# Judea Pearlprofessor of Computer Science and Statistics and

• Slides: 103

Statistical Relations vs. Causal Relations • Statistical dependence may reflect ▫ Random fluctuation (c. i. & p-value) ▫ X caused Y ▫ Y caused X (temporal order; longitudinal data) ▫ X and Y share a common cause (covariate adjustment) ▫ Association between X and is induced by conditioning on a common effect of X and Y (selection bias; collider bias) 資料庫研究與統計方法學 1 06. 09. 06

Pearl’s Back-door Criterion • If one or more back-door paths connects the causal variable to the outcome variable, Pearl shows that the causal effect is identified by conditioning on a set of variables Z if and only if all back-door paths between the causal variable and the outcome variable are blocked after conditioning on Z. 資料庫研究與統計方法學 1 06. 09. 06

Pearl’s Back-door Criterion • A back-door path of D and Y is blocked by Z if and only if the back-door path satisfies any one of the following: ▫ contains a chain of mediation A → Z → B, or ▫ contains a fork of mutual dependence A ← Z → B; ▫ contains an inverted fork of mutual causation A → C* ← B, where C* and all its descendants are not in Z. 資料庫研究與統計方法學 1 06. 09. 06

Example of controlling a collider 資料庫研究與統計方法學 1 06. 09. 06

Example of controlling a collider 資料庫研究與統計方法學 1 06. 09. 06

Example of controlling a collider 資料庫研究與統計方法學 1 06. 09. 06

The Counterfactual Framework • 反事實因果推論的想像 Potential Outcomes Group Treatment group (D = 1) Control group (D = 0) 資料庫研究與統計方法學 Y 1 Y 0 Observable Counterfactual Observable 1 06. 09. 06

The Counterfactual Framework Q：什麼是unreasonable 的 counterfactuals 呢 ？ ▫ 有什麼狀態不適合看成為 causes 的嗎 ？ ▫ 有什麼樣的結果不適合想像 counterfactual情況的嗎？ 資料庫研究與統計方法學 1 06. 09. 06

The Counterfactual Framework • SUTVA：The Stable Unit Treatment Value Assumption – a priori assumption that the value of Y for unit u when exposed to treatment t will be the same no matter what mechanism is used to assign treatment t to unit u and no matter what treatments the other units receive. 資料庫研究與統計方法學 1 06. 09. 06

The Counterfactual Framework • 當使用調查方法得到資料時，即observational data，個人為何會接受或不接受treatment， 往往不是一個隨機的現象。 • Observational data通常有兩個問題： ▫ 接受treatment者與不接受者有baseline differences，以及heterogeneity of treatment effect. ▫ 可能有些影響接受treatment與否的變項，並未 觀察到，亦即omitted variables的問題。 資料庫研究與統計方法學 1 06. 09. 06

The Counterfactual Framework Potential Outcomes Group Treatment group (D = 1) Control group (D = 0) 資料庫研究與統計方法學 Y 1 Y 0 Observable E[Y 1 | D = 1] Counterfactual Observable E[Y 1 | D = 0] E[Y 0 | D = 1] 1 06. 09. 06

The Counterfactual Framework 如果我們只以觀察到接受 treatment 的組與觀察到未接 受 treatment 的組之間的差異做為 Causal Effect 的估計 時，此估計是一種 Naïve Estimate： Naïve Estimate = average causal effect + baseline bias + differential effect bias 資料庫研究與統計方法學 E[Y 1 |D = 1] – E[Y 0|D = 0] = E(δ) + {E(Y 0|D=1) − E(Y 0|D=0)} +{E(δ |D=1) − E(δ |D=0)} (1−π) 1 06. 09. 06

The Counterfactual Framework: A Review 反事實分析架構的五個關鍵概念： • Potential/Hypothetical States & Outcomes: ▫ 因果效應（causal effect）是利用 “potential” 或 “hypothetical”的概念，而不是只用到 actual observations。. • The ceteris paribus condition ▫ 其他條件相同的條件下，也就是將其他因素控制成 等同（equal）、固定不變（fixed）或是constant。 資料庫研究與統計方法學 1 06. 09. 06

The Counterfactual Framework: A Review • Heterogeneity: ▫ 個人對於treatment的反應是因人而異的。亦即因果效應在 個人層次即被認定是有差異的。每個人的因果效應是： [potential outcome under the potential treatment state] ─ [potential outcome under the potential control state] • Fundamental Problem of Causal Inference: ▫ 由於 the counterfactual definition of causal effect 意涵著 評估個人層次的因果效應會有 missing data 的問題。但是 如果我們願意做一些假定的話，我們可以評估幾種 Average Causal Effects。 資料庫研究與統計方法學 1 06. 09. 06

The Counterfactual Framework: A Review • Basic Parameters of Interest: ▫ ATT: Average Treatment effect on the Treated ▫ ATU: Average Treatment effect on the Untreated ▫ ATE: Average Treatment Effect ▫ the most basic one is ATT, and there are other meaningful causal parameters of interest than these three. 資料庫研究與統計方法學 1 06. 09. 06

Propensity Score Matching（PSM） • 實際從事PSM的運算方法有四大類： ▫ ▫ Exact Matching Nearest Neighbor Matching Interval Matching Kernel Matching • 不同運算方法的差異： With or without replacement How many units to match 資料庫研究與統計方法學 1 06. 09. 06

Propensity Score Matching（PSM） • 實際可從事PSM的程式： ▫ Stata: psmatch 2 等 ▫ SPSS: SPSS Macro for Propensity Score Matching (http: //ssw. unc. edu/VRC/Lectures/index. htm) ▫ SAS: “GREEDY” Macro (http: //www 2. sas. com/proceedings/sugi 26/proceed. p df) ▫ R: “Match. It” (http: //gking. harvard. edu/matchit/) 資料庫研究與統計方法學 1 06. 09. 06