Chapter 17 Problems      AGid      Statistical Modeling: A Fresh Approach (2/e)

Reading Questions.

1.
Why does an observed correlation between two variables not provide compelling evidence that one causes the other?
2.
What is a hypothetical causal network? What does the word “hypothetical” signify about these networks?
3.
What is the difference between a correlating pathway and a non-correlating pathway?
4.
How is the appropriate choice of covariates in models to study causation influenced by the structure of the modeler’s hypothetical causal network?
5.
When might two modelers legitimately disagree about which covariates to include in a model?

Prob 17.01. For each of the following pathways connecting A and B, choose the appropriate causal structure.

(a)
ACB

A

A causes B.

B

B causes A.

C

A and B share a common cause.

D

No causal connection between A and B


(b)
ACB

A

A causes B.

B

B causes A.

C

A and B share a common cause.

D

No causal connection between A and B


(c)
ACB

A

A causes B.

B

B causes A.

C

A and B share a common cause.

D

No causal connection between A and B


(d)
ACB

A

A causes B.

B

B causes A.

C

A and B share a common cause.

D

No causal connection between A and B


(e)
ACD B

A

A causes B.

B

B causes A.

C

A and B share a common cause.

D

No causal connection between A and B


(f)
ACD B

A

A causes B.

B

B causes A.

C

A and B share a common cause.

D

No causal connection between A and B


(g)
ACD B

A

A causes B.

B

B causes A.

C

A and B share a common cause.

D

No causal connection between A and B


(h)
ACD EB

A

A causes B.

B

B causes A.

C

A and B share a common cause.

D

No causal connection between A and B


Prob 17.02. Say whether the pathway connecting A and B is correlating or non-correlating.

(a)
ACB
 correlating  noncorrelating  
(b)
ACB
 correlating  noncorrelating  
(c)
ACB
 correlating  noncorrelating  
(d)
ACB
 correlating  noncorrelating  
(e)
ACD B
 correlating  noncorrelating  
(f)
ACD B
 correlating  noncorrelating  
(g)
ACD B
 correlating  noncorrelating  
(h)
ACD EB
 correlating  noncorrelating  

Prob 17.05. Consider this hypothetical causal network:

SVG-Viewer needed.

(a)
Suppose you want to study the effect of B on A. Which of the models is most appropriate?

A

~ B

B

~ C

C

~ B+C

D

Any of the above.


(b)
Suppose you want to study the overall effect of C on A. Which of the models is most appropriate?

A

~ B

B

~ C

C

~ B+C

D

Any of the above.


(c)
Suppose you want to study the direct effect of C on A, neglecting the indirect effect through B. Which of the models is most appropriate?

A

~ B

B

~ C

C

~ B+C

D

Any of the above.


Prob 17.06. Consider this hypothetical causal network:

SVG-Viewer needed.

(a)
Suppose you want to study the effect of B on A. Which of the models is appropriate?

A

~ B

B

~ B+C

C

Neither (A) nor (B).

D

Either (A) or (B).


(b)
Suppose you want to study the overall effect of C on A. Which of the models is appropriate?

A

~ C

B

~ B+C

C

Neither (A) nor (B).

D

Either (A) or (B).


Prob 17.07. Consider this hypothetical causal network:

SVG-Viewer needed.

(a)
Suppose you want to study the overall effect of D on A. Which of the models is most appropriate?

A

~ D

B

~ D+C

C

~ B+C

D

~ D+B+C

E

Any of the above.


(b)
Suppose you want to study the effect of B on A. Which of the models is most appropriate?

A

~ B+D

B

~ B+C

C

~ B+C+D

D

Any of the above.


(c)
Suppose you want to study the overall effect of C on A. Which of the models is most appropriate?

A

~ C+D

B

~ B+C

C

~ B+C+D

D

Any of the above.


Prob 17.08. Consider this hypothetical causal network:

SVG-Viewer needed.

(a)
Suppose you want to study the effect of B on A. Which of the models is most appropriate?

A

~ B

B

~ C

C

~ B+C

D

Any of the above.


(b)
Suppose you want to study the effect of C on A. Which of the models is most appropriate?

A

~ B

B

~ C

C

~ B+C

D

Any of the above.


Prob 17.10. To answer the following questions, refer to the hypothetical causal network shown in Figure 17.9.

Consider studying the direct link between teacher compensation and student test scores with a model of the form Student Test Scores ~ Teacher Compensation + C, where C is one or more covariates. Which of the following choices of C can block the back-door pathways?

(a)
C is class size.
 blocks  does.not.block  
(b)
C is class size and teacher compensation.
 blocks  does.not.block  
(c)
C is family income.
 blocks  does.not.block  
(d)
C is per capita expenditures.
 blocks  does.not.block  
(e)
C is per capita expenditures and family income.
 blocks  does.not.block  
(f)
C is per capita expenditures and class size.
 blocks  does.not.block  
(g)
C is class size and parents’ education.
 blocks  does.not.block