ANALYTIC COMPARISON. Pearl and Rubin CAUSAL FRAMEWORKS

Transcription

1 ANALYTIC COMPARISON of Pearl and Rubin CAUSAL FRAMEWORKS

2 Content Page Part I. General Considerations Chapter 1. What is the question? 16 Introduction Randomization An Example of Randomization An example of observational study The Difference between These Two Examples Observational Study Some Difficulties in Observational Study Common Causes Mutual Effect between Treatment and Response Regression to Mean Adjustment for confounders Matching Classification Conditional Probability and Causal Relationship The Necessity of Assignment Mechanismus Consideration Some Works on Statistical Causal Inference Discussed in this Book How to Approach Causality Causal Languages Outlines Appendix 26 Chapter 2. Required Definitions and Clarifications Introduction Definitions Statistics, Probability and Causality Why Indeterministic Causality? Some of My Observations 33 Chapter 3. Different Causal Views 34 6

3 1. Introduction Different Views to Causal Effect Subjective View Causal Effect Measurement through Inter-Subjective View Objective View Propensity View Conjugate View Combination of Different Causal Views Frameworks and Causal Effect Measurements Causality Interpretation or Probability Interpretation Appendix Causal Effect Measurement in Subjective View Measurement by Observing Two Responses of One Unit Measurement by Subjective Probability Causal Effect Measurement in Intersubjective View My Observations 42 Part II. Rubin's Contributions to Causality and Related Works Chapter 4. Potential Response Framework Introduction Notations Definition of Individual Causal Effect Two Points about Individual Causal Effect Treatment-Unit Additivity Matching in the Potential Outcome Framework Consistency Assumption General Assumptions Some Discussions on SUTVA My Observation Two Points Assignment Mechanism (AM) Formalizing Assignment Mechanism 52 7

4 6. A Particular Assumption Unconfounded AM Prediction from Bayesian View Review of Essential Points in Potential Response Framework The Science Distinguish Between the Science and the Assignment Mechanism Assumptions in potential response framework Some of My Observations 61 Chapter 5. Some Works in Potential Response Framework Introduction Definition of Average Causal Effect First Assumption for Identifiability of Average Causal Effect Summary Second Assumption for Identifiability of Average Causal Effect Discussions on Average Causal Effect Randomization Propensity Score A Comparison of Propensity Sore and Randomization Some Discussions on Propensity Score Some of My Observations 68 Chapter 6. Some Discussions on Potential Response Framework Introduction Piatonic Heaven Potential Outcomes or Counterfactuals? What is the Definition of Causal Effect? The Dependence of Assignment Mechanism on Potential Outcomes My Observations 73 Outlines of Part II 74 Part III. Dawid' S Contributions and the Necessary Preliminaries 8

5 Chapter 7. Extended Conditional Independency Introduction Conditional Independency Some Properties and Axioms Extension of Conditional Independency to Non-Stochastic Variables Some Discussions on Conditional Independency and my Observations 79 Chapter 8. Exchangeability Introduction Exchangeability Bayesian View Two Rules Applied by Bayesians A Bridge between Bayesian and Frequentist One Point about Subjective Probability Conditional Exchangeability 88 Chapter 9. Decision Theory Approach Introduction Decision-Theory Framework Regimes Identification The Language of AM A Comparison of Rubin Causal Framework and Decision Theory Framework In Notation Estimating the Probability of Missing Potential Response Dawid and Rubin's View Some of My Observations in Part III 96 Outlines of Part III 98 Part IV. Pearl's Contributions and Some Computations 9

6 Chapter 10. Probabilistic Graphs Introduction Definition of Graph Kinship Language Three Types of Substructures in DAGs DAG and Joint Distribution Markov Equivalence d-separation Criterion Some of My Observations 109 Chapter 11. Causal Graph Introduction Graphs as an Illumination of AM Two Different Mechanism The Mechanism between Two Variables Illumination of Treatment Assignment Mechanism Representation of Assumptions Missing Arrows as Representation of assumptions Causal Markov Assumption How to Draw Causal Graphs My Definition of Causal Graph Herman and Robin's Definition of Causal Graph Pearl's Word to Draw a Causal Graph A Comparison of Different Frameworks in Terms of Assumption Whether Treatment must be Assignable? Some of My Observations 120 Chapter 12. Causal Inference through Causal Graphs Introduction Missing Step in Pearl's Causal Approach Pearl's Approach to Causal Discovery Intervention The Effect of Intervention in Markovian Model Two Subsequences of Intervention Causal Effect Definition

7 5. 6. Intervention and Observation Computation of the Intervention Effect 6.1 Conclusion Identifiability Identifiability through Other Notations Finding Confounders and Coping with Immeasurable Confounders The Conditions of the Back-door Criteria by Regime Indicator Notation Back-Door Criteria by Regime Indicator Notation Front-door criteria The Intuition behind Front-Door Criteria Some Explanations for the Computation of the Quantity in Front-Door Criteria Application of Front-Door Criteria 9. Computations of Some Causal Quantities Computation of the Quantity in Introduction of Chapter 3, Pearl (2009a) The Difference between immeasurable and Unobservable Confounders 136 ll.summery Appendix Some of My Works 137 Chapter 13. Structural Equation Modeling (SEM) Introduction SEM Surrounded by Controversies Assumptions and Representations The Error Term in Regression and Exogenous Variable U in SEM Discussion Causal Assumptions in Nonparametric Models Intervention in Non-Parametric Models Estimating the Effect of Intervention in Linear Model Estimating the Effect of Intervention in Non-Linear Model My Work 148 Chapter 14. Predictions and Actions Introduction Computation of Prediction and Action through DAGs Indeterministic Model Deterministic Model 150

8 3. Demand and Price Indeterministic Causal Model Deterministic model Counterfactuals Discussion Chain Graph Some Properties of Chain Graphs Dawid's Approach to the Example "Demand and Price" My Observation 158 Outlines of Part IV 159 Part V. Comparison Chapter 15. Assumptions in Causal Inference Introduction The Review of Applied Notations Causality versus Exchangeability The Number of Assumptions to Discover Causal Relationships 164 Chapter 16. Common Lessons from Pearl and Rubin on Average Causal Effect Introduction Formalizing a Causal Quantity for Average Causal Effect Notations Necessary Conditions for Causal Inference Causal Quantity Other Causal Quantities Nonassignable Treatment The Causal Quantity in Rubin and Pearl's Notation A Comparison of Rubin and Pearl's Causal Notations 5.2 Representations of AM through Both Notations Some Points about Dawid's Work in Causality

9 6. Identification of the Causal Element in Observational Study Graphical method Propensity Score Causal Inference toward Individual Causal Effect Individual causal effect 179 Chapter 17. Causal Effect in Different Levels Introduction Definition and Measurement of Individual Causal Effect Rubin's Approach to Unit Level Causal Effect Pearl's Approach to Unit Level Causal Effect Discussion Relationship to the Potential Response Framework In Individual level In Population Level My Observations Causal Effect Measurement Average causal effect Considering more Knowledge rather than Identification of AM One Point about Dawid's Framework The more Covariates the More Accurate Individual Causal Effect 188 Chapter 18. Three Features of a Causal Framework Introduction Probability or Causality Considering AM Intervention Formalizing AM on the Whole Knowledge Potential Responses are not Observations Formalizing AM upon the Potential Responses Brings about Difficulties Confounder 193 Chapter 19. A Summary of Comparison

10 Introduction Association and Causation Causal Effect Definition Deterministically Inference based on Assumption Propensity Score and Graphical Methods Which Framework is more proper in Statistics? Can We Answer any Question in Potential Outcome Framework? Can We Interpret Coefficients in Structural Equations as Causal Parameters? The Main Difference between Pearl and Rubin Assessing Pearl and Rubin's Frameworks in Teaching and Reasoning Teaching Causal Questions Articulation a Causal Question Representation of the Assumptions Transparently Articulation an Example in the Two Frameworks 202 REFERENCE 206 Abbreviation