Methods of Modeling
Interdependence
M. Joy McClure, Adelphi University
Patrick E. Shrout, New York University
Christopher T. Burke, Lehigh University
1
Goals & Plan for Today
• Consider different substantive and methodological
conceptualizations of interdependence
• Individuals
2
Goals & Plan for Today
• Consider different substantive and methodological
conceptualizations of interdependence
• Individuals, Dyads
3
Goals & Plan for Today
• Consider different substantive and methodological
conceptualizations of interdependence
• Individuals, Dyads, Over Time
4
Goals & Plan for Today
• Consider different substantive and methodological
conceptualizations of interdependence
• Individuals, Dyads, Over Time
• Review
• Actor-Partner Interdependence Model (McClure)
5
Goals & Plan for Today
• Consider different substantive and methodological
conceptualizations of interdependence
• Individuals, Dyads, Over Time
• Review
• Actor-Partner Interdependence Model (McClure)
• Common Fate and Dyadic Scores Models (Shrout)
6
Goals & Plan for Today
• Consider different substantive and methodological
conceptualizations of interdependence
• Individuals, Dyads, Over Time
• Review
• Actor-Partner Interdependence Model (McClure)
• Common Fate and Dyadic Scores Models (Shrout)
• Actor-Partner Interdependence Model Over Time (Burke)
7
Goals & Plan for Today
• Consider different substantive and methodological
conceptualizations of interdependence
• Individuals, Dyads, Over Time
• Review
• Actor-Partner Interdependence Model (McClure)
• Common Fate and Dyadic Scores Models (Shrout)
• Actor-Partner Interdependence Model Over Time (Burke)
• Work through an empirical example
8
Slides and handouts at:
https://osf.io/wy5df/
9
The Actor-Partner
Interdependence Model
10
APIM: The Basics
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
• Kashy & Kenny, (1999); Kenny & Cook (1999); Kenny, Kashy, & Cook (2006) Chapter 7, with
updates, clarifications and elaborations at: http://davidakenny.net/kkc/c7/c7.htm
11
APIM: The Basics
Y1
12
APIM: The Basics
Y1
13
APIM: The Basics
X1
a1
Y1
14
APIM: The Basics
X1
a1
Y1
15
APIM: The Basics
X1
a1
Y1
Intrapersonal
process
16
APIM: The Basics
X1
a1
Y1
Intrapersonal
process
17
APIM: The Basics
X1
X2
a1
a2
Y1
Y2
18
APIM: The Basics
X1
a1
Y1
In a relationship!
X2
a2
Y2
19
APIM: The Basics
X1
a1
Y1
Interpersonal processes
X2
a2
Y2
20
APIM: The Basics
X1
a1
Y1
c1
X2
a2
Y2
21
APIM: The Basics
X1
a1
Y1
c1
X2
a2
Y2
22
APIM: The Basics
X1
a1
Y1
c1
X2
a2
Y2
23
APIM: The Basics
X1
a1
Y1
c1
X2
a2
Y2
24
APIM: The Basics
X1
a1
Y1
E1
Y2
E2
c1
X2
a2
25
APIM: The Basics
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
26
The Empirical Example:
Bar Exam Couples
27
The Empirical Example: Participants
• 493 heterosexual couples
• mean age = 30 years
• 76% White
• mean relationship length = 6 years
• 61% married
• One member of the couple is studying to write the NYS bar exam
• Examinees
• Partners
28
The Empirical Example: Methods & Questions
• Background questionnaire and daily diary leading up to the exam.
29
The Empirical Example: Methods & Questions
• Background questionnaire and daily diary leading up to the exam.
• From background:
• Perceived support from partner (7 items from the QRI; Pierce et al., 1991),
•
from 1 (low) to 4 (high)
Closeness (IOS; Aron, Aron, & Smollan, 1992), from 1 (low) to 7 (high)
30
The Empirical Example: Methods & Questions
• Background questionnaire and daily diary leading up to the exam.
• From background:
• Perceived support from partner (7 items from the QRI; Pierce et al., 1991),
from 1 (low) to 4 (high)
Closeness (IOS; Aron, Aron, & Smollan, 1992), from 1 (low) to 7 (high)
•
• Does perceived support affect closeness?
• Perceiving more support from your partner will increase your report
of closeness
31
The Empirical Example: Methods & Questions
• Background questionnaire and daily diary leading up to the exam.
• From background:
• Perceived support from partner (7 items from the QRI; Pierce et al., 1991),
from 1 (low) to 4 (high)
Closeness (IOS; Aron, Aron, & Smollan, 1992), from 1 (low) to 7 (high)
•
• Does perceived support affect closeness?
• Perceiving more support from your partner will increase your report
of closeness
• Perceiving more support from your partner will increase THEIR
report of closeness
32
APIM: What do we need to estimate?
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
33
APIM: What do we need to estimate?
• Correlation between
dyad members on the
predictor
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
34
APIM: What do we need to estimate?
• Correlation between
dyad members on the
predictor
• Two actor effects
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
35
APIM: What do we need to estimate?
• Correlation between
dyad members on the
predictor
• Two actor effects
• Two partner effects
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
36
APIM: What do we need to estimate?
• Correlation between
dyad members on the
predictor
• Two actor effects
• Two partner effects
• Correlation between
the residuals
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
37
APIM: The easy way
38
APIM: The easy way
• Step 1: Set up your dataset with the dyad as the unit of
analysis
DyadID
X1
X2
Y1
Y2
1
2
3
…
N
39
APIM: The easy way
• Step 2: Get correlation
between X1 and X2
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
40
APIM: The easy way
• Step 3: Run two
regressions
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
41
APIM: The easy way
• Step 3: Run two
regressions
• Y1 onto X1 and X2
• A1, P12
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
42
APIM: The easy way
• Step 3: Run two
regressions
• Y1 onto X1 and X2
• A1, P12
• Save residuals!
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
43
APIM: The easy way
• Step 3: Run two
regressions
• Y1 onto X1 and X2
• A1, P12
• Save residuals!
• Y2 onto X1 and X2
• A2, P21
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
44
APIM: The easy way
• Step 3: Run two
regressions
• Y1 onto X1 and X2
• A1, P12
• Save residuals!
• Y2 onto X1 and X2
• A2, P21
• Save residuals!
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
45
APIM: The easy way
• Step 4: Get the
correlation between the
residuals
X1
a1
Y1
E1
c1
c2
X2
a2
Y2
E2
46
The easy way: Results
47
The easy way: Results
PSUP1
IOS1
E1
PSUP2
IOS2
E2
.25***
48
The easy way: Results
PSUP1
1.07***
IOS1
E1
IOS2
E2
.25***
PSUP2
49
The easy way: Results
PSUP1
1.07***
IOS1
E1
IOS2
E2
.25***
PSUP2
1.40 ***
50
The easy way: Results
PSUP1
1.07***
IOS1
E1
.25***
.27 ***
PSUP2
1.40 ***
IOS2
E2
51
The easy way: Results
PSUP1
1.07***
IOS1
E1
.25***
.27 ***
PSUP2
1.40 ***
IOS2
E2
52
The easiest way: Downsides
• Many steps
53
The easiest way: Downsides
• Many steps
• Just descriptive
• What if I want to make inferences?
• Are the links between perceived support and closeness
weaker for examinees than partners?
54
APIM: The Two-Intercept Model
• Everything except c1 in one model!
55
APIM: The Two-Intercept Model
• Everything except c1 in one model!
• Spoilers: The results will be nearly identical
• OLS vs REML
• N/missing data
56
APIM: The Two-Intercept Model
• Restructure your
dataset to stack
the dyad members
• 2 rows per dyad
• Two indicators:
dyad and
person-in-dyad
Did Pid
1
1
1
2
2
1
2
2
...
N
1
N
2
57
APIM: The Two-Intercept Model
• Restructure your
dataset to stack
the dyad members
• 2 rows per dyad
• Two indicators:
dyad and
person-in-dyad
Did Pid
1
1
1
2
2
1
2
2
...
N
1
N
2
58
APIM: The Two-Intercept Model
• Two X variables:
Your own, and
your partner’s (i.e.
the other person)
• Two Y variables:
Your own, and
your partner’s (i.e.
the other person)
Cid Pid
Xown Yown Xoth
Yoth
1
1
X1
Y1
X2
Y2
1
2
X2
Y2
X1
Y1
2
1
2
2
...
N
1
N
2
59
APIM: The Two-Intercept Model
• Data is repeated
once as own and
once as other’s
Cid Pid
Xown Yown Xoth
Yoth
1
1
X1
Y1
X2
Y2
1
2
X2
Y2
X1
Y1
2
1
2
2
...
N
1
N
2
60
APIM: The Two-Intercept Model
• Finally, add two
dummy variables
based on personin-dyad indicator
Did Pid
P1
P2 Xown Yown Xoth
Yoth
1
1
1
0
X1
Y1
X2
Y2
1
2
0
1
X2
Y2
X1
Y1
2
1
1
0
2
2
0
1
N
1
1
0
N
2
0
1
...
61
The Two-Intercept Model: SPSS Syntax
62
The Two-Intercept Model: SPSS Syntax
MIXED Y WITH P1 P2 Xown Xoth
/FIXED = P1 P2 Xown*P1 Xown*P2 Xoth*P1 Xoth*P1 | NOINT
/PRINT = SOLUTION TESTCOV
/REPEATED = Pid| SUBJECT(Did) COVTYPE(CSH).
63
The Two-Intercept Model: SPSS Syntax
MIXED ios WITH examinee partner csupown csupoth
/FIXED = examinee partner csupown*examinee csupown*partner
csupoth*examinee csupoth*partner | NOINT
/PRINT = SOLUTION TESTCOV
/REPEATED = exorpa | SUBJECT(couple) COVTYPE(CSH).
64
The Two-Intercept Model: Results
PSUP1
IOS1
E1
PSUP2
IOS2
E2
.25***
65
The Two-Intercept Model: Results
PSUP1
IOS1
E1
.25***
ρ
.27 ***
PSUP2
IOS2
E2
66
The Two-Intercept Model: Results
PSUP1
IOS1
E1
.25***
.27 ***
PSUP2
csupown*examinee
csupown*partner
IOS2
E2
csupoth*examinee
csupoth*partner
67
The Two-Intercept Model: Results
PSUP1
IOS1
E1
.25***
.27 ***
PSUP2
csupown*examinee
csupown*partner
IOS2
E2
csupoth*examinee
csupoth*partner
68
The Two-Intercept Model: Results
PSUP1
1.07***
IOS1
E1
.25***
.27 ***
PSUP2
csupown*examinee
csupown*partner
1.39 ***
IOS2
E2
csupoth*examinee
csupoth*partner
69
The Two-Intercept Model: Results
PSUP1
1.07***
IOS1
E1
.25***
.27 ***
PSUP2
csupown*examinee
csupown*partner
1.39 ***
IOS2
E2
csupoth*examinee
csupoth*partner
70
The Two-Intercept Model: Results
PSUP1
1.07***
IOS1
E1
.25***
.27 ***
PSUP2
1.39 ***
IOS2
E2
71
APIM: The Two-Intercept Model
• Everything except c1 in one model!
• Results essentially identical
• … still need to contrast examinee with partner though
72
APIM: The Contrast (aka Interaction) Model
• Still using stacked dataset
• Create an effect coded variable for the person-in-dyad (e.g. 0.5 =
examinee, -0.5 partner) or use one of the dummy codes
73
APIM: The Contrast (aka Interaction) Model
• Still using stacked dataset
• Create an effect coded variable for the person-in-dyad (e.g. 0.5 =
examinee, -0.5 partner) or use one of the dummy codes
MIXED ios WITH csupown csupoth partner
/FIXED = csupown csupoth partner csupown*partner
csupoth*partner
/PRINT = SOLUTION TESTCOV
/REPEATED = exorpa | SUBJECT(couple) COVTYPE(CSH).
74
The Two-Intercept Model: Results
PSUP1
1.07***
IOS1
E1
.25***
.27 ***
PSUP2
csupown
csupoth
IOS2
E2
75
The Two-Intercept Model: Results
PSUP1
1.07***
IOS1
E1
.25***
.27 ***
PSUP2
IOS2
csupown
csupoth
csupown*partner, ns
csupoth*partner, ns
E2
76
The Two-Intercept Model: Results
PSUP1
1.07***
IOS1
E1
.25***
.27 ***
PSUP2
csupown
csupoth
1.07+.32=1.39 ***
IOS2
csupown*partner, ns
csupoth*partner, ns
E2
77
APIM: Interim Conclusion
• In our example…
78
APIM: Interim Conclusion
• In our example…
PSUP1
1.07***
IOS1
E1
.25***
.27 ***
PSUP2
1.39 ***
IOS2
E2
79
APIM: Interim Conclusion
• In our example…
PSUP1
1.07***
IOS1
E1
.25***
.27 ***
PSUP2
1.39 ***
IOS2
E2
80
APIM: Interim Conclusion
• In our example…
PSUP1
1.07***
IOS1
E1
.25***
.27 ***
PSUP2
1.39 ***
IOS2
E2
81
APIM: Interim Conclusion
• In our example…
1.07***
PSUP1
.25***
E1
.27 ***
ns
ns
PSUP2
IOS1
1.39 ***
IOS2
E2
82
APIM: Interim Conclusion
• In our example…
1.07***
PSUP1
.25***
E1
.27 ***
ns
ns
PSUP2
IOS1
1.39 ***
IOS2
E2
83
APIM: Interim Conclusion
• More broadly…
• APIM is great for modeling interdependent individuals!
84
APIM: Interim Conclusion
• More broadly…
• APIM is great for modeling interdependent individuals!
• Distinguishable vs exchangeable
85
APIM: Interim Conclusion
• More broadly…
• APIM is great for modeling interdependent individuals!
• Distinguishable vs exchangeable
• Dyadic level?
86