SPS 580 Lecture 7
Data Mining Dummy Variables notes
I.
THE LINEARITY ASSUMPTION
A. It’s called multiple LINEAR regression because Y is assumed to be a linear function of the
each X variable Y = a + B1(X1) + B2(X2) +B3(X3) . . .
a. We like linear models because they are an intuitive way to talk about the effects of
each variable (intervening, control), difference between the zero order and the partial
B. Violations of linear assumption: Curvilinearity
a. look at it with the zero order relationship.,
b. if the relationship is curvilinear, then the linear slope doesn’t do as good a job at
predicting Y as some other alternatives.
c. In most cases the linear model is pretty accurate predictor – not usually the end of the
world.
d. We’re about to learn a way to deal with the situation when there is a curvilinear
relationship.
C. Violations of linear assumption: Interactions
a. look at by examining the conditional slopes in the three-variable graph.
b. If there is an interaction then the effect of an X variable on Y is not linear – because
the magnitude of the slope DEPENDS on a third variable. in most cases interactions
are not significant.
c. But when they are it IS the end of the world. You have to do the analysis separately
for the groups involved in the interaction or incorporate an interaction term in the
linear regression model.
d. We’ll learn about how to deal with them in a couple of weeks.
II.
SUPPRESSOR EFFECT
a. Not a violation of linearity, rather an unusual outcome of causal analysis
B1
Y
X1
B2
X2
 Three variable path diagram
B3
b. Happens when the SIGN of the indirect path B2 * B3 is opposite from the SIGN of
the direct path B1.
c. If this happens then B1 > ZERO ORDER and you get an estimated of suppression
effect rather than explanation.
III.
WHY IS CAUSAL ANALYSIS IMPORTANT?
 Intervening variables often show points of policy input . . . Let’s say you knew higher
income people were moving out of a neighborhood. And that they would often explain their
reasons for doing so in terms of neighborhood pessimism.
 You want to reduce neighborhood turnover.
Income
Neighborhood Pessimism
Move out
???
 You can’t do much about income, but you might be able to find things that cause pessimism
that you can affect.
1
SPS 580 Lecture 7
IV.
Data Mining Dummy Variables notes
HOW TO FIND GOOD INTERVENING VARIABLES
Y
X1
0 Low pessimism
0 Low income
460
1 High Income
580
N
1 High pessimism
540
54%
420
42%
B=
-12%
1,000
1,000
X1  Y
 pretend data, not PQ
How do you find variables that when you put them inside the causal chain X1 Y, the partial is
less than the zero order?
A. reflect on own experience or talk to people
B. literature – an article or a report
C. data mining – there will be certain statistical relationships between X1, X2 and Y
V.
DATA MINING . . . For an intervening to explain part/all of the X1  Y
relationship, two conditions have to be met . . .
CONDITION 1: The explanatory variable X2 has a significant impact on Y
X2
0 Low fear
1 High fear
Y
0 Low pessimism
560
480
N
1 High pessimism
240
30%
720
60%
B=
30%
800
1,200
X2  Y is significant
 pretend data , not PQ
Fear is a cause of pessimism
 This is the intervening CAUSAL process, it comes from psychological theory, literature,
observational studies, it is a reflection of social process  this is the reason you like stx
CONDITION 2: Groups that differ on the independent variable X1 differ on the
explanatory variable X2
X1
0 Low income
1 High Income
X2
0 Low fear
200
600
N
1 High fear
800
80%
400
40%
B=
-40%
1,000
1,000
X1  X2
 pretend data, not PQ
Income groups differ on Fear

In order for fear to be a
reason income causes pessimism, higher income people have to be less fearful than lower
income low income
 In order for X2 to explain X1  Y,
X1 has to be a cause of X2
2
SPS 580 Lecture 7
VI.
Data Mining Dummy Variables notes
OUTCOME OF SUCCESSFUL DATA MINING
A. Mechanically, when you control for X2 the partial is lower than the zero order
Y
X2
X1
0 Low fear
0 Low income
1 High Income
0 Low income
1 High Income
1 High fear
0 Low pessimism
140
420
320
160
1 High pessimism
60
30%
180
30%
480
60%
240
60%
Conditional X2=0 0%
Conditional X2=1 0%
Partial =
0%
N
200
600
800
400
X1  Y controlling X2
 pretend, not PQ
 in this case Partial = 0
B. Intuitively, in X1Y relationship you think you’re looking at groups that differ on X1
X1
0 Low pessimism
Y
1 High pessimism
N
0 Low income (and
higher fear)
460
540
54%
1,000
1 High Income (and
lower fear)
580
420
42%
1,000
B=
-12%
 But actually we’re looking at groups
that differ on X1 and also X2
 So you need to control for X2 to see
the impact of X1 alone (Partial)
VII. SO HOW DO YOU DATA MINE FOR (OTHER) INTERVENING VARIABLES
A. Get a list of candidate intervening variables from the same survey years . . .
A. Read a book in the past month -- readers less pessimistic
B. Frequency of using the local park in the past month – park users less pessimistic
C. Employment status -- unemployed > pessimistic
1 Working Full Time
emp94 Employment Status Of Respondent
56.9%
2 Working Part Time
11.5%
3 Temporary Layoff
0.3%
4 Temporary Illness, D
0.9%
5 On Vacation
0.6%
6 On Strike
0.0%
7 Unemployed, Between
1.6%
8 Looking For Work
0.8%
9 Permanent Layoff
10 Retired
0.2%
0.4%
12 Long Term Disabled,
1.1%
13 Taking Care Of Home
10.0%
14 Going To School
2.3%
15 Other
0.4%
Total
CURRENTLY
UNEMPLOYED
(CODING EMPSTAT) 
96.5%
IN THE
LABOR
FORCE
72.9%
3.5%
12.8%
11 Long Term Ill, Unabl
98 Don't Know
CURRENTLY
EMPLOYED
NOT IN
THE
LABOR
FORCE
0.1%
100.0%
3
27.1%
SPS 580 Lecture 7
Data Mining Dummy Variables notes
B. Recode the candidate variables, look at the xtabs to see if two conditions are met
1. First check X2  Y to see if the explanatory variable actually causes pessimism
Size of X2 --> Y relationship among candidate intervening variables
Candidate variables
Reading Habits
Neighborhood Use
Employment,
Labor Force Status
0 No reading
1 Read book past month
0 No park use
1 Used local park past month
0 In LF Working
1 In LF Unemployed
Pessimism %
37%
34%
40%
30%
31%
45%
2 Not in LF Retired
3 Not in Other
B
-2%
 doesn’t make the cut
-10%
 makes the cut weakly
15%
 makes the cut
36%
43%
2. Then check X1  X2 to see if income groups actually differ on it
Size of X1 --> X2 relationship among candidate intervening variables
Employment, Labor Force Status
Neighborhood Use
Income Group
0 Below median
1 Above median
B
1 Used local park
past month
50%
60%
10%
Weak
X1
Income
0 Below
median
1 Above
median
0 In LF
Working
60%
84%
23%
1 In LF
Unemp
4%
1%
-2%
Sweet
X2
Labor force status
0 Working
1 Not working
0 Working
1 Not working
Conditional X1 = 0
Conditional X1 = 1
Partial =
2 Not in LF
Retired
18%
5%
3 Not in LF
Other
18%
10%
 Park use might
be OK
 Unemp fails
 Working v. Other
seems important
Fails
Y
Pessimism %
39%
47%
25%
24%
7.6%
-1.0%
4.2%
BOTTOM LINE: Go with LF status
coded (1 = working, 0 = other)
 Xtab results -- since y= dichot(0,1)
Pessimism = .40 - .166 (Income) +.042 (Labor Force Status)  slope for LF status is significant
Impact of Household Income on Neighborhood Pessimism
Zero order
-.18
100%
Partial (Direct Effect)
-.17
94%
Intervening effect of non-.01
6%
LF participation
4
 but the impact of the control variable
isn’t very great
Worse yet . . . there might be an
interaction effect
SPS 580 Lecture 7
Data Mining Dummy Variables notes
VIII. DEALING WITH CURVILINEARITY
A. Start by looking at how to deal with Ordinal (3+) variables
resped Highest Level Of Education Completed
1 4th Grade Or Less
0.8%
2 5th-8th Grade
3.2%
3 9-12th Grade, No Diploma
7.2%
4 High School Graduate
0-11 yrs
 Education is a very important
variable for a lot of public policy
analysis
17.8%
5 Trade Or Vocational
6.7%
10 Hs Grad, Non Spec.
0.1%
6 Some College
27.4%
7 College Graduate
20.0%
8 Some Graduate Study
3.9%
9 Graduate Degree
HSG, Trade
Some college
College Grad
12.7%
98 Don't Know
0.1%
Total
 It’s not really usable as an interval
variable, not across the full range, and
not in the US context
 But you don’t want to lose the
gradient, usually best to treat it as a
ordinal variable
missing
100.0%
B. Recode the variable into (k) ordinal categories . . . as shown above
Neighborhood Pessimism
60%
51%
 do a xtab or table of means -- depending on whether
Y is dichotomous(0,1) or interval(3+)
50%
39%
40%
30%
 Look at the pattern in the data
36%
23%
20%
 line goes down, higher education  lower
pessimism
10%
 not much diff between some college vs. HSG/trade
0%
0-11 yrs
HSG, Trade
Some college College Grad
C. Don’t think of the pattern in the data as a line
CONTRASTS
Neighborhood HSG/Trade Some College College Grad
vs. 0-11
vs. 0-11
vs. 0-11
Pessimism
0-11 yrs
51%
51%
51%
51%
HSG, Trade
39%
39%
Some college
36%
36%
College Grad
23%
23%
-12%
-15%
-28%
[WARNING DATA ANALYSIS METHOD AHEAD]
5
Think of the pattern in the data as
(k-1) separate CONTRASTS . . .
SPS 580 Lecture 7
Data Mining Dummy Variables notes
D. Think of each of the (k-1) contrasts as something that is measured with a (0,1)
dichotomous variable.
 (0,1) dichotomies created this way are
knows as DUMMY VARIABLES
DUMMY VARIABLE CODING . . .
Education
0-11 yrs
HSG, Trade
Some college
College Grad
HSG/Trade
vs. 0-11
Some College College Grad
vs. 0-11
vs. 0-11
0
1
0
0
0
0
1
0
 With (k) categories of education, we need
(k-1) dummy variables to estimate the
available contrasts
0
0
0
1
The “left out” category is called the reference category (in this case 0-11 yrs of education)
A dummy var measures the difference between the contrast category and the reference category
E. Creating (K-1) Dummy Variables To Analyze The Impact Of An Ordinal Variable
RECODE education (0=0) (1=1) (2=0) (3=0) (ELSE=9) INTO educHSG.
VARIABLE LABELS educHSG 'dummy var HSG vs 0-11'.
RECODE education (0=0) (3=0) (1=0) (2=1) (ELSE=9) INTO educANYCOLL.
VARIABLE LABELS educANYCOLL 'dummy any coll vs 0-11'.
RECODE education (0=0) (1=0) (3=1) (2=0) (ELSE=9) INTO educCOLLGRAD.
VARIABLE LABELS educCOLLGRAD 'dummy coll grad vs 0-11'.
MISSING VALUES educHSG educANYCOLL educCOLLGRAD (9).
The result will be (k-1) variables, each of which codes the ENTIRE SAMPLE . . .
Original Data
Education
0-11 yrs
HSG, Trade
Some college
College Grad
total
frequency
4,112
8,974
10,023
13,374
36,483
DUMMY VARIABLES
Coding
HSG/Trade vs. 0-11
Some College vs. 0-11
College Grad vs. 0-11
0
1
27,509
26,460
23,109
8,974
10,023
13,374
Total
36,483
36,483
36,483
Regression works the as before, except that instead of having one education variable there are
now 3 dummy variables measuring the effects of education. Whenever you estimate the effect of
education, put all (k-1) dummy vars in the regression equation together
F. For the ZERO ORDER, there are now (k-1) slopes, t-tests
Unstandardized
Coefficients
 All 3 are significant
B
Std. Error
t
Sig.
(Constant)
.494
.018
27.971
.000
educHSG dummy var HSG vs 0-11
-.106
.021
-4.950
.000
educANYCOLL dummy any coll vs 0-11
-.138
.021
-6.600
.000
educCOLLGRAD dummy coll grad vs 0-11
-.269
.020
-13.338
.000
6
 D1 and D2 are pretty
similar to each other
SPS 580 Lecture 7
Data Mining Dummy Variables notes
G. To test Education as a control variable, enter ALL (k-1) dummy variables together in the
multiple regression equation along with income . . .
Unstandardized
Coefficients
B
Std. Error
t
Sig.
(Constant)
.513
.018
27.917
.000
Income (0,1)
-.130
.013
-9.931
.000
HSG/Trade vs. 0-11
Some College vs. 0-11
College Grad vs. 0-11
-.077
.022
-3.440
.001
-.093
.022
-4.204
.000
-.200
.022
-9.080
.000
Impact of Household Income on Neighborhood Pessimism
Zero order
-.18
100%
Partial (Direct Effect)
-.13
74%
Intervening effect of education
-.05
26%
 Income effect is reduced
substantially
 education makes a pretty big
difference as an explanatory
variable
H. The prediction equation works the same way too
Regression equation . . .
Predicted avg(Y) = .513 - .130*(Income)-.077 *(educHSG) -.093 *(educANYCOLL) -.200*(educCOLLGRAD)
60%
 predicted values
50%
40%
30%
20%
0 Below median income
10%
1 Above median
0%
0-11 yrs
HSG, Trade
Some college
College Grad
7
SPS 580 Lecture 7
IX.
Data Mining Dummy Variables notes
DUMMY VARIABLES ARE THE MAIN TECHNIQUE FOR DEALING WITH
CURVILINEARITY
A. Example: Client = WBEZ want to target fundraising
Commission research to explore extent to which Education  Listen to public radio
and reasons why this might be the case
B. ZERO ORDER RESULTS
0-11 yrs
HSG, Trade
Some college
College Grad
Dont Listen to radio, Listen to radio,
Listen to
listen to
not familiar
familiar with
wbez
radio
WBEZ
WBEZ
18%
57%
8%
16%
11%
67%
10%
13%
4%
58%
15%
23%
5%
46%
16%
34%
Listen to wbez
34%
16%
13%
Some
college
 Curvilinear relationship . . .
 . . . is significant Chi sq(3) = 135 p < .04 phi =.204
 Examine Contrasts
Minimal difference HSG/Trade vs. 0-11
Small difference Some College vs. 0-11
Large difference College Grad vs. 0-11
23%
0-11 yrs HSG, Trade
Total
100%
100%
100%
100%
College
Grad
Unstandardized
Coefficients
(Constant)
HSG/Trade vs. 0-11
Some College vs. 0-11
College Grad vs. 0-11
 The listenership variable is nominal
(4 cat), so to proceed with causal
analysis, I’m going to recode it into a
dichotomy
B
.159
Std. Error
.022
t
Sig.
7.331
.000
-.037
.026
-1.395
.163
.069
.026
2.667
.008
.179
.025
7.181
.000
Conclusion . . .
8
One of the DUMMIES is
not significant
SPS 580 Lecture 7
Data Mining Dummy Variables notes
C. INTERVENING VARIABLE:
Theory . . . . . .
Education  Politically Independent  Listen to Public radio
X1

X2

Y
Party
Affiliation
1 Republican
23%
2 Democrat
38%
3 Independent
25%
4 Other
 recode X2 to Independent vs. other
3%
5 No Preference
8 Do Not Know
11%
1%
100%
Unstandardized
Coefficients
(Constant)
HSG/Trade vs. 0-11
Some College vs. 0-11
College Grad vs. 0-11
Independent vs other
X.
B
.155
Std. Error
.022
t
Sig.
7.064
.000
-.038
.026
-1.442
.149
.067
.026
2.584
.010
.176
.025
7.026
.000
.023
.017
1.370
.171
REGRESSION ANALYSIS
 Education effect is still
curvilinear
 Independence isn’t
significant
HOW TO SUMMARIZE THE ZERO ORDER AND PARTIAL EFFECTS OF AN
ORDINAL/NOMINAL VARIABLE MEASURED WITH DUMMY VARIABLES
Impact of Education on Public Radio Listening
Explained by Political
Zero order
Partial
Independence
-.037
-.038
HSG/Trade vs. 0-11
-4%
.069
.067
Some College vs. 0-11
3%
.179
.176
College Grad vs. 0-11
2%
9
 Independence doesn’t
explain much of the
relationship between
education and listenership