Goal: Causation (X  Y)

1. Goal: Causation (X  Y) • Problem: Association  Causation • Why? -- Mainly confounding • Solutions (Designs) • Experiments • Controlled Trials • Randomized Trials • Observational Studies • Quasi-Experiments - Fortuitous Randomization • Instrumental Variables • Statistical Control • Quasi-Experiments – Blocking • Interrupted Time Series

2. Statistical Evidence - Question 1: Is there an Association? rTV,Obsesity= 0 rTV,Obsesity≠ 0

3. rTV,Obsesity≠ 0 Causal Association Produced by: Spurious Association Statistical Evidence – Question 2: Is the Association Spurious?

4. The Problem of Confounding # IEDs BMI Hours of TV Contract $ Ethnic Alignment with Central Govt. Permissiveness of Parents ?? ?? TV Contract $ Obesity # IEDs C1 C2 Cn C1 C2 Cn

5. Randomized Trials eliminate Spurious Association Exposure (treatment) assigned randomly In an RT: association between exposure and outcome: strong evidence of causation:

6. Designs for Dealing With Confounding 1) Experiments - Randomized Trials ?? Randomizer Contract $ # IEDs C1 C2 Cn Ethnic Alignment

7. Designs for Dealing With Confounding 1) Experiments - Randomized Trials Ethnic Alignment ?? Randomizer Contract $ # IEDs C1 C2 Cn All confounders removed Often Ethically or Practically Impossible

8. Designs for Dealing With Confounding 2a) Observational Studies - Statistical Control ?? Contract $ # IEDs Ethnic Alignment C1 C2 Cn rContract$,#IEDs .EthnicAlignment, C1, C2,..,Cn All confounders must be measured

9. Statistical Adjustment (controlling for covariates) All confounders measured? rTV,Obestity.Permissiveness≠ 0 Confounders measured well? rTV,Obestity.PoorMeasure ≠ 0 Eliminating Spurious Association without Randomizing/Assigning/Controlling Exposure rTV,Obestity.Permissiveness = 0 rTV,Obestity.≠ 0

10. Designs for Dealing With Confounding 2b) Observational Studies - Instrumental Variables Ethnic Alignment with Central Govt. ?? Contracting Agent (Z) Contract $ # IEDs C1 C2 Cn • Idea: • Z is a partial natural randomizer • Needed Assumptions: • Z direct cause of Contract $ • Z independent of every confounder

11. Designs for Dealing With Confounding 2c) Observational Studies:Quasi-Experiments – Fortuitous Randomization Random Assignment of Instructor ?? Gender-matched Instructor Learning C1 C2 Cn

12. Designs for Dealing With Confounding 2c) Observational Studies:Quasi-Experiments – Fortuitous Randomization Random Assignment of Instructor ?? Gender-matched Instructor Learning C1 C2 Cn

13. Designs for Dealing With Confounding 2c) Quasi-Experiments - Blocking Identical Twins ?? TV Obesity Permissiveness of Parents C1 C2 Cn Subset Data to only Twins

14. Strategies for Dealing With Confounding 2c) Quasi-Experiments - Blocking Identical Twins Permissiveness of Parents ?? TV Obesity C1 C2 Cn Subset Data to only Twins TV,Obesity in Twin 1 vs. TV,Obesity in Twin 2

15. Establishing Causal Claims Does X  Y ?? • Strategy • Is X a prima facie cause of Y?a) is X prior to Yb) X _||_ Y ? Are X and Y associated, or correlated? • Is X a genuine cause of Y?Any confounder Z prior to X that screens off X and Y?i.e., X _||_ Y | Z ?

16. Establishing Causal Claims Does X  Y ?? • Strategy • Are X and Y associated, or correlated?Bivariate regression: Outcome (response) = Y Input (explanatory variable) = X • Any Z prior to X that screens off X and Y?Multiple regression: Outcome (response) = Y Input (explanatory variable) = X, Z

17. Establishing Causal Claims Does Income  Happiness?? • Strategy • Income and Happiness associated? Regression: Outcome = Happiness Inputs = Income • Income and Happiness still associated, conditional on potential confounders, e.g., Education?Regression: Outcome = Happiness Inputs = Income, Education

18. Establishing Causal Claims Does Income  Happiness??

19. Problems with Regression • Regression reliable if: • X prior to Y • No confounders • Parametric assumptions satisfied Statistical uncertainty ≠ scientific uncertainty Some regression assumptions are not directly testable e.g., do alternative models exist that fit the data and that explain constraints that hold in the data

20. Does Foreign Investment in 3rd World Countries cause Repression? Case Study Timberlake, M. and Williams, K. (1984). Dependence, political exclusion, and government repression: Some cross-national evidence. American Sociological Review 49, 141-146. N = 72 PO degree of political exclusivity CV lack of civil liberties EN energy consumption per capita (economic development) FI level of foreign investment

21. Data File : tw.txt /covariance 72 po fi en cv 1.0 -.175 1.0 -.480 0.330 1.0 0.868 -.391 -.430 1.0

22. Regression Results po = .227*fi - .176*en + .880*cv SE (.058) (.059) (.060) t 3.941 -2.99 14.6 Interpretation: increases in foreign investment cause increases in political exclusion

23. Regression Example

24. X _||_ Y but X  Y X _||_ Y , X  Y but estimate of b is biased Causal Inference and Confounders Question: X  Y ?

25. Controlling for Confounders Question: X  Y ? • Usual Observational Strategy: • Measure potential confounders Z = {Z1, Z2, …Zk} • Regress outcome Y on inputs X and “covariates” Z • Coefficient estimate for input X: • Association of X,Y after controlling/adjusting for Z ~ rX,Y.Z

26. Designs for Dealing With Confounding 2a) Observational Studies - Statistical Control ?? Contract $ # IEDs Ethnic Alignment C1 C2 Cn rContract$,#IEDs . EthnicAlignment, C1, C2,..,Cn

27. Designs for Dealing With Confounding ?? Contract $ # IEDs All confounders must be measured Ethnic Alignment C1 C2 Cn rContract$,#IEDs. EthnicAlignment ≠ rContract$,#IEDs. EthnicAlignment,C1, C2, C3

28. Estimating the Total Effect and the Direct Effect Confounder (C) a2 a1 b Y X a4 a3 Mediator (M) • + a1*a2 + a3*a4 Total Association betweenX and Y = Regress Y on X (rX,Y)) • + a3*a4 Total Effect ofX on Y = Regress Y on X and C (rX,Y.C)) Direct Effect ofX on Y = Regress Y on X and C and M (rX,Y.C,M))

29. Experimental vs. Statistical Control Confounder (C) a2 a1 b Y X a4 a3 Mediator (M) Direct Effect ofX on Y = √ Regress Y on X and C and M (rX,Y.C,M)) Statistical Control : √ Regress Y on randomized X and clamped M Experimental Control :

30. Experimental vs. Statistical Control b Y X a4 a3 Mediator (M) a2 a1 Direct Effect ofX on Y = Confounder (C) X Regress Y on X and M (rX,Y.M)) Statistical Control : √ Experimental Control : Regress Y on randomized X and clamped M

31. Experimental vs. Statistical Control b Y X a4 a3 Mediator (M) a2 a1 Confounder (C) • + a3*a4 Total Association betweenX and Y = Regress Y on X (rX,Y)) Direct Effect ofX on Y = Regress Y on X and C and M(rX,Y.C,M))

32. Statistical Control Question: X  Y ? • To be reliable for assessing the total effect of X on Y: • All confounders (common causes of X and Y) must be measured and statistically controlled for • Confounders must be measured well • No mediators should be measured and statistically controlled for • To be reliable for assessing the direct effect of X on Y: • All confounders (common causes of X and Y) must be measured and statistically controlled for • Confounders must be measured well • All mediators should be measured and statistically controlled for • All confounders of the mediators and Y should be measured and statistically controlled for