1 Searching for Causal Models Richard Scheines Philosophy, Machine Learning, Human-Computer Interaction Carnegie Mellon University

1

Searching for Causal Models

Richard Scheines

Philosophy, Machine Learning,

Human-Computer Interaction

Carnegie Mellon University

2

Goals

1. Basic Familiarity with Causal Model Search:

o What it is

o What it can and cannot do

2. Basic Familiarity with Tetrad IV

o What it is

o What it can and cannot do

3

Outline

1. Motivation

2. Representing Causal Systems

3. Strategies for Causal Inference

4. Causal Model Search

5. Examples

6. Causal Model Search with Latent Variables

1. Motivation

• Conditioning ≠ Intervening : P(Y | X = x ) ≠ P(Y | X set= x)

• When and how can we use non-experimental data to tell us

about the effect of a future intervention?

Motivation

Rumsfeld Problem: Do we know what we don’t know:

Can we tell when there is not enough information

in the data + background knowledge to

infer causation?

Motivation: Example

Online Course:

• As good or better than lecture?

• What student behaviors cause learning?

Full Semester Online Course in Causal & Statistical Reasoning

Full Semester Online Course in Causal & Statistical Reasoning

Course is tooled to record certain events: Logins, page requests, print requests, quiz attempts, quiz

scores, voluntary exercises attempted, etc.

Each event was associated with attributes: Time student-id Session-id

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Experiments

• 2000 : Online vs. Lecture, UCSD

• Winter (N = 180)

• Spring (N = 120)

• 2001: Online vs. Lecture, Pitt & UCSD

• UCSD - winter (N = 190)

• Pitt (N = 80)

• UCSD - spring (N = 110)

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Online vs. Lecture Delivery

• Online:• No lecture / one recitation per week• Required to finish approximately 2 online modules / week

• Lecture:• 2 Lectures / one recitation per week• Printed out modules as reading – extra assignments

• Same Material, same Exams:• 2 Paper and Pencil Midterms• 1 Paper and Pencil Final Exam

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Pitt 2001 - Variables

Pre-test (%)

Midterm1 (%)

Midterm 2 (%)

Final Exam (%)

Recitation attendance (%)

Lecture attendance (%)

Gender

Online (1 = online, 0 = lecture)

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Online vs. Lecture - Pitt

• Online students did 1/2 a St.Dev better than lecture students (p = .059)

• Factors affecting performance: Practice Questions Attempted

• Cost: Online condition costs 1/3 less per student

Final Exam (%)

Recitation Attendance (%)

Online

.22

5.3

.23

-10

Pre-test (%)

df = 2c2 = 0.08p-value = .96

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Printing and Voluntary Comprehension Checks: 2002 --> 2003

.302

-.41

.75

.353

.323

pre

print voluntary questions

quiz

final

2002

-.08

-.16

.41

.25

pre

print voluntary questions

final

2003

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2. Representing Causal Systems

1. Causal structure - qualitatively

2. Interventions

3. Statistical Causal Models

1. Causal Bayes Networks

2. Structural Equation Models

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Causal Graphs

Causal Graph G = {V,E}

Each edge X Y represents a direct causal claim:

X is a direct cause of Y relative to V

Exposure Rash

Exposure Infection Rash

Chicken Pox

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Causal Graphs

Do Not need to be

Cause Complete

Do need to be Common Cause Complete

Exposure Infection Symptoms

Exposure Infection Symptoms

Omitted

Common Causes

Omitted Causes 2Omitted Causes 1

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Sweaters On

Room Temperature

Pre-experimental SystemPost

Modeling Ideal Interventions

Interventions on the Effect

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Modeling Ideal Interventions

SweatersOn

Room Temperature

Pre-experimental SystemPost

Interventions on the Cause

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Interventions & Causal GraphsModel an ideal intervention by adding an “intervention” variable

outside the original system as a direct cause of its target.

Education Income Taxes Pre-intervention graph

Intervene on Income

“Soft” Intervention

Education Income Taxes

I

“Hard” Intervention

Education Income Taxes

I

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Causal Bayes Networks

P(S = 0) = .7

P(S = 1) = .3

P(YF = 0 | S = 0) = .99 P(LC = 0 | S = 0) = .95

P(YF = 1 | S = 0) = .01 P(LC = 1 | S = 0) = .05

P(YF = 0 | S = 1) = .20 P(LC = 0 | S = 1) = .80

P(YF = 1 | S = 1) = .80 P(LC = 1 | S = 1) = .20

Smoking [0,1]

Lung Cancer[0,1]

Yellow Fingers[0,1]

P(S,YF, L) = P(S) P(YF | S) P(LC | S)

The Joint Distribution Factors

According to the Causal Graph,

i.e., for all X in V

P(V) = P(X|Immediate Causes of(X))

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Tetrad Demo

http://www.phil.cmu.edu/projects/tetrad_download/


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Structural Equation Models

1. Structural Equations

2. Statistical Constraints

Education

LongevityIncome

Statistical Model

Causal Graph

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Structural Equations: One Equation for each variable V in the graph:

V = f(parents(V), errorV)for SEM (linear regression) f is a linear function

Statistical Constraints: Joint Distribution over the Error terms

Education

LongevityIncome

Causal Graph

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Equations:

Education = ed

Income =Educationincome

Longevity =EducationLongevity

Statistical Constraints:

(ed, Income,Income ) ~N(0,2)

2diagonal

- no variance is zero

Education

LongevityIncome

Causal Graph

Education

Income Longevity

1 2

LongevityIncome

SEM Graph

(path diagram)

Calculating the Effect of Interventions

Pre-manipulation Joint Distribution (YF,S,L)

Intervention, Causal Graph

Post-manipulation Joint Distribution (YF,S,L)

Calculating the Effect of Interventions

Smoking [0,1]

Lung Cancer[0,1]

Yellow Fingers[0,1]

P(YF,S,L) = P(S) P(YF|S) P(L|S)

P(YF,S,L)m = P(S) P(YF|Manip) P(L|S)

Smoking [0,1]

Lung Cancer[0,1]

Yellow Fingers[0,1]

Manipulation

Replace pre-manipulation causes

with manipulation

Structural Equations:

Education = ed

Longevity =f1(Education)Longevity

Income = f2(Education)income

Education

LongevityIncome

Modularity of Intervention/Manipulation

Causal

Graph

Manipulated Structural Equations:

Education = ed


Income = f3(M1)

Manipulated

Causal

Graph

Education

Longevity Income

M1

Structural Equations:

Education = ed


Income = f2(Education)income

Education

LongevityIncome

Modularity of Intervention/Manipulation

Causal

Graph

Manipulated Structural Equations:

Education = ed


Income = f3(M2,Education) income

Manipulated

Causal

Graph

Education

Longevity Income

M2

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3. Strategies for Causal Inference

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

o Causal Model Search

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Statistical Evidence - Question 1: Is there an Association?

rTV,Obsesity ≠ 0

rTV,Obsesity = 0

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Statistical Evidence – Question 2: Is the Association Spurious?

rTV,Obsesity ≠ 0

Permissiveness of Parents

TV Obesity

Produced by:

TV Obesity

TV Obesity

Spurious Association

Causal Association

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The Problem of Confounding

TV Obesity


C1 C2 Cn

??Contract $ # IEDs

Ethnic Alignment with Central Govt.

C1 C2 Cn

??

Hours of TV

BMI

Contract $

# IEDs

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Randomized Trials eliminate Spurious Association

Exposure (treatment) assigned randomly

In an RT: association between exposure and outcome: strong evidence of causation:

TV Obesity Randomizer

TV Obesity Randomizer

Permissiveness

TV Obesity

Randomizer

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Designs for Dealing With Confounding

Contract $

# IEDs

Ethnic Alignment

C1 C2 Cn

??Randomizer

1) Experiments - Randomized Trials

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Contract $

# IEDs

Ethnic Alignment

C1 C2 Cn

??Randomizer

1) Experiments - Randomized Trials

All confounders removed

Often Ethically or Practically Impossible

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Contract $ # IEDs

Ethnic Alignment

C1 C2 Cn

??

2a) Observational Studies - Statistical Control

rContract$,#IEDs

All confounders must be measured

.EthnicAlignment, C1, C2,..,Cn

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Eliminating Spurious Association without Randomizing/Assigning/Controlling Exposure

All confounders measured?

Permissiveness

of Parents

TV Obesity

Physical Activity

rTV,Obestity.Permissiveness ≠ 0

Confounders measured well?

Permissiveness

of Parents

TV Obesity

Poor Measure of

Permissiveness

rTV,Obestity.PoorMeasure ≠ 0

Statistical Adjustment

(controlling for covariates)


TV Obesity

rTV,Obestity.Permissiveness = 0rTV,Obestity.≠ 0

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2b) Observational Studies - Instrumental Variables

Contracting Agent(Z)

Needed Assumptions:• Z direct cause of Contract $• Z independent of every confounder

Contract $ # IEDs

Ethnic Alignment with Central Govt.

C1 C2 Cn

??

Idea:• Z is a partial natural randomizer

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Gender-matchedInstructor Learning

C1 C2 Cn

??

2c) Observational Studies:Quasi-Experiments – Fortuitous Randomization

RandomAssignment of

Instructor

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Gender-matchedInstructor Learning

C1 C2 Cn

??

2c) Observational Studies:Quasi-Experiments – Fortuitous Randomization

RandomAssignment of

Instructor

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TV Obesity


C1 C2 Cn

??

2c) Quasi-Experiments - Blocking

Identical Twins

Subset Data to only Twins

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Strategies for Dealing With Confounding

TV Obesity


C1 C2 Cn

??

2c) Quasi-Experiments - Blocking

Identical Twins

TV,Obesity in Twin 1 vs. TV,Obesity in Twin 2

Subset Data to only Twins

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Regression & Causal Inference

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2. So, identifiy and measure potential confounders Z:

a) prior to X,

b) associated with X,

c) associated with Y

Typical (non-experimental) strategy:1. Establish a prima facie case (X associated with Y)

3. Statistically adjust for Z (multiple regression)

X Y

Z

But, omitted variable bias

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Strategy threatened by measurement error – ignore this for now

Multiple regression is provably unreliable

for causal inference unless:• X prior to Y • X, Z, and Y are causally sufficient (no confounding)

Examples

X

Y

Z

X

Y

Z2 Z1

T1

T2

X

Y

Z

T2

T1

Truth Regression Alternative?

bX = 0

bZ ≠ 0

bX ≠ 0

bZ ≠ 0

bX ≠ 0

bZ1 ≠ 0

bZ2 ≠ 0

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Better Methods Exist

Causal Model Search (since 1988):

• Provably Reliable

• Provably Rumsfeld

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4. Causal Model Search

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Causal Discovery

Statistical Data Causal Structure

Background Knowledge

- X2 before X3

- no unmeasured common causes

X3 | X2 X1

Independence Relations

Data

Statistical Inference

X2 X3 X1

Equivalence Class of Causal Graphs

X2 X3 X1

X2 X3 X1

Discovery Algorithm

Causal Markov Axiom (D-separation)

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Faithfulness

Constraints on a probability distribution P generated by a causal structure G hold for all parameterizations of G.

Revenues = aRate + cEconomy + eRev.

Economy = bRate + eEcon.

Faithfulness: a ≠ -bcTax Revenues

Economyc

ba

Tax Rate

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The Problem of Alternatives:Observationally Equivalent Models

Given an Experimental Setup, and Background Knowledge, and Theory, and a set of independence relations, what are all the models that would entail those independence relations that are consistent with BK and Theory?

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Equivalence Classes

• Independence (d-separation equivalence)• DAGs : Patterns• PAGs : Latent variable models• Intervention Equivalence Classes

• Measurement Model Equivalence Classes• Linear Non-Gaussian Model Equivalence Classes

Equivalence:• Independence (M1 ╞ X _||_ Y | Z M2 ╞ X _||_ Y | Z)

• Distribution (q1 q2 M1(q1) = M2(q2))

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Representations ofIndependence Equivalence Classes

We want the representations to:

• Characterize the Independence Relations Entailed by the Equivalence Class

• Represent causal features that are shared by every member of the equivalence class

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Patterns & PAGs

• Patterns (Verma and Pearl, 1990): graphical representation of Markov equivalence - with no latent variables.

• PAGs: (Richardson 1994) graphical representation of an equivalence class including latent variable models and sample selection bias that are Markov equivalent over a set of measured variables X

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Patterns

X2 X1

X2 X1

X2 X1

X4 X3

X2 X1

Possible Edges Example

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Patterns

X2

X4 X3

X1

X2

X4 X3

Represents

Pattern

X1 X2

X4 X3

X1

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PAGs: Partial Ancestral Graphs

X2

X3

X1

X2

X3

Represents

PAG

X1 X2

X3

X1

X2

X3

T1

X1

X2

X3

X1

etc.

T1

T1 T2

Regression vs. PAGs

X

Y

Z

X

Y

Z2 Z1

T1

T2

X

Y

Z

T2

T1

X

Y

Z2 Z1

Truth Regression PAG

X

Y

Z1

X

Y

Z1bX = 0

bZ ≠ 0

bX ≠ 0

bZ ≠ 0

bX ≠ 0

bZ1 ≠ 0

bZ2 ≠ 0

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Causal Model Search

Background Knowledge

Data

Patterns

X2 X3 X1

PC, GES,

CPC

PAGs

X2 X3 X1

FCI, CFCI

DAGs

X2 X3 X1

Impossible

61

Overview of Search Methods

Constraint Based Searches• TETRAD (SGS, PC, FCI)• Very fast – capable of handling 1,000 variables• Pointwise, but not uniformly consistent

Scoring Searches• Scores: BIC, AIC, etc.• Search: Hill Climb, Genetic Alg., Simulated Annealing• Difficult to extend to latent variable models• Meek and Chickering Greedy Equivalence Class (GES)• Very slow – max N ~ 30-40• Pointwise, but not uniformly consistent

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5. Examples

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Case Study 1: Foreign Investment

Does Foreign Investment in 3rd World Countries cause Political 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

64

Correlations

po fi en fi -.175 en -.480 0.330 cv 0.868 -.391 -.430


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Regression Results

po = .227*fi - .176*en + .880*cv

SE (.058) (.059) (.060)

t 3.941 -2.99 14.6

Interpretation: foreign investment increases political repression


Alternatives

.217

FI

PO

CV En

Regression

.88 -.176

FI

PO

CV En

Tetrad - FCI

FI

PO

CV En

Fit: df=2, 2=0.12, p-value = .94

.31 -.23

.86 -.48


There is no model with testable constraints (df > 0) in which FI has a positive effect on PO that is not rejected by the data.

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Variables

Tangibility/Concreteness (Exp manipulation)

Imaginability (likert 1-7)

Impact (avg. of 2 likerts)

Sympathy (likert)

Donation ($)

Case Study 2: Charitable Giving

Cryder & Loewenstein (in prep)

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Theoretical Model


Imaginability Tangibility

Impact

Sympathy

Donation

study 1 (N= 94) df = 5, c2 = 52.0, p= 0.0000

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GES Outputs



Impact

Sympathy

Donation

study 1: df = 5, c2 = 5.88, p= 0.32


Impact

Sympathy

Donation

study 1: df = 5, c2 = 3.99, p= 0.55

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Theoretical Model



Impact

Sympathy

Donation

study 2 (N= 115) df = 5, c2 = 62.6, p= 0.0000


Impact

Sympathy

Donation


Impact

Sympathy

Donation

study 2: df = 5, c2 = 8.23, p= 0.14

study 2: df = 5, c2 = 7.48, p= 0.18

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GES Outputs



Impact

Sympathy

Donation

study 1: df = 5, c2 = 5.88, p= 0.32


Impact

Sympathy

Donation

study 2: df = 5, c2 = 8.23, p= 0.14

study 1: df = 5, c2 = 3.99, p= 0.55

study 2: df = 5, c2 = 7.48, p= 0.18

Lead and IQ: Variable Selection

BackwardsStepwise Regression

Measured Lead +5 Covariates

Measured Lead +39 Covariates

Final Variables (Needleman)

-lead baby teeth-fab father’s age-mab mother’s age-nlb number of live

births-med mother’s

education-piq parent’s IQ-ciq child’s IQ

Needleman Regression

- standardized coefficient

- (t-ratios in parentheses)

- p-value for significance

ciq = - .143 lead - .204 fab - .159 nlb + .219 med + .237 mab + .247 piq

(2.32) (1.79) (2.30) (3.08) (1.97) (3.87)

0.02 0.09 0.02 <0.01 0.05 <0.01

All variables significant at .1 R2 = .271

TETRAD Variable Selection

Tetradmab _||_ ciq

fab _||_ ciq

nlb _||_ ciq | med

ciq

mab fab nlb

lead piq med

Regressionmab _||_ ciq | { lead, med, piq, nlb fab} fab _||_ ciq | { lead, med, piq, nlb mab}

nlb _||_ ciq | { lead, med, piq, mab, fab}

Regressions

- standardized coefficient

- (t-ratios in parentheses)

- p-value for significance

Needleman (R2 = .271)

ciq = - .143 lead - .204 fab - .159 nlb + .219 med + .237 mab + .247 piq

(2.32) (1.79) (2.30) (3.08) (1.97) (3.87)

0.02 0.09 0.02 <0.01 0.05 <0.01

TETRAD (R2 = .243)

ciq = - .177 lead + .251 med + .253 piq

(2.89) (3.50) (3.59)

<0.01 <0.01 <0.01

Measurement Error Measured regressor variables are proxies that involve

measurement error Errors-in-all-variables model for Lead’s influence on IQ

- underidentified

Actual LeadExposure

EnvironmentalStimulation

ciq

lead 3

2

111

1

ciq

lead

med

med

piq

piq

Geneticfactors

Strategies:

• Sensitivity Analysis

• Bayesian Analysis

Prior over Measurement Error

Proportion of Variance from Measurement Error

Measured Lead Mean = .2, SD = .1 Parent’s IQ Mean = .3, SD = .15 Mother’s Education Mean = .3, SD = .15

Prior Otherwise uninformative

Actual LeadExposure

EnvironmentalStimulation

ciq

lead 3

2

111

1

ciq

lead

med

med

piq

piq

Geneticfactors

Posterior

Expected if Normal

0

50

100

150

200

250

0

50

100

150

200

250

Expected if Normal

Frequency

LEAD->ciq

Distribution of LEAD->ciq

Zero

Robust over similar priors

Using Needleman’s CovariatesWith similar prior, the marginal posterior:

Expected if Normal

0

20

40

60

80

100

120

140

020

40

60

80

100

120

140

160Expected if Normal

Frequency

LEAD->ciq

Distribution of LEAD->ciq

Very Sensitive to Prior Over Regressors

TETRAD eliminated

Zero

80

6. Causal Model Search with Latent Variables

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The Causal Theory Formation Problem for Latent Variable Models

Given observations on a number of variables, identify the latent variables that underlie these variables and the causal relations among these latent concepts.

Example: Spectral measurements of solar radiation intensities. Variables are intensities at each measured frequency.

Example: Quality of a Child’s Home Environment, Cumulative Exposure to Lead, Cognitive Functioning

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The Most Common Automatic Solution: Exploratory Factor Analysis

Chooses “factors” to account linearly for as much of the variance/covariance of the measured variables as possible.

Great for dimensionality reduction Factor rotations are arbitrary Gives no information about the statistical and thus the

causal dependencies among any real underlying factors.

No general theory of the reliability of the procedure

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Other Solutions

Independent Components, etcBackground TheoryScales

84

Other Solutions: Background Theory

St1

12

Home

St2

12

St21

12

.

.

T1

Lead

.

.

Cognitive Function

T2

T20

C1 C2 C20 . .

?

Key Causal Question

Thus, key statistical question: Lead _||_ Cog | Home ?

Specified Model

85

St1

12

Home

St2

12

St21

12

.

.

T1

Lead

.

.

Cognitive Function

T2

T20

C1 C2 C20 . .

F

Lead _||_ Cog | Home ?

Yes, but statistical inference will say otherwise.

Other Solutions: Background Theory

True Model

“Impurities”

86

F1

x1 x2

F2 F3

x3 x4 y1 y2 y3 y4 z1 z2 z3 z4

Purify

Specified Model

87

F1

x1 x2

F

F2 F3

x3 x4 y1 y2 y3 y4 z1 z2 z3 z4

Purify

True Model

88

F1

x1 x2

F

F2 F3

x3 x4 y1 y2 y3 y4 z1 z2 z3 z4

Purify

True Model

89

F1

x1 x2

F

F2 F3

x3 x4 y1 y2 y3 y4 z1 z2 z3 z4

Purify

True Model

90

F1

x1 x2

F

F2 F3

x3 x4 y1 y2 y3 y4 z1 z2 z3 z4

Purify

True Model

91

F1

x1 x2

F

F2 F3

x3 y1 y2 y3 y4 z1 z3 z4

Purify

Purified Model

92

Scale = sum(measures of a latent)

Other Solutions: Scales

St1

12

Home

St2

12

St21

12

.

.

Homescale = i=1 to 21 (Sti)

Homescale

93

True Model

Other Solutions: Scales

Pseudo-Random Sample: N = 2,000

94

Scales vs. Latent variable Models

Regression:Cognition on Home, Lead

Predictor Coef SE Coef T PConstant -0.02291 0.02224 -1.03 0.303Home 1.22565 0.02895 42.33 0.000Lead -0.00575 0.02230 -0.26 0.797 S = 0.9940 R-Sq = 61.1% R-Sq(adj) = 61.0%

Insig.

True Model

95


Scales

homescale = (x1 + x2 + x3)/3leadscale = (x4 + x5 + x6)/3cogscale = (x7 + x8 + x9)/3

True Model

96


Cognition = - 0.0295 + 0.714 homescale - 0.178 Lead Predictor Coef SE Coef T PConstant -0.02945 0.02516 -1.17 0.242homescal 0.71399 0.02299 31.05 0.000Lead -0.17811 0.02386 -7.46 0.000

Regression:Cognition on homescale,

Lead

Sig.

True Model

97


Modeling Latents

True Model

Specified Model

98


(c2 = 29.6, df = 24, p = .19)

B5 = .0075, which at t=.23, is correctly insignificant

True Model

Estimated Model

99


Mixing Latents and Scales

(c2 = 14.57, df = 12, p = .26)

B5 = -.137, which at t=5.2, is incorrectly highly significantP < .001

True Model

100

Build Pure Clusters

Output - provably reliable (pointwise consistent):

Equivalence class of measurement models over a pure subset of measures

L1 L2 L3

m1 m2 m3 m4 m5 m6 m7 m8 m9

Stress Dep Health

m1 m2 m3 m4 m5 m6 m7 m8 m9 m11 m10

m

BPC

True Model

Output

101

Build Pure ClustersQualitative Assumptions

1. Two types of nodes: measured (M) and latent (L)

2. M L (measured don’t cause latents)

3. Each m M measures (is a direct effect of) at least one l L

4. No cycles involving M

Quantitative Assumptions:

1. Each m M is a linear function of its parents plus noise

2. P(L) has second moments, positive variances, and no deterministic relations

102

Case Study 4: Stress, Depression, and Religion

MSW Students (N = 127) 61 - item survey (Likert Scale)

• Stress: St1 - St21

• Depression: D1 - D20

• Religious Coping: C1 - C20

p = 0.00

St1

12

Stress

St2

12

St21

12

.

.

Dep1

12

Coping

.

.

Depression

Dep2

12

Dep20

12

C1 C2 C20 . .

+

- +

Specified Model

103

Build Pure Clusters St3

12

Stress

St4

12 St16

12

Dep9

12

Coping

Depression Dep13

12 Dep19

12

C9 C12 C15

St18

12

St20

12

C14


104

Assume Stress temporally prior:

MIMbuild to find Latent Structure: St3

12

Stress

St4

12 St16

12

Dep9

12

Coping

Depression Dep13

12 Dep19

12

C9 C12 C15

St18

12

St20

12

C14

+

+

p = 0.28


105

Case Study 5: Test Anxiety

Bartholomew and Knott (1999), Latent variable models and factor analysis

12th Grade Males in British Columbia (N = 335)

20 - item survey (Likert Scale items): X1 - X20:

X2

Emotionality Worry

X8

X9

X10

X15

X16

X18

X3

X4

X5

X6

X7

X14

X17

X20

Exploratory Factor Analysis:

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Build Pure Clusters:

X2

Emotionalty

X8

X9

X10

X11

X16

X18

X3

X5

X7

X14

X6

Cares About Achieving

Self-Defeating


107

Build Pure Clusters:

X2

Emotionalty

X8

X9

X10

X11

X16

X18

X3

X5

X7

X14

X6

Worries About Achieving

Self-Defeating

X2

Emotionality Worry

X8

X9

X10

X15

X16

X18

X3

X4

X5

X6

X7

X14

X17

X20

p-value = 0.00 p-value = 0.47

Exploratory Factor Analysis:


108

X2

Emotionalty

X8

X9

X10

X11

X16

X18

X3

X5

X7

X14

X6

Worries About Achieving

Self-Defeating

MIMbuild

p = .43

Emotionalty-Scale

Worries About Achieving-Scale

Self-Defeating

Unininformative

Scales: No Independencies or Conditional

Independencies


109

Economics

Bessler, Pork Prices

Hoover, multiple

Other Cases

Educational Research

Easterday, Bias & Recall

Laski, Numerical coding

Climate Research

Glymour, Chu, , Teleconnections

Biology

Shipley,

SGS, Spartina Grass

Neuroscience

Glymour & Ramsey, fMRI

Epidemiology

Scheines, Lead & IQ

Software

Education:

- Causality Lab: www.phil.cmu.edu/projects/causality-lab

- Web Course on Causal and Statistical Reasoning, and Empirical Research Methods: http://www.cmu.edu/oli/

Research:

Tetrad: www.phil.cmu.edu/projects/tetrad_download/

http://www.phil.cmu.edu/projects/causality-lab

http://www.cmu.edu/oli/


References

Causation, Prediction, and Search, 2nd Edition, (2000), by P. Spirtes, C. Glymour, and R. Scheines ( MIT Press)

Causality: Models, Reasoning, and Inference (2000). By Judea Pearl, Cambridge Univ. Press

Computation, Causation, & Discovery (1999), edited by C. Glymour and G. Cooper, MIT Press

112

References

Biology

Chu, Tianjaio, Glymour C., Scheines, R., & Spirtes, P, (2002). A Statistical Problem for Inference to Regulatory Structure from Associations of Gene Expression Measurement with Microarrays. Bioinformatics, 19: 1147-1152.

Shipley, B. Exploring hypothesis space: examples from organismal biology. Computation, Causation and Discovery. C. Glymour and G. Cooper. Cambridge, MA, MIT Press.

Shipley, B. (1995). Structured interspecific determinants of specific leaf area in 34 species of

herbaceous angeosperms. Functional Ecology 9.

113

References

Scheines, R. (2000). Estimating Latent Causal Influences: TETRAD III Variable Selection and Bayesian Parameter Estimation: the effect of Lead on IQ, Handbook of Data Mining, Pat Hayes, editor, Oxford University Press.

Jackson, A., and Scheines, R., (2005). Single Mothers' Self-Efficacy, Parenting in the Home Environment, and Children's Development in a Two-Wave Study, Social Work Research , 29, 1, pp. 7-20.

Timberlake, M. and Williams, K. (1984). Dependence, political exclusion, and government repression: Some cross-national evidence. American Sociological Review 49, 141-146.

114

ReferencesEconomics

Akleman, Derya G., David A. Bessler, and Diana M. Burton. (1999). ‘Modeling corn exports and exchange rates with directed graphs and statistical loss functions’, in Clark Glymour and Gregory F. Cooper (eds) Computation, Causation, and Discovery, American Association for Artificial Intelligence, Menlo Park, CA and MIT Press, Cambridge, MA, pp. 497-520.

Awokuse, T. O. (2005) “Export-led Growth and the Japanese Economy: Evidence from VAR and Directed Acyclical Graphs,” Applied Economics Letters 12(14), 849-858.

Bessler, David A. and N. Loper. (2001) “Economic Development: Evidence from Directed Acyclical Graphs” Manchester School 69(4), 457-476.

Bessler, David A. and Seongpyo Lee. (2002). ‘Money and prices: U.S. data 1869-1914 (a study with directed graphs)’, Empirical Economics, Vol. 27, pp. 427-46.

Demiralp, Selva and Kevin D. Hoover. (2003) !Searching for the Causal Structure of a Vector Autoregression," Oxford Bulletin of Economics and Statistics 65(supplement), pp. 745-767.

Haigh, M.S., N.K. Nomikos, and D.A. Bessler (2004) “Integration and Causality in International Freight Markets: Modeling with Error Correction and Directed Acyclical Graphs,” Southern Economic Journal 71(1), 145-162.

Sheffrin, Steven M. and Robert K. Triest. (1998). ‘A new approach to causality and economic growth’, unpublished typescript, University of California, Davis.

115

ReferencesEconomics

Swanson, Norman R. and Clive W.J. Granger. (1997). ‘Impulse response functions based on a causal approach to residual orthogonalization in vector autoregressions’, Journal of the American Statistical Association, Vol. 92, pp. 357-67.

Demiralp, S., Hoover, K., & Perez, S. A Bootstrap Method for Identifying and Evaluating a Structural Vector Autoregression Oxford Bulletin of Economics and Statistics, 2008, 70, (4), 509-533

- Searching for the Causal Structure of a Vector Autoregression Oxford Bulletin of Economics and Statistics, 2003, 65, (s1), 745-767

Kevin D. Hoover, Selva Demiralp, Stephen J. Perez, Empirical Identification of the Vector Autoregression: The Causes and Effects of U.S. M2*, This paper was written to present at the Conference in Honour of David F. Hendry at Oxford University, 2325 August 2007.

Selva Demiralp and Kevin D. Hoover , Searching for the Causal Structure of a Vector Autoregression, OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 65, SUPPLEMENT (2003) 0305-9049

A. Moneta, and P. Spirtes “Graphical Models for the Identification of Causal Structures in Multivariate Time Series Model”, Proceedings of the 2006 Joint Conference on Information Sciences, JCIS 2006, Kaohsiung, Taiwan, ROC, October 8-11,2006, Atlantis Press, 2006.

References

Eberhardt, F., and Scheines R., (2007).“Interventions and Causal Inference”, in PSA-2006, Proceedings of the 20th biennial meeting of the Philosophy of Science Association 2006 http://philsci.org/news/PSA06

Silva, R., Glymour, C., Scheines, R. and Spirtes, P. (2006) “Learning the Structure of Latent Linear Structure Models,” Journal of Machine Learning Research, 7, 191-246.

http://philsci.org/news/PSA06

Documents

1 Searching for Causal Models Richard Scheines Philosophy, Machine Learning, Human-Computer Interaction Carnegie Mellon University