SPS 580 Lecture 10 Causal order 2.0 Blocks Chains beta
I.
SPECIFYING CAUSAL ORDER
A. The way you specify the causal order has a big impact on the statistical results
a. If you change the order of variables, you change the measure of CAUSAL
IMPACT and. the measure of SPURIOUS CORRELATION
b. It will affect the conclusions
B. There is no statistical test for determining causal order, it comes from theory, logic,
and your knowledge of how the world works. It is arbitrary. It is approximate.
C. Rules for assigning causal order X  Y
1. HISTORICAL SEQUENCE
a) X happened first, earlier in life, … adolescent experiences  adult experiences
b) Y starts after X stops … education  earnings
c) Change in X precedes change in Y … divorced  happiness
d) Intrinsic connection . . . distance to work  travel time
e) Cultural transmission . . . ethnicity  small business ownership
f) Response to experience . . . Victimization  Fear of crime
g) Evaluation . . . Program  Outcome
2. STICKINESS
a) X never changes, Y sometimes changes … gender  employment status
b) X doesn’t change much, Y changes more often … income  TV usage, opinions
3. CONSISTENCY THEORY
a) attitude  attitude consistency
general (prior)  specific (current)
0
1
2
3
General
Environmental
Priority Scale
19%
22%
25%
34%
100%
 “Very Important” to spend on: The Environment, Waste management,
Recycling
How consistent with opinions on specific, current issues . . .
 Taxes on gasoline should be increased 10 cents a gallon to improve mass transit and
cleaner air
 People should be charged for garbage collection based on the amount they throw away
 People in Illinois who buy soft drinks should pay a 10 cent deposit per can or bottle that
they would get back when it is recycled
1
SPS 580 Lecture 10 Causal order 2.0 Blocks Chains beta
Consistency of general opinions and specific policy proposals
60%
% Strongly agree
50%
Soft drink deposit
40%
30%
Trash fee by use
20%
Gas tax
10%
0%
0
1
2
3
Scale of general opinions on environmental spending
Also: Information Processing . . Prior belief  response to new information
b) Attitude  Behavior consistency . . .
0
1
2
3
Environmental
Tax Policy
Scale
16%
32%
35%
17%
100%
 Agree/Disagree gas tax, garbage collection charge, pop can deposit
How consistent with current behavior . . .
Consistency of attitudes and behavior
60%
% Currently use
energy efficient . . .
50%
40%
Garbage Bags
30%
Shower Head
20%
Termostat
10%
Light Bulbs
0%
0
1
2
3
Environmental tax policy scale
Also: Impact of information Awareness  Information  Decision  Action . . . Message
testing, media studies
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SPS 580 Lecture 10 Causal order 2.0 Blocks Chains beta
c) Behavior  attitude consistency
Contributes to Environmental
Causes
Active In Environmental
Organizations
0 no dk
1 yes
0 no dk
2,056
459
1 yes
176
303
Environmental Causes:
Current Contribution/Activity
75%
15%
None or time
only
Money
10%
Money and
time
 Interesting choice on how to
construct the scale
 Additive, or stepwise ???
How consistent with . . .
 There is a proposal to close the Meigs Field
airport and turn the land into an open prairie and picnic
area for visitors to the lakefront. Do you favor or oppose
this proposal?
Donate/Volunteer . . .
None or time only
Money
Money and time
Favor Meigs
Field Proposal
44%
43%
53%
d) Behavior  Behavior consistency
Consistency of behavior with behavior
80%
More likely to VISIT
60%
40%
20%
More likely to JOIN
0%
Neither
Money
Money + Time
Environmental Contribution/Activity Scale
3
How consistent with . . .
 If you knew that a cultural
organization was active in
environmental causes, would you
be more likely
to… Visit there? Become a
member?
SPS 580 Lecture 10 Causal order 2.0 Blocks Chains beta
4. SOCIAL THEORY
a) Social capital theory
Extent of Social Network  Available Resources  Positive Outcome
Extent of social network . . .
15+
10-14
5-9
2-5
1
0
Number of
neighbors known
personally
26%
21%
26%
17%
4%
7%
100%
 About how many of your neighbors do you know personally?
How strongly related to. . .
 Do you have a personal friend in the Chicago area who could
help you if you wanted to know a good place to learn about computers
or mathematics?
 Do you have a friend in the Chicago area who is a lawyer, or
someone who can give you free advice on legal issues?
Social Capital Theory
80%
70%
Has a friend
for . . .
60%
Advice about
computers/
math
50%
Free advice on
legal issues
40%
30%
0
1
2-5
5-9 10-14 15+
4
 This becomes an
intervening variable in a
model predicting benefits of
social capital (reduced fear,
better employment
opportunities, etc.)
SPS 580 Lecture 10 Causal order 2.0 Blocks Chains beta
b) Rational decision making theory . . .
Perceived Risk/Reward  Attitudes, Behavior
Opportunity to profit from home improvement (Select for home owners) . . .
As far as you know, have any of the people who live on your block been spending money to fix up their property?
How strongly related to
Perception
Intention
Action
Neighborhood
Improved
Would like
is good
home
to remodel
investment
recently
Neighbors are NOT investing
78%
46%
39%
Neighbors ARE investing
87%
65%
63%
Rational Decision Making Theory
60%
40%
20%
Would LIKE to remodel
HAS IMPROVED home recently
0%
Neighbors are NOT investing
Neighbors ARE investing
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SPS 580 Lecture 10 Causal order 2.0 Blocks Chains beta
II.
BLOCK MODELS
A. Intervening block
B1
X1
B2
Y
 Multiple intervening variables
Don’t know causal order between them
B3
X2
B4
B5
X3
B. Prior Block
B1
X1
B3
B2
X2
 Multiple causally prior variables
Don’t know causal order between them
Y
B5
B4
X3
C. Full block system
X1
B1
 Know causal order between blocks, but not
within blocks
(Not all paths labeled)
Y
B3
X2
B7
X4
X3
B5
B9
X5
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SPS 580 Lecture 10 Causal order 2.0 Blocks Chains beta
income
health
age
D. How to Analyze, Report
Results with a Block System
 6 variable causal system
HSG
 2 causally prior, education =
dummy with 3 contrasts
outdoor
some
coll
 2 intervening
coll
grad+
smoker
REGRESSION RESULTS
Income Percentile
Education
Slope
0.0025
**
0.0919
0.1168
0.2106
**
**
**
Age 46 yrs or older
-0.1114
**
Outdoor Activity scale
Smoker at present time
0.0041
-0.0596
**
**
** p < .05
HSG
Some college
College grad+
(Ref = 0-11)
 The format for reporting the regression
equation is the same, there are just more
variables in the list
 Order the list according to some
principle . . . e.g., causal order,
importance to the story, significant vs. not
CAUSAL ANALYSIS
Impact of Income on Proportion "Excellent" Health
Zero Order Effect
0.0042
Causal Effect
Direct
Indirect
Total Causal Effect
Spurious Effect
0.0025
0.0002
0.0027
61%
5%
66%
0.0014
34%
7
 The method for decomposing the zero
order effect is the same, there are just
more variables being considered in each
of the component regression models
 In this example the decomposition
does not change even though two
variables are added, this is because age
explained some of the impact of
education and smoking explained some
of the effect of health habits
SPS 580 Lecture 10 Causal order 2.0 Blocks Chains beta
E. Block modeling is the method for handling multiple dummy variables in a system – i.e.,
treat each set of contrasts as a block variable; in the REGRESSION RESULTS report the
slope for each contrast; in the CAUSAL ANALYSIS include them in the intervening
block or the causally prior block depending on where they fit in your theory
III.
ANALYSIS OF CAUSAL CHAINS
A. The 4-block chain consists of component causal models
X1
Y
 MODEL 1: Causes of X1 . . . relation
between age, education and income
Y
 MODEL 2: Causes of X3 . . . age, education
and income as predictors of healthy outdoor
activity
X2
X4
X3
X5
X1
X2
X4
X3
X5
X1
Y
 MODEL 3: Causes of X5 . . . age, education
and income as predictors of smoking
X2
X4
X3
X5
B. The component models can be analyzed with separate regression equations
REGRESSION RESULTS
Income Percentile
Education
HSG
Some college
College grad+
(Ref = 0-11)
Age 46 yrs or older
Slope
-0.0008
**
0.0150
-0.0402
-0.1640
**
-0.0652
**
** p < .05
 Regression results for Model 3 . . . Who Smokes?
 Note: HSG and College not significant
 Use regression analysis of component models to tell
the story about how spurious and intervening impact
works
 To do this, run the REGRESSION routine with all of
the variables in the original 4-block model; put the
variables NOT INCLUDED (X3, Y) in the LAST
BLOCK of the REGRESSION program and ignore the
results for them.
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SPS 580 Lecture 10 Causal order 2.0 Blocks Chains beta
IV.
STANDARDIZED SLOPES
Q: In the 4-block model the partial for income is .0025 and the slope for Outdoor activity is
.0041 – does that mean that Outdoor Activity is MORE IMPORTANT than income in predicting
health status?
A: No . . . the metric of the variables are different, it would be like asking if something that costs
500 Rupees is more valuable than something that costs $100. The difference in METRIC is
shown by looking at the RANGE and STANDARD DEVIATION for the two variables.
Variable
Measured as
Range
Income
percentile of income
distribution
Number of trail uses / year
Under/over age 45
Smoke at present or not
Education dummy
Education dummy
Education dummy
Excellent vs. other
0 to 100
Standard
deviation
28.6272
0 to 20
0,1
0,1
0,1
0,1
0,1
0,1
8.0133
0.4887
0.4472
.4351
.4454
.4744
0.4928
Outdoor Activity
Age
Smoking
HSG
Some College
College grad+
Health status
 NOTE: ask for
DESCRIPTIVES as
part of the
REGRESSION
procedure and use
those standard
deviations
A. To see which slope is MORE IMPORTANT . . . Multiply the SLOPE by the ratio (Std Dev X
/ Std Dev Y) -- the result is known as the STANDARDIZED SLOPE . . . the interpretation is
the number of standard deviation units change in Y per 1 standard deviation change in X
Variable
Slope
Income
.0025
Std Dev
X
28.6272
Std Dev
Y
0.4928
Adjustment
factor
58.0899
Standardized
slope
0.15

B. In SPSS the standardized slope is called the beta. Compare betas to see which variable is the
most important cause of Y
Controlling for everything else in the
equation . . .
 Income is 2nd most important
Slope
0.0025
**
beta
0.15
0.0919
0.1168
0.2106
**
**
**
0.08
0.11
0.20
Age 46 yrs or older
-0.1114
**
-0.11
 Age is 3rd most important (sign is
irrelevant, magnitude is the issue)
Outdoor Activity scale
Smoker at present time
0.0041
-0.0596
**
0.07
**
-0.05
** p < .05
 Outdoor activity is further down
the list
REGRESSION RESULTS
Income Percentile
Education
HSG
Some college
College grad+
(Ref = 0-11)
9
 College Grad is MOST important