Cluster Directed Mixed Graphs (over DMGs)
Cluster Directed Mixed Graphs (over DMGs)
Causal Inference with Linear Regression: A Modern Approach (Part II)
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Learn more
Why Simple Linear Models Fall Short in Applied Causal Analysis
Introduction
1
Slides
How to Use This Course
Course Guidelines
Required Python Packages
ATE & CATE
Causal Graphs, Backdoor Adjustment, Adjustment Formula
Linear Regression as a CEF Approximator
Limitations of the Simple Linear Model
Unmodelled Non-Linearity
Heterogeneity in Linear Models
Unmodelled Effect Heterogeneity — Part I
Unmodelled Effect Heterogeneity — Part II
Residual Confounding
Exercises
Resources
Making Linear Regression Models More Flexible
Introduction
Slides
Exploring the Dataset
Simple Models with Continuous Predictors
Simple Models with Categorical Predictors
Modelling Nonlinearity with Binning
Modelling Nonlinearity with Polynomial Terms
Modelling Nonlinearity with Log Transformations
Interaction Terms: Continuous X Continuous
Interaction Terms: Continuous X Binary
Interaction Terms: Continuous X Multicategorical
Interaction Terms: Categorical X Categorical
Nonlinearity and Interaction Terms
Moderating Non-Linear Relationships — Part I
Moderating Non-Linear Relationships — Part II
Non-Linear Moderation of Non-Linear Relationships
Flexible Linear Models in Causal Inference
Recap
Exercises
Resources
Study Design and Causal Graph Construction in Applied Settings
Introduction
Slides
What Makes a Causal Project Well-Defined?
Consistency and Treatment Variation Irrelevance
No Interference
Target Trial Emulation
"Non-Causal Edges" In Causal Graphs
True Causal Drivers or Proxies?
The Need for an Explicit Notion of Time in Causal Graphs
Time Acyclicity and Effect Acyclicity
What Graph Are We Actually Working With?
Cluster Directed Mixed Graphs (over ADMGs) — Part I
Cluster Directed Mixed Graphs (over ADMGs) — Part II
Cluster Directed Mixed Graphs (over DMGs)
Theoretical Exercises
Introducing The Case Study
Applied Exercises
Emulating the Target Trial — Part I
Emulating the Target Trial — Part II
How to Start Building a Causal Graph
Note
Pre-Treatment Structure: Nodes — Part I
Pre-Treatment Structure: Nodes — Part II
Pre-Treatment Structure: Nodes — Part III
Pre-Treatment Structure: Edges — Part I
Pre-Treatment Structure: Edges — Part II
Pre-Treatment Structure: Edges — Part III
So, We Have Cycles…
The Final Pre-Treatment Structure
Post-Treatment Structure — Part I
Post-Treatment Structure — Part II
Post-Treatment Structure — Part III
The Final Causal Graph
From Causal Graph to Dataset — Identifying a Sufficient Adjustment Set
From Causal Graph to Dataset — Proxy Variables and Practical Compromises
From Causal Graph to Dataset — Exploring The Data
Recap
Resources
Challenges in the Estimation Stage
Introduction
Slides
Statistical Inference
Sampling Distribution — Part I
Sampling Distribution — Part II
Standard Error
Confidence Intervals — Part I
Confidence Intervals — Part II
Positivity: Formal Definitions
The Positivity-Unconfoundedness Trade-off
Positivity: Simulation Study — Part I
Positivity: Simulation Study — Part II
The Consequences of Positivity Violations
1
High-Dimensionality and Multicollinearity — Part I
High-Dimensionality and Multicollinearity — Part II
High-Dimensionality and Multicollinearity — Part III
Challenges of Polynomial and Interaction Terms
Recap
Exercises
Resources
The Estimation Stage in Applied Causal Analysis
Introduction
Slides
Dealing With Heteroskedasticity
Diagnosing Multicollinearity
Dealing With Multicollinearity
Diagnosing Positivity with Binary Treatments — Part I
Diagnosing Positivity with Binary Treatments — Part II
Dealing with Positivity Violations in Binary Treatment Settings
Diagnosing Positivity with Multicategorical Treatments — Part I
Diagnosing Positivity with Multicategorical Treatments — Part II
Dealing with Positivity Violations in Multicategorical Treatment Settings
Diagnosing Positivity with Continuous Treatments — Part I
Diagnosing Positivity with Continuous Treatments — Part II
Dealing with Positivity Violations in Continuous Treatment Settings
Diagnosing Positivity for CATE Estimation
Tools, Tips, and Considerations for Positivity Diagnostics
Applying Positivity Diagnostics in the Case Study
Best Practices for Interaction and Polynomial Terms
Functional Form Selection: Reasoning About Treatment and Control Terms
Functional Form Selection: Why Standard Selection Methods Don’t Work
Why Post-LASSO OLS Is Generally Invalid for Causal Inference: A Technical Derivation
Why Double ML with LASSO in Partially Linear Models Can Help: A Technical Derivation
What Does It Take for LASSO to Work Well in Double ML? A Practical Perspective
Extending Double ML with LASSO to Allow for Treatment Effect Heterogeneity
Implementing Double ML with LASSO in Python — Part I
Implementing Double ML with LASSO in Python — Part II
OLS Implementation for the Case Study: The Setup
OLS Implementation for the Case Study: Code — Part I
OLS Implementation for the Case Study: Code — Part II
OLS Implementation for the Case Study: Code — Part III
Double ML Implementation for the Case Study: The Setup
Double ML Implementation for the Case Study: Code — Part I
Double ML Implementation for the Case Study: Code — Part II
Double ML Implementation for the Case Study: Code — Part III
Interpreting our ATE and CATE estimates
Looking Back: A Critical Evaluation of Our Own Causal Analysis
Course Wrap-Up
Exercises
Resources
Feedback and Reviews
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Causal Inference with Linear Regression: A Modern Approach (Part II)
Buy now
Learn more
Why Simple Linear Models Fall Short in Applied Causal Analysis
Introduction
1
Slides
How to Use This Course
Course Guidelines
Required Python Packages
ATE & CATE
Causal Graphs, Backdoor Adjustment, Adjustment Formula
Linear Regression as a CEF Approximator
Limitations of the Simple Linear Model
Unmodelled Non-Linearity
Heterogeneity in Linear Models
Unmodelled Effect Heterogeneity — Part I
Unmodelled Effect Heterogeneity — Part II
Residual Confounding
Exercises
Resources
Making Linear Regression Models More Flexible
Introduction
Slides
Exploring the Dataset
Simple Models with Continuous Predictors
Simple Models with Categorical Predictors
Modelling Nonlinearity with Binning
Modelling Nonlinearity with Polynomial Terms
Modelling Nonlinearity with Log Transformations
Interaction Terms: Continuous X Continuous
Interaction Terms: Continuous X Binary
Interaction Terms: Continuous X Multicategorical
Interaction Terms: Categorical X Categorical
Nonlinearity and Interaction Terms
Moderating Non-Linear Relationships — Part I
Moderating Non-Linear Relationships — Part II
Non-Linear Moderation of Non-Linear Relationships
Flexible Linear Models in Causal Inference
Recap
Exercises
Resources
Study Design and Causal Graph Construction in Applied Settings
Introduction
Slides
What Makes a Causal Project Well-Defined?
Consistency and Treatment Variation Irrelevance
No Interference
Target Trial Emulation
"Non-Causal Edges" In Causal Graphs
True Causal Drivers or Proxies?
The Need for an Explicit Notion of Time in Causal Graphs
Time Acyclicity and Effect Acyclicity
What Graph Are We Actually Working With?
Cluster Directed Mixed Graphs (over ADMGs) — Part I
Cluster Directed Mixed Graphs (over ADMGs) — Part II
Cluster Directed Mixed Graphs (over DMGs)
Theoretical Exercises
Introducing The Case Study
Applied Exercises
Emulating the Target Trial — Part I
Emulating the Target Trial — Part II
How to Start Building a Causal Graph
Note
Pre-Treatment Structure: Nodes — Part I
Pre-Treatment Structure: Nodes — Part II
Pre-Treatment Structure: Nodes — Part III
Pre-Treatment Structure: Edges — Part I
Pre-Treatment Structure: Edges — Part II
Pre-Treatment Structure: Edges — Part III
So, We Have Cycles…
The Final Pre-Treatment Structure
Post-Treatment Structure — Part I
Post-Treatment Structure — Part II
Post-Treatment Structure — Part III
The Final Causal Graph
From Causal Graph to Dataset — Identifying a Sufficient Adjustment Set
From Causal Graph to Dataset — Proxy Variables and Practical Compromises
From Causal Graph to Dataset — Exploring The Data
Recap
Resources
Challenges in the Estimation Stage
Introduction
Slides
Statistical Inference
Sampling Distribution — Part I
Sampling Distribution — Part II
Standard Error
Confidence Intervals — Part I
Confidence Intervals — Part II
Positivity: Formal Definitions
The Positivity-Unconfoundedness Trade-off
Positivity: Simulation Study — Part I
Positivity: Simulation Study — Part II
The Consequences of Positivity Violations
1
High-Dimensionality and Multicollinearity — Part I
High-Dimensionality and Multicollinearity — Part II
High-Dimensionality and Multicollinearity — Part III
Challenges of Polynomial and Interaction Terms
Recap
Exercises
Resources
The Estimation Stage in Applied Causal Analysis
Introduction
Slides
Dealing With Heteroskedasticity
Diagnosing Multicollinearity
Dealing With Multicollinearity
Diagnosing Positivity with Binary Treatments — Part I
Diagnosing Positivity with Binary Treatments — Part II
Dealing with Positivity Violations in Binary Treatment Settings
Diagnosing Positivity with Multicategorical Treatments — Part I
Diagnosing Positivity with Multicategorical Treatments — Part II
Dealing with Positivity Violations in Multicategorical Treatment Settings
Diagnosing Positivity with Continuous Treatments — Part I
Diagnosing Positivity with Continuous Treatments — Part II
Dealing with Positivity Violations in Continuous Treatment Settings
Diagnosing Positivity for CATE Estimation
Tools, Tips, and Considerations for Positivity Diagnostics
Applying Positivity Diagnostics in the Case Study
Best Practices for Interaction and Polynomial Terms
Functional Form Selection: Reasoning About Treatment and Control Terms
Functional Form Selection: Why Standard Selection Methods Don’t Work
Why Post-LASSO OLS Is Generally Invalid for Causal Inference: A Technical Derivation
Why Double ML with LASSO in Partially Linear Models Can Help: A Technical Derivation
What Does It Take for LASSO to Work Well in Double ML? A Practical Perspective
Extending Double ML with LASSO to Allow for Treatment Effect Heterogeneity
Implementing Double ML with LASSO in Python — Part I
Implementing Double ML with LASSO in Python — Part II
OLS Implementation for the Case Study: The Setup
OLS Implementation for the Case Study: Code — Part I
OLS Implementation for the Case Study: Code — Part II
OLS Implementation for the Case Study: Code — Part III
Double ML Implementation for the Case Study: The Setup
Double ML Implementation for the Case Study: Code — Part I
Double ML Implementation for the Case Study: Code — Part II
Double ML Implementation for the Case Study: Code — Part III
Interpreting our ATE and CATE estimates
Looking Back: A Critical Evaluation of Our Own Causal Analysis
Course Wrap-Up
Exercises
Resources
Feedback and Reviews