You're reading from Causal Inference in R Decipher complex relationships with advanced R techniques for data-driven decision-making

Product type Paperback

Published in Nov 2024

Publisher Packt

ISBN-13 9781837639021

Length 382 pages

Edition 1st Edition

Languages

Concepts

Data Science

Author (1):

Subhajit Das

View More author details

Table of Contents (21) Chapters

Preface

1. Part 1:Foundations of Causal Inference

2. Chapter 1: Introducing Causal Inference FREE CHAPTER

3. Chapter 2: Unraveling Confounding and Associations

4. Chapter 3: Initiating R with a Basic Causal Inference Example

5. Part 2: Practical Applications and Core Methods

6. Chapter 4: Constructing Causality Models with Graphs

7. Chapter 5: Navigating Causal Inference through Directed Acyclic Graphs

8. Chapter 6: Employing Propensity Score Techniques

9. Chapter 7: Employing Regression Approaches for Causal Inference

10. Chapter 8: Executing A/B Testing and Controlled Experiments

11. Chapter 9: Implementing Doubly Robust Estimation

12. Part 3: Advanced Topics and Cutting-Edge Methods

13. Chapter 10: Analyzing Instrumental Variables

14. Chapter 11: Investigating Mediation Analysis

15. Chapter 12: Exploring Sensitivity Analysis

16. Chapter 13: Scrutinizing Heterogeneity in Causal Inference

17. Chapter 14: Harnessing Causal Forests and Machine Learning Methods

18. Chapter 15: Implementing Causal Discovery in R

19. Index

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Linear regression for causal inference

Linear regression models are employed to estimate the causal effect of one or more independent variables (your treatments or interventions) on a dependent variable (the outcome). This section delves into the application of linear regression for causal inference, highlighting its assumptions, methodologies, and practical considerations.

The theory

Linear regression models predict the value of a dependent variable based on the linear combination of one or more independent variables. Here is the equation for this model:

(1)

In this context, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>Y</mml:mi></mml:math> is the dependent variable we want to predict. The independent variables are <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>X</mi><mn>1</mn></msub><mo>,</mo><msub><mi>X</mi><mn>2</mn></msub><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><msub><mi>X</mi><mi>n</mi></msub></mrow></mrow></math> . The intercept <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msub><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math> represents the value of when all <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>X</mi></mrow></math> values are zero.

The coefficients <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>β</mi><mn>1</mn></msub><mo>,</mo><msub><mi>β</mi><mn>2</mn></msub><mo>,</mo><mo>…</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><msub><mi>β</mi><mi>n</mi></msub></mrow></mrow></math> show how changes in each <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>X</mml:mi></mml:math> affect , keeping other variables constant. Each coefficient indicates the impact of a unit change in its corresponding on .