Transcript Introductions - David A. Kenny

Specification Issues in
Relational Models
David A. Kenny
University of Connecticut
Talk can be downloaded at:
http://davidakenny.net/talks/nd.ppt
Overview
Preliminaries
Group Effects: Univariate
X  Y Effects with Group Data
What Is a Group?
• dyads
– husband-wife
– teacher-student
– siblings
• more than two people
– families
– work groups
– classrooms
A. Distinguishability
• In some groups, members can be
distinguished by the role: e.g., heterosexual
couples are usually distinguished by gender.
• In other groups, e.g., some work groups,
members are indistinguishable. That is,
members of the group cannot be ordered.
B. Distinguishability
•
•
•
•
Both a theoretical and empirical issue.
Differences by variable.
Partial distinguishability.
Will assume in the rest of the talk that
members are indistinguishable.
Design
Presume that each person in the group
measured once.
Alternative designs
one measure per group
each dyad in the group is measured
(Social Relations Model)
one informant or target in the group
Example Data
Acitelli Study
148 married heterosexual couples
Y (outcome): satisfaction
X: how positively the partner is viewed
Will use SPSS to illustrate some of the
computations
Univariate Case
Nonindependence


Definition: the degree of greater similarity
(or dissimilarity) between two observations
from members of the same group than
between two scores from members of
different groups
How to model: a group effect
Group Y
Y11
Y12
Person 2 in
Group 1
Y13
Y14
Intraclass Correlation
Group is treated as the independent variable in
a one-way, between-subjects ANOVA:
MSB  MSW
rI 
MSB  (k  1) MSW
where: MSB is the mean square between groups,
MSW is the mean square within groups, and k is
the group size.
Interpretation
2
s
G
rI = 2
2
sG + s E
The intraclass correlation can be viewed as the
proportion of variance due to the group.
Computing Group
Variance by SPSS
MIXED
Y
/FIXED =
/PRINT = SOLUTION TESTCOV
/RANDOM INTERCEPT |
SUBJECT(GROUP) COVTYPE(VC) .
Person is the unit of analysis. “GROUP” is a
variable that codes what group each person is in.
Example
Error Variance (sE2)
Group Variance (sG2)
.094
.153
rI = .153/(.094 + .153) = .621
Husbands and wives similar in satisfaction.
What if Negative?
• Nonindependence is a correlation.
• A correlation can be negative, but the
proportion of group variance cannot be.
• Why would nonindependence be a negative
intraclass correlation?
A. How Negative Correlations
Might Arise?
• Compensation: If one person has a large score, the
other person lowers his or her score. For example,
if one person acts very friendly, the partner may
distance him or herself,
• Social comparison: The members of the dyad use
the relative difference on some measure to
determine some other variable. For instance,
satisfaction after a tennis match is determined by
the score of that match.
B. How Negative Correlations
Might Arise?
• Zero-sum: The sum of two scores is the
same for each dyad. For instance, the two
members divide a reward that is the same
for all dyads.
• Division of labor: Dyad members assign
one member to do one task and the other
member to do another. For instance, the
amount of housework done in the household
may be negatively correlated.
Group Processes
• Make members similar:
Solidarity
• Differentiate members:
Status
Negative Intraclass Correlations
Using SPSS
MIXED
Y
/FIXED =
/PRINT = SOLUTION TESTCOV
/REPEATED = MEMBER |
SUBJECT(GROUP) COVTYPE(CS).
“MEMBER” is a variable that codes the
different person in the group; e.g., it is “1,” “2,”
and “3” in a three-person group.
Not going to consider this any more.
II. X  Y Effects
with Group Data
Group Y
Y11
Y12
Y13
Y14
Group Y
Y11
X11
Y12
X12
Y13
X13
Y14
X14
Computing X  Y Effects
in SPSS
MIXED
Y WITH X
/FIXED = X
/PRINT = SOLUTION TESTCOV
/RANDOM INTERCEPT |
SUBJECT(GROUP) COVTYPE(VC) .
X for example = .314 (CI of .219 to .408)
X  Y as a Random Variable
• The effect of X  Y varies across groups.
• Requires groups of size 3 or more.
Random X  Y Effects in
SPSS
MIXED
Y WITH X
/FIXED = X
/PRINT = SOLUTION TESTCOV
/RANDOM INTERCEPT X |
SUBJECT(GROUP) COVTYPE(IN) .
“IN” allows for intercept and X effects to be
correlated
Not going to consider this any more.
X  Y Effect May Occur
at the Group Level
Just because X is measured at the individual
level does not mean that the effect of X on Y
occurs only at that level.
Need to model the effect of X on Y at more
than the individual level.
A simple idea but not so simple to do.
Consider Four Ways To
Do So
Group Mean (Contextual Analysis)
Group Mean with Group Centering
(Between-Within Analysis)
Group Effect as a Latent Variable
Group Effect as “Everyone Else” (ActorPartner Interdependence Model)
Group Y
Y11
X11
Y12
X12
Mean X
Y13
X13
Y14
X14
Computing X  Y Effects
at Two Levels by SPSS
MIXED
Y WITH X XMEAN
/FIXED = X XMEAN
/PRINT = SOLUTION TESTCOV
/RANDOM INTERCEPT |
SUBJECT(GROUP) COVTYPE(VC) .
Example: Group Mean
X
.112 (CI: -.001 to .226)
XMEAN .576 (CI: .390 to .762)
Suggests that when couples idealize, the
couples are more satisfied.
Centering
Group centering: Subtract from X the mean of
X for the group in which the person is in.
SPSS syntax is the same but now X become
X′ or X minus the mean of X for the group.
Example: Group Centering
X′
.112 (CI: -.001 to .226)
XMEAN .689 (CI: .539 to .837)
Suggests that when couples view partner more
favorably, the couples are more satisfied.
Group X as a Random
Variable
Group Mean may be an imperfect measure of
the couple score.
Treat X11 and X12 as indicators of a latent
variable.
Proposed by Kenny & La Voie in 1984 and a
modified version by Griffin & Gonzalez
used here.
Group Y
Y11
Y13
Y12
Y14
Group X
X11
X12
X13
X14
Estimation
• Not so easy to estimate the model with
multilevel modeling
• Can use the Olsen & Kenny procedure
(Psychological Methods, June issue).
0, .09
0, .19
f1
e1
1
1
3.13
4.26
Male Perception
of the Partner
Male
Satisfaction
.11
1.00
1.00
Couple
Perception
0, .00
0
0, .06
1.53
Couple
Satisfaction
1
U
1.00
1.00
4.26
Female Perception
of the Partner
1
.11
3.13
Female
Satisfaction
1
0, .19
e2
0, .09
f2
Example: Latent Group
CI
Variable
Effect Lower Upper
Individual
.112
.000 .224
Latent Couple 1.532
.574 2.490
Partner Effects
• Actor Effect or X
– Member A’s X affects the member A’s Y
• Partner Effect or XMEAN′
– Member A’s X affects the member B’s Y
Group Y
Y11
X11
Y12
X12
Y13
X13
Group Y
Y11
X11
Y12
X12
Y13
X13
Estimating Partner Effects
by SPSS
MIXED
Y WITH X XPART
/FIXED = X XPART
/PRINT = SOLUTION TESTCOV
/RANDOM INTERCEPT |
SUBJECT(GROUP) COVTYPE(VC) .
XPART is the mean of X of the other members
in the group or XMEAN′
Example: Partner Effects
Effect
b
Actor or X
.400
Partner (XMEAN′) .288
CI
Lower Upper
.307 .494
.195 .381
Four Answers
Effect
X & Mean
X′ & Mean
X & Latent
X & Mean′
Individual Couple
.112
.576
.112
.689
.112
1.532
.400
.288
Four Ways
Group Mean (Contextual Analysis)
Group Mean with Group Centering
(Between-Within Analysis)
Group Effect as a Latent Variable
Group Effect as “Everyone Else” (ActorPartner Interdependence Model)
Which Is Right?
All four are right!
Each has advantages and disadvantages.
X & Mean
Long history: contextual analysis
Easily embedded within multilevel modeling
X′ & Mean (Between-Within)
Statistical advantage: two effects orthogonal
Easily embedded within multilevel modeling
as group centered
X & Latent
Cannot work if the intraclass for X is not
positive and estimates are unstable when
intraclass is small
Latent variable must make sense
Not easily estimated
Can lead to anomalous results
Not frequently adopted by practitioners.
X & Mean′ (APIM)
Has a simple interpretation
Interaction can be meaningful
Very popular in dyadic analysis
Not used frequently in group research
Translation of Effects
We use the X and XMEAN analysis as the basic
analysis.
Denote i as the effect of X and g as the effect of
XMEAN and k as group size:
within= i and between = g + i
actor = i + g/k and partner = (k – 1)g/k
For the latent variable model, the X effect is again i,
and the group effect equals p[1/(k – 1) + rx]/rx
where p is the partner effect and rx is the intraclass
correlation for X.
Concluding Comments
• In studying groups you need to give careful
thought as to what type of effects might
occur.
THINK!!!
• No one “right” way to model effects.
• Be open to alternative ways to estimate
effects.
• Beware of over-simplification
• Beware of over-complexity
Kenny, D. A., Mannetti, L., Pierro, A., Livi, S., & Kashy, D. A.
(2002). The statistical analysis of data from small groups.
Journal of Personality and Social Psychology, 83, 126-137.
Kenny, D. A., Kashy, D. A., & Cook, W. L. (2007) Dyadic data
analysis. New York: The Guilford Press.
Talk can be downloaded at:
http://davidakenny.net/talks/nd.ppt