowledge Support
        • 47.7. Relation to Other Algorithms
        • 47.8. References
        • 47.9. Summary
      • 48. StabilitySelection
        • 48.1. Key Idea
        • 48.2. When to Use
        • 48.3. Prior Knowledge Support
        • 48.4. Strengths
        • 48.5. Limitations
        • 48.6. Key Parameters in Tetrad
        • 48.7. Reference
        • 48.8. Summary
      • 49. StARS
        • 49.1. Key Idea
        • 49.2. When to Use
        • 49.3. Prior Knowledge Support
        • 49.4. Strengths
        • 49.5. Limitations
        • 49.6. Key Parameters in Tetrad
        • 49.7. Reference
        • 49.8. Summary
      • 50. TSC — Trek Separation Clusters
        • 50.1. Intended use
        • 50.2. Model assumptions (NOLAC version)
        • 50.3. High-level algorithm sketch
        • 50.4. Inputs and outputs
        • 50.5. Key parameters
        • 50.6. Practical guidance
        • 50.7. Limitations
        • 50.8. Related methods
        • 50.9. Summary
  • Tests & Scores
    • Choosing Tests & Scores
      • 1. Continuous, Approximately Gaussian Data
        • Recommended Tests
        • Recommended Scores
        • Best-Fit Algorithms
      • 2. Discrete Data (Binary / Ordinal / Categorical)
        • Recommended Tests
        • Recommended Scores
        • Best-Fit Algorithms
      • 3. Mixed Continuous/Discrete Data
        • A. Conditional Gaussian (CG)
        • B. Degenerate Gaussian (DGC)
        • C. Basis Function (BF) Tests/Scores
      • 4. Non-Gaussian Linear Models
        • Recommended Tests
        • Recommended Scores
        • Best-Fit Algorithms
      • 5. Nonlinear Models
        • A. Kernel Conditional Independence Test (KCI)
        • B. Random Conditional Independence Test (RCIT)
        • B. Basis Function Test / Score (Recommended for scalability)
      • 6. Latent Variable Workflows (Block-Based Search)
        • Block-Based Tests/Scores
        • Compatible Algorithms
        • Typical Workflow
      • Summary Table (Practical Defaults)
      • Next Steps
    • Tests and Scores: By Type
      • Independence Tests
        • Independence Tests Overview
      • Scores
        • Scores Overview
      • How Tests and Scores Are Used in Algorithms
    • Tests and Scores — Alphabetical
      • 1. Basis Function BIC Score
        • 1.1. Summary
        • 1.2. When to use
        • 1.3. Model class
        • 1.4. Score form (conceptual)
        • 1.5. Parameters
        • 1.6. Strengths
        • 1.7. Limitations
        • 1.8. References
      • 2. Basis Function Likelihood Ratio Test
        • 2.1. Summary
        • 2.2. When to use
        • 2.3. Assumptions
        • 2.4. Test details (conceptual)
        • 2.5. Parameters
        • 2.6. Strengths
        • 2.7. Limitations
        • 2.8. References
      • 3. BDeu Score
        • 3.1. Summary
        • 3.2. When to use
        • 3.3. Model class
        • 3.4. Score form (conceptual)
        • 3.5. Parameters
        • 3.6. Strengths
        • 3.7. Limitations
        • 3.8. References
      • 4. Chi-Square Test
        • 4.1. Summary
        • 4.2. When to use
        • 4.3. Assumptions
        • 4.4. Test details (conceptual)
        • 4.5. Parameters
        • 4.6. Strengths
        • 4.7. Limitations
        • 4.8. References
      • 5. Conditional Gaussian BIC Score
        • 5.1. Summary
        • 5.2. When to use
        • 5.3. Model class
        • 5.4. Score form (conceptual)
        • 5.5. Parameters
        • 5.6. Strengths
        • 5.7. Limitations
        • 5.8. References
      • 6. Conditional Gaussian Likelihood Ratio Test
        • 6.1. Summary
        • 6.2. When to use
        • 6.3. Assumptions
        • 6.4. Test details (conceptual)
        • 6.5. Parameters
        • 6.6. Strengths
        • 6.7. Limitations
        • 6.8. References
        • 6.9. References
      • 7. Degenerate Gaussian BIC Score
        • 7.1. Summary
        • 7.2. When to use
        • 7.3. Model class
        • 7.4. Score form (conceptual)
        • 7.5. Parameters
        • 7.6. Strengths
        • 7.7. Limitations
        • 7.8. References
      • 8. Degenerate Gaussian Likelihood Ratio Test
        • 8.1. Summary
        • 8.2. When to use
        • 8.3. Assumptions
        • 8.4. Test details (conceptual)
        • 8.5. Parameters
        • 8.6. Strengths
        • 8.7. Limitations
        • 8.8. References
      • 9. Discrete BIC Score
        • 9.1. Summary
        • 9.2. When to use
        • 9.3. Model class
        • 9.4. Score form (conceptual)
        • 9.5. Parameters
        • 9.6. Strengths
        • 9.7. Limitations
      • 10. Extended BIC (EBIC) Score
        • 10.1. Summary
        • 10.2. When to use
        • 10.3. Model class
        • 10.4. Score form (conceptual)
        • 10.5. Parameters
        • 10.6. Strengths
        • 10.7. Limitations
        • 10.8. References
      • 11. Fisher Z Test
        • 11.1. Summary
        • 11.2. When to use
        • 11.3. Assumptions
        • 11.4. Test details (conceptual)
        • 11.5. Parameters
        • 11.6. Strengths
        • 11.7. Limitations
        • 11.8. References
      • 12. G-Square Test
        • 12.1. Summary
        • 12.2. When to use
        • 12.3. Assumptions
        • 12.4. Test details (conceptual)
        • 12.5. Parameters
        • 12.6. Strengths
        • 12.7. Limitations
        • 12.8. References
      • 13. Generalized Information Criterion (GIC) Scores
        • 13.1. Summary
        • 13.2. When to use
        • 13.3. Model class
        • 13.4. Score form (conceptual)
        • 13.5. Parameters
        • 13.6. Strengths
        • 13.7. Limitations
        • 13.8. References
      • 14. Kernel Conditional Independence Test (KCI)
        • 14.1. Summary
        • 14.2. When to use
        • 14.3. Assumptions
        • 14.4. Test details (conceptual)
        • 14.5. Parameters
        • 14.6. Strengths
        • 14.7. Limitations
        • 14.8. References
      • 15. m-Separation Test
        • 15.1. Summary
        • 15.2. When to use
        • 15.3. Assumptions
        • 15.4. Test details (conceptual)
        • 15.5. Parameters in Tetrad
        • 15.6. Strengths
        • 15.7. Limitations
        • 15.8. References
      • 16. m-Separation Score
        • 16.1. Summary
        • 16.2. When to use
        • 16.3. Model class
        • 16.4. Score form (conceptual)
        • 16.5. Parameters in Tetrad
        • 16.6. Strengths
        • 16.7. Limitations
      • 17. MVP BIC Score
        • 17.1. Summary
        • 17.2. When to use
        • 17.3. Model class
        • 17.4. Score form (conceptual)
        • 17.5. Parameters
        • 17.6. Strengths
        • 17.7. Limitations
      • 18. Multivariate Polynomial Likelihood Ratio Test (MVPLRT)
        • 18.1. Summary
        • 18.2. When to use
        • 18.3. Assumptions
        • 18.4. Test details (conceptual)
        • 18.5. Parameters
        • 18.6. Strengths
        • 18.7. Limitations
      • 19. Poisson BIC Test
        • 19.1. Summary
        • 19.2. When to use
        • 19.3. Relation to Poisson Prior Score
        • 19.4. Test details (conceptual)
        • 19.5. Parameters
        • 19.6. Strengths
        • 19.7. Limitations
      • 20. Poisson Prior Score
        • 20.1. Summary
        • 20.2. When to use
        • 20.3. Model class
        • 20.4. Score form (conceptual)
        • 20.5. Parameters
        • 20.6. Strengths
        • 20.7. Limitations
        • 20.8. Relation to other penalties
      • 21. Probabilistic Independence Test
        • 21.1. Summary
        • 21.2. When to use
        • 21.3. Assumptions
        • 21.4. Test details (conceptual)
        • 21.5. Parameters
        • 21.6. Strengths
        • 21.7. Limitations
      • 22. Random Conditional Independence Test (RCIT)
        • 22.1. Summary
        • 22.2. When to use
        • 22.3. Assumptions
        • 22.4. Test details (conceptual)
        • 22.5. Parameters
        • 22.6. Strengths
        • 22.7. Limitations
        • 22.8. Relationship to other CI tests in Tetrad
        • 22.9. References
      • 23. SEM BIC Score
        • 23.1. Summary
        • 23.2. When to use
        • 23.3. Model class
        • 23.4. Score form (conceptual)
        • 23.5. Parameters
        • 23.6. Strengths
        • 23.7. Limitations
      • 24. SEM BIC Test
        • 24.1. Summary
        • 24.2. When to use
        • 24.3. Relation to SEM BIC Score
        • 24.4. Test details (conceptual)
        • 24.5. Strengths
        • 24.6. Limitations
      • 25. Zhang–Shen Bound Score
        • 25.1. Summary
        • 25.2. When to use
        • 25.3. Model class
        • 25.4. Score form (conceptual)
        • 25.5. Parameters
        • 25.6. Strengths
        • 25.7. Limitations
        • 25.8. References
  • Parameters
  • Contributors
    • 🌟 Founders & Early Leadership
    • 🧭 Project Direction & Architecture
    • 🔬 Algorithmic & Research Contributions
    • 🛠 Software Engineering & Infrastructure
    • 🏛 Funding Acknowledgment
  • Papers and Books
  • Change Log
Tetrad Manual
  • Tests & Scores
  • Tests and Scores — Alphabetical
  • View page source

:orphan:

Tests and Scores — Alphabetical

Below is the complete set of per-test and per-score documentation pages for Tetrad’s statistical tests and scoring methods.

  • 1. Basis Function BIC Score
  • 2. Basis Function Likelihood Ratio Test
  • 3. BDeu Score
  • 4. Chi-Square Test
  • 5. Conditional Gaussian BIC Score
  • 6. Conditional Gaussian Likelihood Ratio Test
  • 7. Degenerate Gaussian BIC Score
  • 8. Degenerate Gaussian Likelihood Ratio Test
  • 9. Discrete BIC Score
  • 10. Extended BIC (EBIC) Score
  • 11. Fisher Z Test
  • 12. G-Square Test
  • 13. Generalized Information Criterion (GIC) Scores
  • 14. Kernel Conditional Independence Test (KCI)
  • 15. m-Separation Test
  • 16. m-Separation Score
  • 17. MVP BIC Score
  • 18. Multivariate Polynomial Likelihood Ratio Test (MVPLRT)
  • 19. Poisson BIC Test
  • 20. Poisson Prior Score
  • 21. Probabilistic Independence Test
  • 22. Random Conditional Independence Test (RCIT)
  • 23. SEM BIC Score
  • 24. SEM BIC Test
  • 25. Zhang–Shen Bound Score
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