Causal Inference in R E-Book

Subhajit Das

• Herausgeber: Packt Publishing
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 614

Veröffentlichungsjahr: 2024

Beschreibung

Determining causality in data is difficult due to confounding factors. Written by an applied scientist specializing in causal inference with over a decade of experience, Causal Inference in R provides the tools and methods you need to accurately establish causal relationships, improving data-driven decision-making.
This book helps you get to grips with foundational concepts, offering a clear understanding of causal models and their relevance in data analysis. You’ll progress through chapters that blend theory with hands-on examples, illustrating how to apply advanced statistical methods to real-world scenarios. You’ll discover techniques for establishing causality, from classic approaches to contemporary methods, such as propensity score matching and instrumental variables. Each chapter is enriched with detailed case studies and R code snippets, enabling you to implement concepts immediately. Beyond technical skills, this book also emphasizes critical thinking in data analysis to empower you to make informed, data-driven decisions. The chapters enable you to harness the power of causal inference in R to uncover deeper insights from data.
By the end of this book, you’ll be able to confidently establish causal relationships and make data-driven decisions with precision.

Leseprobe

Causal Inference in R

Decipher complex relationships with advanced R techniques for data-driven decision-making

Subhajit Das

Causal Inference in R

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I dedicate this book to my mother, Tapasi, and my father, Rabi Sankar, whose immense belief and steadfast faith kept me going even when the journey seemed impossible. To my wife, Florina, for her incredible confidence in me, especially on my darkest days. To my brother, Biswajit, whose smiles and joy in life’s little moments have always inspired and encouraged me.

– Subhajit Das

Contributors

About the author

Subhajit Das holds a PhD in computer science from Georgia Institute of Technology, USA, specializing in machine learning (ML) and visual analytics. With 10+ years of experience, he is an expert in causal inference, revealing complex relationships and data-driven decision-making. His work has influenced millions in AI, e-commerce, logistics, and 3D software sectors. He has collaborated with leading companies, such as Amazon, Microsoft, Bosch, UPS, 3M, and Autodesk, creating solutions that seamlessly integrate causal reasoning and ML. His research, published in top conferences, focuses on developing AI-powered interactive systems for domain experts. He also holds a master’s degree in design computing from the University of Pennsylvania, USA.

I am deeply grateful to my parents, brother, and my wife for their consistent faith in me. Their support, along with the confidence and patience they instilled, made this gift to the community possible.

About the reviewer

Harshita Asnani is an accomplished applied scientist, specializing in data-driven decision-making across teams. She holds a master’s degree in applied data science from Syracuse University and possesses expertise in ML, deep learning, and AI. Harshita excels in developing ML solutions throughout the ML/AI life cycle, from data collection to model deployment and evaluation. She has specialized knowledge in recommender systems and experience with graph ML and causal inference techniques. Harshita is passionate about leveraging advanced analytics, and she aims to solve complex challenges and enhance organizational performance through innovative data solutions.

Table of Contents

Preface

Part 1: Foundations of Causal Inference

1

Introducing Causal Inference

Defining causal inference

Historical perspective on causal inference

Why do we need causality?

Is it an association or really causation?

Deep dive causality in real-life settings

Exploring the technical aspects of causality

Simpson’s paradox

Defining variables

Summary

References

2

Unraveling Confounding and Associations

A deep dive into associations

Causality and a fundamental issue

Individual treatment effect

Average treatment effect

The distinction between confounding and associations

Discussing the concept of bias in causality

Assumptions in causal inference

Strategies to address confounding

Regression adjustment

Propensity score methods

Summary

References

3

Initiating R with a Basic Causal Inference Example

Technical requirements

What is R? Why use R for causal inference?

Getting started with R

Setting up the R environment

Navigating the RStudio interface

Basic R programming concepts

Data types in R

Advanced data structures

Packages in R

Preparing for causal inference in R

Preparing and loading data

Exploratory data analysis (EDA)

Simple causal inference techniques

Comparing means (t-tests)

Regression analysis

Propensity score matching

Case study – a basic causal analysis in R

Data preparation and inspection

Understanding the data

Performing causal analysis

Summary

References

Part 2: Practical Applications and Core Methods

4

Constructing Causality Models with Graphs

Technical requirements

Basics of graph theory

Types of graphs – directed versus undirected

Other graph typologies

Why we need DAGs in causal science

Graph representations of variables

Mathematical interpretation

Representing graphs in R

Bayesian networks

Conditional independence

Exploring Graphical Causal Models

Comparison with Bayesian networks

Assumptions in GCMs

Case study example of a graph model in R

Problem to solve using graphs

Implementing in R

Interpreting results

Summary

References

5

Navigating Causal Inference through Directed Acyclic Graphs

Technical requirements

Understanding the flow in Graphs

Chains and forks

Colliders

Adjusting for confounding in graphs

D-separation

Do-operator

The back door adjustment

The front door adjustment

Practical R example – back door versus front door

Synthetic data

Back door adjustment in R

Front door adjustment in R

Summary

6

Employing Propensity Score Techniques

Technical requirements

Introduction to propensity scores

A deep dive into these scores

Balancing confounding variables

Check for confounding using propensity scores

Challenges and caveats

Stratification and subsampling

Theory

Application of propensity scores in R

Understanding Propensity Score Matching

Considerations and limitations

Practical application of PSM in R

Balancing methods

Sensitivity analysis

Visualizing the results

Weighting in PSM using R

Summary

References

7

Employing Regression Approaches for Causal Inference

Technical requirements

Role of regression in causality

Choosing the appropriate regression model

Understanding the nature of the outcome variable

Consideration of confounding and interaction effects

Model complexity, parsimony, and assumptions

Linear regression for causal inference

The theory

Application of regression modeling in R

Single versus multivariate regression

Treatment orthogonalization

Example of the FWL theorem

Model diagnostics and assumptions

Non-linear regression for causal inference

Other types of non-linear models

Application of a non-linear regression problem in R

Important considerations in regression modeling

Which covariates to consider in the model?

Dummy variables? What are they?

Orthogonalization effect in R

Summary

References

8

Executing A/B Testing and Controlled Experiments

Technical requirements

Designing and conducting A/B tests

Concepts

Planning your A/B test

Implementation details

Controlled experiments and causal inference

Enhancing causal inference

Beyond A/B testing – multi-armed bandit tests and factorial designs

Ethical considerations

Common pitfalls and challenges

Strategies for dealing with incomplete data

Mitigating spill-over effects

Adaptive experimentation – when and how to adjust your experiment

Implementing A/B test analysis in R

Step 1 – Generating synthetic data

Step 2 – Exploratory data analysis (EDA)

Step 3 – Statistical testing

Step 4 – Multivariate analysis

Step 5 – Interpreting results

Step 6 – Checking assumptions of the t-test

Step 7 – Effect-size calculation

Step 8 – Power analysis

Step 9 – Post-hoc analyses

Step 10 – Visualizing interaction effects

Summary

9

Implementing Doubly Robust Estimation

Technical requirements

What is doubly robust estimation?

An overview of DR estimation

Technique behind DR

Comparison with other estimation methods

Implementing doubly robust estimation in R

Preparing data for DR analysis

Implementing basic DR estimators

Calculating weight

Crafting the DR estimator

Discussing doubly robust methods

Estimating variance

Advanced DR techniques (using the tmle and SuperLearner packages)

Balancing flexibility and reliability with DR estimation

Summary

References

Part 3: Advanced Topics and Cutting-Edge Methods

10

Analyzing Instrumental Variables

Technical requirements

Introduction to instrumental variables

The concept of instrumental variables

The importance of instrumental variables in causal inference

Criteria for instrumental variables

Relevance of the instrumental variable

Exogeneity of the instrumental variable

Exclusion restriction

Strategies for identifying valid instrumental variables

Relevance condition

Exogeneity condition

Demonstrating instrumental variable analysis in R

Using gmm for generalized method of moments

Diagnostics and tests in instrumental variable analysis

Interpretation of results

Challenges and limitations of instrumental variable analysis

Weak instrumental variables

Measurement errors in instrumental variables

Interpretation of instrumental variable estimates

Summary

References

11

Investigating Mediation Analysis

Technical requirements

What is mediation analysis?

Definition and overview

The importance of mediation analysis

Identifying mediation effects

Criteria for mediation

Testing for mediation

Mediation analysis in R

Setting up the R environment

Preparing data for mediation analysis

Conducting mediation analysis

Interpretation and further steps

Advanced mediation models

Summary

References

12

Exploring Sensitivity Analysis

Technical requirements

Introduction to sensitivity analysis

Why do we need sensitivity analysis?

Historical context

Sensitivity analysis for causal inference

How do we use sensitivity analysis?

Types of sensitivity analysis

Key concepts and measures

Implementing sensitivity analysis in R

Using R for sensitivity analysis

Visualizing our findings

Case study

Practical guidelines for conducting sensitivity analysis

Choosing parameters for sensitivity analysis

Limitations and challenges

Advanced topics in sensitivity analysis

Venturing beyond binary treatment

ML approaches

Future directions

Summary

References

13

Scrutinizing Heterogeneity in Causal Inference

Technical requirements

What is heterogeneity?

Definition of heterogeneity in causality

Case studies and discussion

Examples (more of them)

Understanding the types of heterogeneity

Pre-treatment heterogeneity

Post-treatment heterogeneity

Contextual heterogeneity

Heterogeneous causal effects deep dive

Interaction terms in regression models

Subgroup analysis

ML techniques

Estimation methods for identifying HCEs

Regression Discontinuity Designs

Instrumental variables

Propensity Score Matching

Case study – Heterogeneity in R

Generating synthetic data

Exploratory data analysis

Matching for causal inference

Estimating the ATE

Tailoring interventions to different groups

Conceptual framework

Case study 1 – Educational interventions and their varied effects on different student demographics

Case study 2 – Public health campaigns and their differential impacts on various population segments

Summary

References

14

Harnessing Causal Forests and Machine Learning Methods

Technical requirements

Introduction to causal forests for causal inference

Historical development and key researchers

Theoretical foundations of causal forests

Conditions necessary for causal forest applications

Advantages and limitations

Understanding the math behind causal forests

Deep-dive into causal forests

Scenario – classroom cohort

Using R to understand causal forests

Installing and loading necessary packages

Simulating data

Training a causal forest

Estimating treatment effects

Validating the model

Extracting leaf indices

Machine learning approaches to heterogeneous causal inference

Impact of social media using causal forests in R

Setting up the environment

Data preparation and preprocessing

Building and tuning causal forest models

Interpreting results and model validation

Summary

References

15

Implementing Causal Discovery in R

Technical requirements

Introduction to causal discovery

Definition and importance

Historical background

Theoretical foundations

Methods for causal discovery

Constraint-based methods

Score-based methods

Hybrid methods

Functional Causal Models

Which causal discovery method should we use?

Implementing causal discovery with Bayesian networks in R

Using R packages

Scenario for our problem

Creating the dataset

Implementing PC algorithm

Using bnlearn for Bayesian networks

More causal discovery methods

Estimating causal effects

A multi-algorithm comparative approach to causal discovery in R

Setting up and generating data

Constraint-based methods in R

Score-based methods in R

Hybrid methods in R

Visualizing causal relationships

Interpretation from code

Future steps

Summary

References

Index

Other Books You May Enjoy

Part 1:Foundations of Causal Inference

This part introduces the core principles of causal inference, focusing on distinguishing causation from association and correlation. It covers fundamental concepts such as confounding variables, biases, and assumptions in causal analysis, providing a solid theoretical base. Additionally, it introduces the use of R for basic causal inference, preparing you for practical applications using R.

This part has the following chapters:

Chapter 1, Introducing Causal InferenceChapter 2, Unraveling Confounding and AssociationsChapter 3, Initiating R with a Basic Causal Inference Example

1

Introducing Causal Inference

In this inaugural chapter, let’s explore the topic of causal inference a bit. For some, this may be a new topic; for others, it might be somewhat familiar. However, whether you find this topic intimidating or not depends less on your existing statistical knowledge and more on your interest in the subject and your consistent effort throughout the book.

Our exploration begins with three pivotal questions: What exactly is causal inference? Why is it indispensable? How can it be effectively utilized? To clarify these concepts, we’ll use both fictitious and real-life scenarios.

Approach this chapter with unhindered curiosity and an open mind. Be prepared to encounter concepts and terminology that might initially seem abstruse. Don’t worry, though—we will be with you every step of the way, ensuring you understand everything clearly and thoroughly as we explore causal inference together.

In this chapter, we will cover the following topics:

Defining causal inferenceHistorical perspectives on causal inferenceWhy do we need causality?Is it an association or really causation?Deep diving into causality in real-life settingsExploring the technical aspects of causality

Defining causal inference

Picture yourself as a teacher contemplating a curious phenomenon among high school students: the relationship between sleeping late and catching the school bus. An initial hypothesis might be, “Sleeping late causes students to miss their school bus.” This stems from a personal experience: I slept late and consequently missed the bus. However, this hypothesis might be challenged upon observing graduate students, who, despite sleeping late, consistently catch their buses.

This scenario exemplifies the complex, often misleading nature of causality. The observed association—sleeping late and missing buses—doesn’t inherently imply causation. Here, various other factors could be at play. Perhaps high school students have earlier bus schedules, or graduate students, despite sleeping late, can wake up early and not miss their transportation. It’s plausible that the initial observation of sleeping late and causing one to miss the bus was a mere coincidence, not a universal rule.

Causal inference in this context goes beyond the superficial observation of relationships. It goes deeper, exploring whether one factor (sleeping late) actively influences another (missing the bus). This is not just about associating events but understanding thoroughly the underlying mechanisms that link them. Is the relationship direct, or are there hidden variables that mediate this connection?

Practically, this kind of analysis is vital. Consider a school administrator who, based on initial observations, might advocate for earlier bedtimes to ensure students catch their buses. However, a more nuanced causal analysis could reveal that the issue isn’t bedtime but perhaps bus scheduling or student time management. Making decisions based on superficial associations could lead to ineffective or even counterproductive policies.

In statistical terms, particularly when employing tools such as R, causal inference is the methodology that allows us to rigorously test these relationships. It helps us differentiate between mere assumptions and substantiated causality.

Reflecting on our initial hypothesis, a thorough causal analysis would involve examining all potential variables—bus schedules, student routines, and even the difference between high school and graduate lifestyles. Only a comprehensive study can reveal whether sleeping late directly causes a student to miss the bus or is just a coincidental factor in a student's life. Now that we have defined what causal inference is, let’s learn where it came from.

Historical perspective on causal inference

In Hellenic philosophy, ancient Greece played a pivotal role. Pre-Socratic philosophers such as Thales and Heraclitus explored the nature of change and causality. Ancient Greek philosophers contributed significantly to systematic approaches to understanding causality by examining cause-and-effect relationships. They introduced important causal concepts, including the idea that nothing comes from nothing (attributed to Parmenides). While not originating the principle of sufficient reason, their work laid the foundations for later philosophical developments. Their ideas have influenced our understanding of causation, though modern concepts have evolved significantly, incorporating insights from various traditions, scientific advancements, and mathematical frameworks.

Aristotle, however, provided a more structured approach to causality with his four causes theory:

Material cause: The material from which something is made (e.g., the bronze in a statue)Formal cause: The essence or shape of something (e.g., the design of a statue)Efficient cause: The initiator of change or stability (e.g., the sculptor of the statue)Final cause: The intended purpose of an object (e.g., the statue’s artistic or religious function)

Aristotle’s framework significantly advanced the systematic study of causality, influencing philosophical and scientific thought for centuries.

In Eastern philosophies, causality was similarly a significant concept. Hindu texts, such as the Upanishads, explore causality within material and spiritual realms, often using metaphors such as a spider spinning a web to depict inherent causation.

Buddhism introduces Pratītyasamutpāda, or dependent origination, conceptualizing the interdependence and interconnectedness of all phenomena. This principle suggests that everything arises in dependency on conditions, forming a complex causal network.

The initial forays into the concept of causality by ancient civilizations provided the cornerstone ideas that would ultimately give rise to the scientific method. While these early thinkers were not conducting causality studies as understood in contemporary terms, their philosophical examination of cause and effect laid the groundwork that profoundly influenced later generations. Their efforts exemplify the varied approaches through which human societies have endeavored to comprehend the linkages between actions and their consequences—a pursuit that persists in the intricate causal analyses of modern times.

In studying causal inference, it’s important to acknowledge the many thinkers who have improved our understanding of causality. This field has many key ideas, ranging from basic philosophical concepts to complex mathematical models.

20th-century statisticians and economists, such as Ronald A. Fisher, Jerzy Neyman, Egon Pearson, and Donald Rubin, laid significant groundwork in the field of causal inference. Fisher was instrumental in experimental design, particularly with his contributions to randomization and analysis of variance. Neyman and Pearson developed a framework for hypothesis testing and the Neyman-Rubin causal model, which are fundamental to contemporary causal inference methods. Rubin, co-developing the Rubin causal model (RCM) [3], introduced pivotal concepts such as potential outcomes and propensity score matching (both covered in this book), essential in observational studies.

In thought leadership within causal science, Judea Pearl [7] and James Heckman stand out. Pearl, renowned in artificial intelligence and statistics, formulated the do-calculus and a theoretical framework for causal relationships using graphical models. Heckman, a Nobel laureate in economics, made significant strides in understanding causal relationships through his work on selection bias and the Heckman correction.

Furthermore, these pioneers teach the foundational elements of causal inference:

Mill’s methods [4] provide logical strategies for causal identification in observational studies.Fisher’s Design of Experiments [5] emphasizes the importance of randomization and control in establishing causalityThe Neyman-Pearson framework [6] underlines statistical rigor and meticulous hypothesis testing forcausal conclusionsRubin’s potential outcomes [3] approach stresses understanding what might have happened under different scenariosPearl’s Causal diagrams for empirical research [7] introduce graphical models for managing various confounding factorsHeckman’s Handbook of Econometrics [8] addresses selection bias and endogeneity in economic and social data analysis

We have provided a comprehensive overview of causality, highlighting its distinction from simple association. A pertinent inquiry emerges: Why is the knowledge of causality essential? Let’s discuss it in the next section.

Why do we need causality?

Beyond understanding the theoretical and historical underpinnings, one must ponder the practical necessity of causality first. We shall discuss examples of the ubiquitous application of causality across various industries. For instance, enterprises leverage causal inference techniques to gain deeper insights into customer behaviors, needs, and preferences. They employ these methods to elucidate both natural and anthropogenic phenomena. Mastery of causal inference equips you with an extremely powerful tool, rendering you an invaluable asset in any team or organizational context. Your proficiency in this domain can significantly contribute to the overarching objective of delivering value to stakeholders.

Let's discuss further why causality is not only an intellectually rewarding area but also practically indispensable.

In medical and public health arenas, causal inference is vital for assessing treatment efficacy. Randomized controlled trials (RCTs) stand as the pinnacle of causal inference methods, isolating drug effects from external variables. RCTs are experiments where participants are randomly assigned to an intervention or control group to measure the intervention’s effects, minimizing bias for reliable results.

A pertinent example is its role during the COVID-19 pandemic, where causal inference underpinned the evaluation of vaccines’ efficacy and safety, informing critical decisions on their approval and distribution strategies, thereby saving lives.

Economists utilize causal inference to decode market behaviors and policy impacts. Analyzing the effects of a minimum wage hike on employment, for instance, requires separating the causative effects from economic trends and other policy shifts. Techniques such as difference-in-differences analysis enable economists to extract causal insights from observational data, influencing policies that impact millions.

In business, causal inference informs the effectiveness of marketing efforts and strategic decisions. A/B testing, a direct application of causal principles, guides companies in optimizing profits and enhancing customer experience. By comparing conversion rates from different advertising campaigns, businesses can determine which strategies are more effective.

Statistically, causality is paramount for accurate data interpretation. Identifying associations between variables is one aspect, but establishing causation is a more complex and significant task. This distinction shapes the conclusions and recommendations derived from data analysis.

In survey methodology, understanding causality is critical. When analyzing survey data, statisticians must discern potential causal links between variables to avoid erroneous conclusions based on merely correlated associations. Causal inference, therefore, is not just a statistical tool but a fundamental approach to deciphering the dynamics of various phenomena. Now, in the next section, let’s learn about more critical aspects of causality.

Is it an association or really causation?

It’s tempting to attribute causality to superficial observations, mistaking mere associations for causation. Take, for instance, the observation that social media posts made later in the day receive fewer likes and comments, suggesting reduced engagement. One might hastily conclude that the timing of these posts is the causal factor. However, without rigorous statistical testing, such claims remain speculative. In this book, we will teach you how to conduct these necessary tests, distinguishing between simple association and true causation.

In statistics, we discuss association, causation, and correlation. While correlation is often used interchangeably with association in everyday conversations, they have distinct meanings in statistical contexts. So, what is the difference between association and correlation?

In causality, association encapsulates a general linkage between two variables, without explicitly characterizing the nature or magnitude of this relationship. This concept encompasses both linear and non-linear associations. Contrastingly, correlation denotes a specific statistical measure, exemplified by metrics such as Pearson’s correlation coefficient, which quantifies the strength and direction of a linear relationship between variables. The coefficient’s value spans from -1 to 1, indicating a spectrum from strong negative to strong positive linear relationships.

Now that the distinction is clear between association and correlation, let’s see what the relationship between correlation and causation is.

To understand this, let’s examine a real-life example. Picture the observed increase in motorcycle accidents coinciding with a rise in rainfall. This simultaneous upsurge could suggest a strong positive linear correlation, particularly if their correlation coefficient hovers near 1. However, it’s crucial to recognize that correlation does not equate to causation. Increased rain does not cause motorcycle accidents.

To unpack this further, we need to consider the role of confounding variables, a concept we will explore more comprehensively later in this chapter. In our case, the overarching weather conditions serve as a potential confounder. Rainy days are associated with more motorcycle accidents. However, rainy days also often come with other weather factors, such as strong winds and poor visibility. These overall weather conditions affect both rainfall and driving safety. Why is this important? Because bad weather not only increases rainfall but also creates hazardous driving conditions. This dual impact can lead to a spike in motorcycle accidents, primarily due to slippery roads, reduced visibility, and challenging driving environments.

Thus, while rainfall and motorcycle accidents are correlated, the actual causative factor may be the broader weather patterns, a subtle yet significant distinction in data interpretation (see Figure 1.1).

Figure 1.1 – A directed acyclic graph (DAG)

This diagram illustrates that while there's a direct path from Rainfall to Motorcycle Accidents, there's also another path from Weather Conditions to Motorcycle Accidents through Rainfall. Additionally, Weather Conditions directly influences Motorcycle Accidents. This is a case of confounding.

Confounding variable

It is an external variable that is not the primary focus of a study but can affect both the independent variable (the variable you are changing) and the dependent variable (the variable you are measuring).

The primary objective of causal inference is to ascertain whether observed correlations genuinely reflect causal relationships, by meticulously controlling for potential confounding factors. While both association and correlation can hint at possible causal connections, they do not inherently validate causality. Consequently, further empirical investigation, through experimental or quasi-experimental methodologies, is frequently necessitated to establish causal links definitively.

Did you know that our tendency to interpret past experiences as causality is a classic human trait? It’s quite amusing, yet deeply ingrained in our psychology, to mix up association with causation.

Let’s consider the age-old practice of burning the midnight oil before exams or project deadlines, often linked to better grades or outcomes. This belief stems from those all-nighters that seemed to coincide with academic triumphs. However, what really leads to higher grades? It might not just be the long hours spent studying but factors such as the precision of your work, regular class attendance, the flair in your presentations, and being punctual. This shows us that the supposed connection between night-time study marathons and academic success might just be a classic case of mistaking association for causality, without accounting for other important elements.

Globally, there’s a popular notion that kids studying STEM (science, technology engineering, or mathematics) subjects are on a fast track to higher earnings. This originates from observing that folks with a STEM background often land lucrative jobs. But let’s pause and think—is it just the STEM education driving higher income? Other elements, such as the quality of education, networking, where you live, economic factors, individual talents outside STEM, or even one’s social and economic background, play a significant role. This example shines a light on the potential error of directly linking STEM education with higher income, without considering these extra factors, and reminds us not to confuse correlation or association with causation.

Going back to associations, you should know by now that association means events or variables occurring together, while causation implies one variable brings about a change in another. Understanding this difference is critical.

Let us go deeper into understanding how causality is fundamentally embedded in the fabric of our everyday world, encompassing a vast array of industrial settings, diverse use cases, and problem formulations.

Deep dive causality in real-life settings

Let's walk through a study titled Inked into Crime? An Examination of the Causal Relationship between Tattoos and Life-Course Offending among Males from the Cambridge Study in Delinquent Development [1]. It’s about a study to ascertain whether or not there exists a causal connection between the presence of tattoos and the propensity for criminal behavior across one’s lifespan. Analyzing data from 411 British males, the researchers utilized propensity score matching—a statistical technique frequently used to ascertain causal inference (which we shall learn about later in this book, in Chapter 6). This approach meticulously dissects the complexity between the ink on skin and the propensity for crime, offering a more refined perspective on this age-old debate.

Rooted in the shadow of 19th-century criminological thought, specifically the theories of Lombroso, tattoos have long been cast in the dim light of criminality. This study, however, peels back layers of historical bias and cultural assumptions, examining how tattoos have been portrayed across both academic and pop culture spectrums. It’s crucial to note here that while there exists a tangible correlation between tattoos and a gamut of criminal behaviors and psychological markers—such as impulsivity and substance abuse—this link is more correlational than causal.

Based on the causal analysis, the study concludes that tattoos and crime are linked not by causality but through shared risk factors and personality traits. This study clearly elucidates how a strong correlation does not necessarily imply causality. Now, one may wonder how this study can be utilized across industries. Well, that’s a great question. It can actually be used in many settings, such as in human resources and employment practices; the study’s conclusion that tattoos do not have a causal link to criminal behavior could encourage businesses to reassess and potentially modify their employment policies. This adjustment could result in a more inclusive hiring process, expanding the talent pool by eliminating biases against tattooed individuals. Similarly, in marketing and advertising, these findings can be instrumental in dismantling stereotypes associated with tattooed individuals, aiding in the creation of advertising content that is both inclusive and diverse, reflective of a more nuanced understanding of tattoos as personal or cultural expressions rather than indicators of criminal tendencies. Furthermore, the tattoo industry can harness these findings to address and mitigate stigmas associated with tattoos, employing this information in marketing strategies to foster a normalized perception of tattoos in professional and social contexts. For industries such as insurance and risk assessment, the study’s conclusions provide a critical perspective for refining risk profiling models, ensuring that tattoos are not erroneously factored as indicators of criminal propensity, leading to more equitable and accurate risk assessments.

By looking at how the study separates correlation from causation, you can develop a more critical and analytical mindset. This is important in causal inference, where understanding details and mechanisms is crucial.

The next case study helps you engage more deeply with causal analysis principles.

The paper titled Causal or Spurious: Using Propensity Score Matching to Detangle the Relationship between Violent Video Games and Violent Behavior [2] undertakes a rigorous investigation into the often-debated link between the playing of violent video games and the manifestation of violent behavior, non-violent deviance, and substance use. Utilizing propensity score matching, the researchers learned a more nuanced understanding of causality in this context.

The study’s initial findings, based on an unmatched sample (where participants are not paired based on similar characteristics), indicate a noticeable correlation: children who engage in violent video games exhibit a higher propensity for various forms of deviant behavior. If you don’t understand what an unmatched sample is, don’t worry now. We’ll cover it later in the book. Coming back to the study, the trend is observed across genders, with males showing a particularly heightened likelihood of engaging in non-violent deviance, violent acts, and substance use. Females, while following a similar pattern, exhibit slightly lower rates. However, when they looked deeper using propensity score matching to create a quasi-experimental framework, a striking shift emerged. For males, the apparent negative effects attributed to playing violent video games dissipate significantly in the matched sample, suggesting that the initial correlational relationships might be spurious rather than indicative of a causal link.

In terms of gender differences, the study underscores a fascinating divergence. The propensity score matching, while effectively nullifying most of the significant correlations for males, reveals persistence in certain deviant behaviors among females. This includes an increased likelihood of engaging in group fights and carrying weapons, hinting at a potential causal connection between playing violent video games and certain types of violent behavior in females. Conclusively, the study challenges the prevalent notion of a robust causal link between violent video games and violent behavior. A robust causal link would be a strong, consistent relationship where changes in one factor (such as playing violent video games) directly and reliably lead to changes in another (such as violent behavior), even when accounting for other potential influences. The study here posits that for males, personality and background factors are likely more influential in the observed correlations with deviant behavior. For females, although there is some evidence of causality, it is not as pronounced as previously believed. This research serves as a critical reminder of the importance of dissecting underlying factors in the analysis of complex social phenomena, urging a reconsideration of commonly held beliefs about the impact of violent video games.

This work also offers strategic insights that are of significant utility to the video game industry and its related sectors. In advocacy and legal defense, the findings provide a robust foundation for the industry to counter regulatory or legislative actions that might be predicated on the assumption of a direct causal link between violent video games and aggressive behavior, particularly in male demographics. This evidence, showcasing a more complex and less definitive connection, empowers the industry to resist measures that would unjustifiably censor or restrict video game content. Additionally, in the sphere of marketing and public relations, these insights afford an opportunity to reshape the public narrative surrounding video games. By leveraging the study’s findings, the industry can challenge and mitigate negative stereotypes, potentially enhancing the public image of video games and broadening their appeal across a more diverse audience base.

Moreover, the nuanced understanding of gender-specific impacts of violent content highlighted in the study can inform content development strategies within the industry. This includes tailoring game design elements to cater to or responsibly address different demographic groups, thus fostering more conscientious content creation. In parallel, these insights can guide the industry in enhancing parental guidance and educational campaigns. Such initiatives could involve refining age-rating systems or creating informative material to assist parents and guardians in making more informed choices regarding video game suitability for their children. Beyond these immediate applications, there is a scope for the industry to delve deeper into research and development, building upon these findings to explore the broader behavioral impacts of video games. This proactive approach could not only contribute to the development of socially responsible gaming products but also equip the industry to pre-emptively address potential controversies or regulatory challenges. Furthermore, the potential for collaboration with the healthcare and educational sectors emerges as a significant opportunity, wherein video games could be utilized as tools for positive development in therapeutic or educational settings. Lastly, these findings can enable the video game industry to engage more effectively with a range of stakeholders, including policymakers, educators, and advocacy groups, ensuring that discussions and policies related to media consumption and youth behavior are informed by comprehensive, evidence-based insights. By strategically leveraging these findings, the video game industry stands to not only safeguard its interests but also contribute meaningfully to the broader societal discourse on the impact of media consumption on behavior.

Drawing inspiration from the previous examples, can you recall two or three instances from your own life or work experiences where you might have employed causal inference to explore the underlying causes of certain events? Taking our exploration into causality further, let’s explore the technical aspects of this topic. This exploration aims to equip you with the necessary knowledge and skills to adeptly apply these principles in your specific use cases.

Exploring the technical aspects of causality

From the previous section, it is evident that causal inference involves employing observational or experimental data to establish causal links, utilizing various statistical methods and theories to measure the influence of one variable (the “treatment” or “intervention”) on another (the “outcome” or the “effect”).

From a statistical vantage point, it focuses on estimating the counterfactual, hypothesizing the outcomes in alternate scenarios where the treatment was absent. This necessitates assumptions about data and underlying mechanisms, including the exclusion of unmeasured confounders. Let’s go over these concepts one by one.

Counterfactual analysis

Counterfactual analysis involves exploring "what-if" scenarios to understand the effects of actions that didn't occur. It is used to estimate the causal impact of interventions by imagining alternative outcomes. In e-commerce, for example, this method helps assess new sales strategies by using statistical techniques to estimate what would have happened to customers who didn't experience the strategy. It answers the question: what if the strategy hadn't been implemented? By combining rigorous causal inference methods with practical business insights, this approach effectively evaluates strategies.

Central to this approach is the potential outcomes concept, positing that each subject has a hypothetical outcome for every potential treatment level. The causal effect is the variance between these potential outcomes. However, since only one outcome per subject is observable (the one pertaining to the actual treatment), causal inference techniques aim to deduce what would have occurred under different treatment scenarios.

Causal inference methods range from randomized experiments, the benchmark for controlling confounders, to techniques used in observational studies, such as matching, stratification, instrumental variables, regression discontinuity designs, difference-in-differences methods, and causal diagrams (such as DAGs). These methods seek to emulate randomized experiment conditions and extract causal conclusions from non-experimental data.

Ultimately, causal inference empowers you to quantify the causal effect as accurately and unbiasedly as possible, grounded in the available data and justifiable assumptions.

Simpson’s paradox

Next, we learn a unique phenomenon crucial to the deeper understanding of causality. It is called Simpson’s paradox, and it represents a statistical conundrum where a trend observed in separate groups vanishes or reverses when these groups are amalgamated. This paradox highlights the challenges and potential missteps in interpreting causality from observational data.

To exemplify Simpson’s paradox and its impact on causal analysis, consider the case of university admissions with these statistics (see Figure 1.2).

In a university comprising the literature and engineering departments, an investigation into potential gender bias in admissions is conducted. The applicant data for the past year is analyzed:

In the literature department, of 100 male applicants, 60 are admitted (60% admission rate), while out of 200 female applicants, 150 are admitted (75% admission rate)In the engineering department, 450 of 900 male applicants (50% admission rate) and 20 of 100 female applicants (20% admission rate) are admitted

In examining the admissions data department-wise, we observe a preference for female applicants within the literature department, contrasted starkly by the engineering department’s noticeable inclination to favor male applicants.

Combining the figures from both departments presents the following picture:

Total male applicants: 1,000 (100 in literature, 900 in engineering)Total female applicants: 300 (200 in literature, 100 in engineering)Total accepted males: 510 (60 in literature, 450 in engineering)Total accepted females: 170 (150 in Literature, 20 in engineering)

This amalgamation yields these overall admission rates:

Male admission rate: 51% (510/1,000)Female admission rate: 56.7% (170/300)

Figure 1.2 – Simpson’s paradox in the context of university admissions

Despite the apparent bias against females in the engineering department and favor toward them in the literature department, the combined data misleadingly suggests a higher overall admission rate for females.

Surprisingly, when viewed collectively, the data suggests a marginally higher admission rate for females than males. This seems to contradict the specific trends observed in each department and might hint at an absence of gender bias against women or even a potential bias against men. Simpson's paradox arises when group sizes vary significantly and outcomes within each group differ, leading to misleading aggregate results. In this case, the disparity in the number of male and female applicants across departments and the varying admission rates create an illusion that contradicts the trends seen in individual departments.

However, this apparent paradox stems from the disparate sizes and admission rates of the departments involved. A greater number of men apply to the engineering program, which has a notably lower admission rate, while a larger contingent of women seeks entry into literature, where the acceptance rate is significantly higher. When merged, these figures disproportionately elevate the overall female admission rate, thanks to their dominant presence in the more lenient literature department. This scenario masks the stark gender bias evident in engineering.

This instance is a classic demonstration of Simpson’s paradox, underscoring the intricacies involved in drawing conclusions from aggregated data, especially in causal analysis. To accurately discern whether gender affects admission rates, it’s essential to dissect the data by relevant categories, such as departments in this case. A departmental breakdown reveals potential biases that are not apparent when data is lumped together.

Such scenarios highlight the need for careful analysis in causal studies. It’s vital to consider underlying variables, such as departmental choice, that can significantly alter outcomes. Overlooking these elements can lead to false interpretations of causal relationships.

In summary, effective causal analysis requires meticulous management of confounding variables, data stratification, and an acute awareness of phenomena such as Simpson’s paradox, which can skew our understanding and interpretations.

Moving forward, let’s make a slight yet crucial distinction between the kinds of variables we may find as we solve complex problems of causality.

Defining variables

In statistical analysis, particularly when dissecting causal relationships, the concepts of confounding and lurking variables play a pivotal role. These elements can significantly skew how we interpret data, often leading to misleading conclusions:

Confounding variables: These are the behind-the-scenes actors influencing both the independent variable (what we think is causing the change) and the dependent variable (the change we’re observing). This variable can create the illusion of a causal link where none exists or can hide a real connection. They are a frequent headache in observational studies, where control over variables is limited. Take, for instance, a study probing the connection between regular exercise and heart health. Here, diet could be a confounder, impacting both a person’s exercise routine and their heart health.Lurking variables: These are the stealthy variables not initially included in your study but still capable of affecting both your independent and dependent variables, thus potentially derailing your study’s conclusions. Think of them as hidden influencers, similar to confounders, but often overlooked or unidentified in your analysis. For example, when examining how education level impacts income, geographic location could be a lurking variable. It might influence both educational opportunities and income levels but goes unnoticed in the study’s framework.

In a nutshell, lurking variables are hidden factors affecting the variables of interest, while confounding variables are known factors influencing both dependent and independent variables.

Overlooking confounding and lurking variables can confuse us in understanding causal links. Identifying and managing these variables is crucial, especially in observational studies where the luxury of randomization isn’t available. Being vigilant about these variables ensures the integrity and accuracy of your conclusions. Remember, in the world of data, what you see isn’t always what you get!

Summary

This chapter introduced the concept of causality and its importance across various fields. A brief historical overview acknowledged the contributions of ancient philosophers and modern statisticians in developing causal inference methods. We started by defining causal inference and distinguishing it from association and correlation with practical examples. We also touched on complex ideas such as potential outcomes, confounding variables, and Simpson’s paradox, explaining how they affect causal studies.

Finally, the chapter underscored the importance of causal inference in making informed decisions in our data-driven world. This foundation prepares you for a deeper exploration of causal inference in subsequent chapters.

References

Inked into Crime: https://www.sciencedirect.com/science/article/abs/pii/S0047235213001189.Causal or Spurious: Using Propensity Score Matching to Detangle the Relationship between Violent Video Games and Violent Behavior: https://www.researchgate.net/publication/257252863_Causal_or_Spurious_Using_Propensity_Score_Matching_to_Detangle_the_Relationship_between_Violent_Video_Games_and_Violent_Behavior.Imbens, G.W., Rubin, D.B. (2010). Rubin Causal Model. In: Durlauf, S.N., Blume, L.E. (eds) Microeconometrics. The New Palgrave Economics Collection. Palgrave Macmillan, London. https://doi.org/10.1057/9780230280816_28.Mill’s methods, https://beisecker.faculty.unlv.edu/Courses/Phi-102/Mills_Methods.htm.Peter Armitage, Fisher, Bradford Hill, and randomization, International Journal of Epidemiology, Volume 32, Issue 6, December 2003, Pages 925–928, https://doi.org/10.1093/ije/dyg286.BIOS 6611 (2021, July 31) , Neyman-Pearson Approach to Statistics. YouTube. https://www.youtube.com/watch?v=4boPRRKl0GY.Judea Pearl, Causal diagrams for empirical research, Biometrika, Volume 82, Issue 4, December 1995, Pages 669–688, https://doi.org/10.1093/biomet/82.4.669.Characterizing Selection Bias Using Experimental Data, J. Heckman, Hidehiko Ichimura, Jeffrey A. Smith, Petra E. Todd.

2

Unraveling Confounding and Associations

In this chapter, we deepen our knowledge of causal inference, exploring more complex aspects of the theory, including an overview of treatment effects. We also clarify the often-muddled concepts of confounding and associations, using real-world examples to illustrate how associations are frequently misinterpreted as causality. We introduce a mathematical framework designed to clearly distinguish between confounding, associations, and causality.

A key distinction is drawn between statistical and causal inference, particularly in the context of infinite data. In addition, we discuss two common strategies to mitigate confounding and highlight various biases inherent in causal analysis. Alright, we are all set to explore these intricate concepts in detail.

The following are the topics covered in this chapter:

A deep dive into associationsCausality and a fundamental issueThe distinction between confounding and associationsThe concept of bias in causalityAssumptions in causal inferenceStrategies to address confounding

A deep dive into associations

Traditional statistical