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建立目录层次
3.3.3 Example: Smoking and the Genotype Theory 83
3.3.3 Example: Smoking and the Genotype Theory 83
3.4 A Calculus of Intervention 85
'''3.4 A Calculus of Intervention 85'''
3.4.1 Preliminary Notation 85
3.4.1 Preliminary Notation 85
3.4.4 Causal Inference by Surrogate Experiments 88
3.4.4 Causal Inference by Surrogate Experiments 88
3.5 Graphical Tests of Identifiability 89
'''3.5 Graphical Tests of Identifiability 89'''
3.5.1 Identifying Models 91
3.5.1 Identifying Models 91
3.5.2 Nonidentifying Models 93
3.5.2 Nonidentifying Models 93
3.6 Discussion 94
'''3.6 Discussion 94'''
3.6.1 Qualifications and Extensions 94
3.6.1 Qualifications and Extensions 94
3.6.4 Relations to Robins’s G-Estimation 102
3.6.4 Relations to Robins’s G-Estimation 102
4 Actions, Plans, and Direct Effects 107
'''<big>4 Actions, Plans, and Direct Effects 107</big>'''
4.1 Introduction 108
'''4.1 Introduction 108'''
4.1.1 Actions, Acts, and Probabilities 108
4.1.1 Actions, Acts, and Probabilities 108
4.1.3 Actions and Counterfactuals 112
4.1.3 Actions and Counterfactuals 112
4.2 Conditional Actions and Stochastic Policies 113
'''4.2 Conditional Actions and Stochastic Policies 113'''
4.3 When Is the Effect of an Action Identifiable? 114
'''4.3 When Is the Effect of an Action Identifiable? 114'''
4.3.1 Graphical Conditions for Identification 114
4.3.1 Graphical Conditions for Identification 114
4.3.2 Remarks on Efficiency 116
4.3.2 Remarks on Efficiency 116
4.3.3 Deriving a Closed-Form Expression
4.3.3 Deriving a Closed-Form Expression for Control Queries 117
for Control Queries 117
4.3.4 Summary 118
4.3.4 Summary 118
4.4 The Identification of Dynamic Plans 118
'''4.4 The Identification of Dynamic Plans 118'''
4.4.1 Motivation 118
4.4.1 Motivation 118
4.4.4 Plan Identification: A Procedure 124
4.4.4 Plan Identification: A Procedure 124
4.5 Direct and Indirect Effects 126
'''4.5 Direct and Indirect Effects 126'''
4.5.1 Direct versus Total Effects 126
4.5.1 Direct versus Total Effects 126
4.5.5 Indirect Effects and the Mediation Formula 132
4.5.5 Indirect Effects and the Mediation Formula 132
5 Causality and Structural Models in Social Science and Economics 133
'''<big>5 Causality and Structural Models in Social Science and Economics 133</big>'''
5.1 Introduction 134
'''5.1 Introduction 134'''
5.1.1 Causality in Search of a Language 134
5.1.1 Causality in Search of a Language 134
5.1.3 Graphs as a Mathematical Language 138
5.1.3 Graphs as a Mathematical Language 138
5.2 Graphs and Model Testing 140
'''5.2 Graphs and Model Testing 140'''
5.2.1 The Testable Implications of Structural Models 140
5.2.1 The Testable Implications of Structural Models 140
5.2.3 Model Equivalence 145
5.2.3 Model Equivalence 145
5.3 Graphs and Identifiability 149
'''5.3 Graphs and Identifiability 149'''
5.3.1 Parameter Identification in Linear Models 149
5.3.1 Parameter Identification in Linear Models 149
5.3.2 Comparison to Nonparametric Identification 154
5.3.2 Comparison to Nonparametric Identification 154
5.3.3 Causal Effects: The Interventional Interpretation of
5.3.3 Causal Effects: The Interventional Interpretation of Structural Equation Models 157
Structural Equation Models 157
5.4 Some Conceptual Underpinnings 159
'''5.4 Some Conceptual Underpinnings 159'''
5.4.1 What Do Structural Parameters Really Mean? 159
5.4.1 What Do Structural Parameters Really Mean? 159
5.4.3 Exogeneity, Superexogeneity, and Other Frills 165
5.4.3 Exogeneity, Superexogeneity, and Other Frills 165
5.5 Conclusion 170
'''5.5 Conclusion 170'''
5.6 Postscript for the Second Edition 171
'''5.6 Postscript for the Second Edition 171'''
5.6.1 An Econometric Awakening? 171
5.6.1 An Econometric Awakening? 171
5.6.3 Robustness of Causal Claims 172
5.6.3 Robustness of Causal Claims 172
6 Simpson’s Paradox, Confounding, and Collapsibility 173
'''<big>6 Simpson’s Paradox, Confounding, and Collapsibility 173</big>'''
6.1 Simpson’s Paradox: An Anatomy 174
'''6.1 Simpson’s Paradox: An Anatomy 174'''
6.1.1 A Tale of a Non-Paradox 174
6.1.1 A Tale of a Non-Paradox 174
6.1.4 A Paradox Resolved (Or: What Kind of Machine Is Man?) 180
6.1.4 A Paradox Resolved (Or: What Kind of Machine Is Man?) 180
6.2 Why There Is No Statistical Test for Confounding, Why Many
'''6.2 Why There Is No Statistical Test for Confounding, Why Many Think There Is, and Why They Are Almost Right 182'''
Think There Is, and Why They Are Almost Right 182
6.2.1 Introduction 182
6.2.1 Introduction 182
6.2.2 Causal and Associational Definitions 184
6.2.2 Causal and Associational Definitions 184
6.3 How the Associational Criterion Fails 185
'''6.3 How the Associational Criterion Fails 185'''
6.3.1 Failing Sufficiency via Marginality 185
6.3.1 Failing Sufficiency via Marginality 185
6.3.4 Failing Necessity via Incidental Cancellations 188
6.3.4 Failing Necessity via Incidental Cancellations 188
6.4 Stable versus Incidental Unbiasedness 189
'''6.4 Stable versus Incidental Unbiasedness 189'''
6.4.1 Motivation 189
6.4.1 Motivation 189
6.4.3 Operational Test for Stable No-Confounding 192
6.4.3 Operational Test for Stable No-Confounding 192
6.5 Confounding, Collapsibility, and Exchangeability 193
'''6.5 Confounding, Collapsibility, and Exchangeability 193'''
6.5.1 Confounding and Collapsibility 193
6.5.1 Confounding and Collapsibility 193
6.5.3 Exchangeability versus Structural Analysis of Confounding 196
6.5.3 Exchangeability versus Structural Analysis of Confounding 196
6.6 Conclusions 199
'''6.6 Conclusions 199'''
7 The Logic of Structure-Based Counterfactuals 201
'''<big>7 The Logic of Structure-Based Counterfactuals 201</big>'''
7.1 Structural Model Semantics 202
'''7.1 Structural Model Semantics 202'''
7.1.1 Definitions: Causal Models, Actions, and Counterfactuals 202
7.1.1 Definitions: Causal Models, Actions, and Counterfactuals 202
7.1.4 The Twin Network Method 213
7.1.4 The Twin Network Method 213
7.2 Applications and Interpretation of Structural Models 215
'''7.2 Applications and Interpretation of Structural Models 215'''
An Example 215
7.2.1 Policy Analysis in Linear Econometric Models: An Example 215
7.2.2 The Empirical Content of Counterfactuals 217
7.2.2 The Empirical Content of Counterfactuals 217
7.2.5 Simon’s Causal Ordering 226
7.2.5 Simon’s Causal Ordering 226
7.3 Axiomatic Characterization 228
'''7.3 Axiomatic Characterization 228'''
7.3.1 The Axioms of Structural Counterfactuals 228
7.3.1 The Axioms of Structural Counterfactuals 228
7.3.3 Axioms of Causal Relevance 234
7.3.3 Axioms of Causal Relevance 234
7.4 Structural and Similarity-Based Counterfactuals 238
'''7.4 Structural and Similarity-Based Counterfactuals 238'''
7.4.1 Relations to Lewis’s Counterfactuals 238
7.4.1 Relations to Lewis’s Counterfactuals 238
7.4.4 Relations to the Neyman–Rubin Framework 243
7.4.4 Relations to the Neyman–Rubin Framework 243
7.4.5 Exogeneity and Instruments: Counterfactual and
7.4.5 Exogeneity and Instruments: Counterfactual and Graphical Definitions 245
Graphical Definitions 245
7.5 Structural versus Probabilistic Causality 249
'''7.5 Structural versus Probabilistic Causality 249'''
7.5.1 The Reliance on Temporal Ordering 249
7.5.1 The Reliance on Temporal Ordering 249
7.5.5 Summary 256
7.5.5 Summary 256
8 Imperfect Experiments: Bounding Effects and Counterfactuals 259
'''<big>8 Imperfect Experiments: Bounding Effects and Counterfactuals 259</big>'''
8.1 Introduction 259
'''8.1 Introduction 259'''
8.1.1 Imperfect and Indirect Experiments 259
8.1.1 Imperfect and Indirect Experiments 259
8.1.2 Noncompliance and Intent to Treat 261
8.1.2 Noncompliance and Intent to Treat 261
8.2 Bounding Causal Effects with Instrumental Variables 262
'''8.2 Bounding Causal Effects with Instrumental Variables 262'''
8.2.1 Problem Formulation: Constrained Optimization 262
8.2.1 Problem Formulation: Constrained Optimization 262
8.2.2 Canonical Partitions: The Evolution of
8.2.2 Canonical Partitions: The Evolution of Finite-Response Variables 263
Finite-Response Variables 263
8.2.3 Linear Programming Formulation 266
8.2.3 Linear Programming Formulation 266
8.2.6 Example: The Effect of Cholestyramine 270
8.2.6 Example: The Effect of Cholestyramine 270
8.3 Counterfactuals and Legal Responsibility 271
'''8.3 Counterfactuals and Legal Responsibility 271'''
8.4 A Test for Instruments 274
'''8.4 A Test for Instruments 274'''
8.5 A Bayesian Approach to Noncompliance 275
'''8.5 A Bayesian Approach to Noncompliance 275'''
8.5.1 Bayesian Methods and Gibbs Sampling 275
8.5.1 Bayesian Methods and Gibbs Sampling 275
8.5.2 The Effects of Sample Size and Prior Distribution 277
8.5.2 The Effects of Sample Size and Prior Distribution 277
8.5.3 Causal Effects from Clinical Data with Imperfect
8.5.3 Causal Effects from Clinical Data with Imperfect Compliance 277
Compliance 277
8.5.4 Bayesian Estimate of Single-Event Causation 280
8.5.4 Bayesian Estimate of Single-Event Causation 280
8.6 Conclusion 281
'''8.6 Conclusion 281'''
9 Probability of Causation: Interpretation and Identification 283
'''<big>9 Probability of Causation: Interpretation and Identification 283</big>'''
9.1 Introduction 283
'''9.1 Introduction 283'''
9.2 Necessary and Sufficient Causes: Conditions of Identification 286
'''9.2 Necessary and Sufficient Causes: Conditions of Identification 286'''
9.2.1 Definitions, Notation, and Basic Relationships 286
9.2.1 Definitions, Notation, and Basic Relationships 286
9.2.4 Identifiability under Monotonicity and Nonexogeneity 293
9.2.4 Identifiability under Monotonicity and Nonexogeneity 293
9.3 Examples and Applications 296
'''9.3 Examples and Applications 296'''
9.3.1 Example 1: Betting against a Fair Coin 296
9.3.1 Example 1: Betting against a Fair Coin 296
9.3.3 Example 3: The Effect of Radiation on Leukemia 299
9.3.3 Example 3: The Effect of Radiation on Leukemia 299
9.3.4 Example 4: Legal Responsibility from Experimental and
9.3.4 Example 4: Legal Responsibility from Experimental and Nonexperimental Data 302
Nonexperimental Data 302
9.3.5 Summary of Results 303
9.3.5 Summary of Results 303
9.4 Identification in Nonmonotonic Models 304
'''9.4 Identification in Nonmonotonic Models 304'''
9.5 Conclusions 307
'''9.5 Conclusions 307'''
10 The Actual Cause 309
'''<big>10 The Actual Cause 309</big>'''
10.1 Introduction: The Insufficiency of Necessary Causation 309
'''10.1 Introduction: The Insufficiency of Necessary Causation 309'''
10.1.1 Singular Causes Revisited 309
10.1.1 Singular Causes Revisited 309
10.1.3 Overdetermination and Quasi-Dependence 313
10.1.3 Overdetermination and Quasi-Dependence 313
10.1.4 Mackie’s INUS Condition 313
10.1.4 Mackie's INUS Condition 313
10.2 Production, Dependence, and Sustenance 316
'''10.2 Production, Dependence, and Sustenance 316'''
10.3 Causal Beams and Sustenance-Based Causation 318
'''10.3 Causal Beams and Sustenance-Based Causation 318'''
10.3.1 Causal Beams: Definitions and Implications 318
10.3.1 Causal Beams: Definitions and Implications 318
10.3.5 Temporal Preemption 325
10.3.5 Temporal Preemption 325
10.4 Conclusions 327
'''10.4 Conclusions 327'''
11 Reflections, Elaborations, and Discussions with Readers 331
'''<big>11 Reflections, Elaborations, and Discussions with Readers 331</big>'''
11.1 Causal, Statistical, and Graphical Vocabulary 331
'''11.1 Causal, Statistical, and Graphical Vocabulary 331'''
11.1.1 Is the Causal-Statistical Dichotomy Necessary? 331
11.1.1 Is the Causal-Statistical Dichotomy Necessary? 331
11.1.2 d-Separation without Tears (Chapter 1, pp. 16–18) 335
11.1.2 d-Separation without Tears (Chapter 1, pp. 16–18) 335
11.2 Reversing Statistical Time (Chapter 2, p. 58–59) 337
'''11.2 Reversing Statistical Time (Chapter 2, p. 58–59) 337'''
11.3 Estimating Causal Effects 338
'''11.3 Estimating Causal Effects 338'''
11.3.1 The Intuition behind the Back-Door Criterion (Chapter 3, p. 79) 338
11.3.1 The Intuition behind the Back-Door Criterion (Chapter 3, p. 79) 338
11.3.7 The Validity of G-Estimation 352
11.3.7 The Validity of G-Estimation 352
11.4 Policy Evaluation and the do-Operator 354
'''11.4 Policy Evaluation and the do-Operator 354'''
11.4.1 Identifying Conditional Plans (Section 4.2, p. 113) 354
11.4.1 Identifying Conditional Plans (Section 4.2, p. 113) 354
11.4.7 The Illusion of Nonmodularity 364
11.4.7 The Illusion of Nonmodularity 364
11.5 Causal Analysis in Linear Structural Models 366
'''11.5 Causal Analysis in Linear Structural Models 366'''
11.5.1 General Criterion for Parameter Identification (Chapter 5, pp. 149–54) 366
11.5.1 General Criterion for Parameter Identification (Chapter 5, pp. 149–54) 366
11.5.5 External Variation versus Surgery 376
11.5.5 External Variation versus Surgery 376
11.6 Decisions and Confounding (Chapter 6) 380
'''11.6 Decisions and Confounding (Chapter 6) 380'''
11.6.1 Simpson’s Paradox and Decision Trees 380
11.6.1 Simpson’s Paradox and Decision Trees 380
11.6.4 Why Isn’t Confounding a Statistical Concept? 387
11.6.4 Why Isn’t Confounding a Statistical Concept? 387
11.7 The Calculus of Counterfactuals 389
'''11.7 The Calculus of Counterfactuals 389'''
11.7.1 Counterfactuals in Linear Systems 389
11.7.1 Counterfactuals in Linear Systems 389
11.7.3 d-Separation of Counterfactuals 393
11.7.3 d-Separation of Counterfactuals 393
11.8 Instrumental Variables and Noncompliance 395
'''11.8 Instrumental Variables and Noncompliance 395'''
11.8.1 Tight Bounds under Noncompliance 395
11.8.1 Tight Bounds under Noncompliance 395
11.9 More on Probabilities of Causation 396
'''11.9 More on Probabilities of Causation 396'''
11.9.1 Is “Guilty with Probability One” Ever Possible? 396
11.9.1 Is “Guilty with Probability One” Ever Possible? 396