Goal: Causation (X  Y)
Problem: Association  Causation
Why? -- Mainly confounding
Solutions (Designs)
o Experiments
 Controlled Trials
 Randomized Trials
o Observational Studies
 Quasi-Experiments - Fortuitous Randomization
 Instrumental Variables
 Statistical Control
 Quasi-Experiments – Blocking
 Interrupted Time Series
1
Statistical Evidence - Question 1: Is there an Association?
rTV,Obsesity = 0
rTV,Obsesity ≠ 0
2
Statistical Evidence – Question 2: Is the Association Spurious?
rTV,Obsesity ≠ 0
Causal
Association
TV
Obesity
TV
Obesity
Permissiveness
of Parents
Produced by:
TV
Obesity
Spurious
Association
3
The Problem of Confounding
# IEDs
BMI
Hours of TV
Contract $
Permissiveness
of Parents
Ethnic Alignment with
Central Govt.
??
TV
C1
??
Obesity
C2
Cn
Contract $
C1
# IEDs
C2
Cn
4
Randomized Trials eliminate Spurious Association
Exposure (treatment) assigned randomly
In an RT: association between exposure and outcome:
strong evidence of causation:
Randomizer
TV
Obesity
Randomizer
TV
Randomizer
TV
Permissiveness
Obesity
Obesity
5
Designs for Dealing With Confounding
1) Experiments - Randomized Trials
Ethnic
Alignment
??
Randomizer
Contract
$
C1
# IEDs
C2
Cn
6
Designs for Dealing With Confounding
1) Experiments - Randomized Trials
Ethnic
Alignment
??
Randomizer
Contract
$
C1
# IEDs
C2
Cn
All confounders removed
Often Ethically or Practically Impossible
7
Designs for Dealing With Confounding
2a) Observational Studies - Statistical Control
Ethnic
Alignment
??
Contract $
C1
# IEDs
C2
Cn
rContract$,#IEDs.EthnicAlignment, C1, C2,..,Cn
All confounders must be measured
8
Eliminating Spurious Association without
Randomizing/Assigning/Controlling Exposure
Permissiveness
of Parents
Statistical Adjustment
(controlling for covariates)
Obesity
TV
rTV,Obestity.≠ 0
rTV,Obestity.Permissiveness = 0
Permissiveness
of Parents
All confounders measured?
TV
Physical
Activity
Obesity
rTV,Obestity.Permissiveness ≠ 0
Permissiveness
of Parents
Confounders measured well?
TV
Poor Measure
of
Permissiveness
Obesity
rTV,Obestity.PoorMeasure ≠ 0
9
Designs for Dealing With Confounding
2b) Observational Studies - Instrumental Variables
Ethnic Alignment with
Central Govt.
Contracting Agent
(Z)
??
Contract $
C1
# IEDs
C2
Cn
Idea:
• Z is a partial natural randomizer
Needed Assumptions:
• Z direct cause of Contract $
• Z independent of every confounder
10
Designs for Dealing With Confounding
2c) Observational Studies:
Quasi-Experiments – Fortuitous Randomization
Random
Assignment of
Instructor
??
Gender-matched
Instructor
C1
Learning
C2
Cn
11
Designs for Dealing With Confounding
2c) Observational Studies:
Quasi-Experiments – Fortuitous Randomization
Random
Assignment of
Instructor
??
Gender-matched
Instructor
C1
Learning
C2
Cn
12
Designs for Dealing With Confounding
2c) Quasi-Experiments - Blocking
Identical
Twins
Permissiveness
of Parents
??
TV
C1
Obesity
C2
Cn
Subset Data to only Twins
13
Strategies for Dealing With Confounding
2c) Quasi-Experiments - Blocking
Identical
Twins
Permissiveness
of Parents
??
TV
C1
Obesity
C2
Cn
Subset Data to only Twins
TV,Obesity in Twin 1 vs. TV,Obesity in Twin 2
14
Establishing Causal Claims
Does X  Y ??
Strategy
1) Is X a prima facie cause of Y?
a) is X prior to Y
b) X _||_ Y ? Are X and Y associated, or correlated?
2) Is X a genuine cause of Y?
Any confounder Z prior to X that screens off X and Y?
i.e., X _||_ Y | Z ?
15
Establishing Causal Claims
Does X  Y ??
Strategy
1) Are X and Y associated, or correlated?
Bivariate regression:
Outcome (response) =
Y
Input (explanatory variable) =
X
2) Any Z prior to X that screens off X and Y?
Multiple regression:
Outcome (response) =
Y
Input (explanatory variable) =
X, Z
16
Establishing Causal Claims
Does Income  Happiness??
Strategy
1) Income and Happiness associated?
Regression:
Outcome =
Happiness
Inputs =
Income
2) Income and Happiness still associated,
conditional on potential confounders, e.g.,
Education?
Regression:
Outcome =
Inputs =
True Model
Ed
Inc
Happy
Happiness
Income, Education
17
Establishing Causal Claims
Does Income  Happiness??
True Model
Regression
Estimated Model
Ed
Inc
Inc
Ed
ed
Happy
inc
Happy
inc = 0
(in population)
18
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
19
Case Study
Does Foreign Investment in 3rd World Countries
cause Repression?
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
20
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
21
Regression Results
po =
.227*fi
SE
t
(.058)
3.941
- .176*en + .880*cv
(.059)
-2.99
(.060)
14.6
Interpretation: increases in foreign
investment cause increases in political
exclusion
22
Regression Example
En
FI
CV
En
FI
.217
.88
-.176
PO
Regression
PO
Tetrad
CV
Causal Inference and Confounders
Question: X  Y ?
True Model
True Model
C
C
X
X

Y
Y
X _||_ Y but X  Y
X _||_ Y , X  Y
but estimate of 
is biased
24
Controlling for Confounders
Question: X  Y ?
Usual Observational Strategy:
1. Measure potential confounders Z = {Z1, Z2, …Zk}
2. Regress outcome Y on inputs X and “covariates” Z
Coefficient estimate for input X:
1. Association of X,Y after controlling/adjusting for Z
~rX,Y.Z
25
Designs for Dealing With Confounding
2a) Observational Studies - Statistical Control
Ethnic
Alignment
??
Contract $
C1
# IEDs
C2
Cn
rContract$,#IEDs. EthnicAlignment, C1, C2,..,Cn
26
Designs for Dealing With Confounding
Ethnic
Alignment
??
Contract $
C1
# IEDs
C2
Cn
All confounders must be measured
rContract$,#IEDs. EthnicAlignment
≠
rContract$,#IEDs. EthnicAlignment,C1, C2, C3
27
Estimating the Total Effect and the Direct Effect
Confounder (C)
a2
a1

X
Y
a4
a3
Mediator (M)
Total Association between X and Y = +
a1*a2 + a3*a4
Regress Y on X (rX,Y))
Total Effect of X on Y =
+ a3*a4
Regress Y on X and C (rX,Y.C))
Direct Effect of X on Y = 
Regress Y on X and C and M (rX,Y.C,M))
Experimental vs. Statistical Control
Confounder (C)
a2
a1

X
Y
a4
a3
Mediator (M)
Direct Effect of X on Y = 
Statistical Control :
Regress Y on X and C and M (rX,Y.C,M))
√
Experimental Control : Regress Y on randomized X and clamped M
√
Experimental vs. Statistical Control

X
Y
a4
a3
Mediator (M)
a2
a1
Direct Effect of X on Y = 
Statistical Control :
Confounder (C)
Regress Y on X and M (rX,Y.M))
X
Experimental Control : Regress Y on randomized X and clamped M
√
Experimental vs. Statistical Control

X
Y
a4
a3
Mediator (M)
a2
a1
Confounder (C)
Total Association between X and Y = +
a3*a4
Regress Y on X (rX,Y))
Direct Effect of X on Y = 
Regress Y on X and C and M(rX,Y.C,M))
Statistical Control
Question: X  Y ?
To be reliable for assessing the total effect of X on Y:
1. All confounders (common causes of X and Y) must be
measured and statistically controlled for
2. Confounders must be measured well
3. No mediators should be measured and statistically controlled for
To be reliable for assessing the direct effect of X on Y:
1. All confounders (common causes of X and Y) must be
measured and statistically controlled for
2. Confounders must be measured well
3. All mediators should be measured and statistically controlled for
4. All confounders of the mediators and Y should be measured and
statistically controlled for
32