Download 1 David A. Kenny APS Boston May 29, 2010 David A. Kenny APS

David A. Kenny
APS Boston May 29, 2010
DataToText Examples
Example 1: Moderation Example
In moderation, the causal effect of one variable is assumed to vary as a function of another
variable, the moderator. As an example, consider a study by Livi, Carrus, and Gentile, M. (2010)
that investigated the causal of effect that noise sensitivity (X) leads to stress (Y). However, this
effect might be moderated by the need for cognitive closure (M). Those high in the need for closure
may show a weaker effect noise sensitivity on stress. Moreover, we are controlling for gender (C)
in all of our analyses.
A DataToText macro has been written is SPSS (can be downloaded at
http://davidakenny.net/dtt/modtext.sps) called ModText. After the macro is downloaded, it is run
and the dataset is also opened. The syntax command to run the macro for the example dataset is:
ModText x = sens_RumoreC /y = GHQ_tot/m = BccrttC/xn='Noise'
yn='Stress' mn='Need for Cognitive Closure' clist=gender.
where sens_rumoreC, GHQ_tot/m, BccrttC, and gender are the variable names in the SPSS data
file.
The output of ModText is as follows:
WARNING: 1. There is one outlier in the dataset. Examine the output to see what cases
are considered to be outliers.
MODERATION MODEL
The causal variable is Noise Sensitivity, the outcome variable is Stress, and the moderator
variable is Need for Need for Cognitive Closure. The causal model is as follows: The variable
Noise Sensitivity is presumed to cause Stress linearly whose causal effect is presumed to be altered
linearly by Need for Cognitive Closure.
RESULTS
Descriptives
There are a total of 90 cases. The power of the test of moderation assuming that f squared is
.02 (a small effect size, but optimistic according to Aguinis (2004)) is .10, and the power of the test
of moderation assuming that f squared is .15 (a moderate effect size) is .44. The means and
standard deviations are presented in Table 1. There is one covariate that is controlled in all
analyses. The covariate does not explain a statistically significant proportion of variance (.0048) of
Stress (F(1, 86) = .468, p = .496). The unexplained standard deviation in Stress is equal to .386, and
the multiple correlation for the regression equation is .393.
Effects of Noise Sensitivity and Need for Cognitive Closure
The results of the moderated regression analysis are summarized in Table 2. The overall
effect of Noise Sensitivity on Stress, when Need for Cognitive Closure is equal to zero, is .151 (p =
David A. Kenny
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APS Boston May 29, 2010
.006), with a small effect size (r = .291). The overall effect of Need for Cognitive Closure on Stress,
when Noise Sensitivity is equal to zero, is .034 (p = .686), with a less than small effect size (r =
.044).
Interaction Effects
The interaction between Noise Sensitivity and Need for Cognitive Closure is equal to -.244
and is not statistically significant (p = .061), with a small effect size (f squared = .0405). As the
Need for Cognitive Closure increases, the causal effect of Noise Sensitivity, though not statistically
significant, is moderated or weakened. The effect of Noise Sensitivity for persons who are one
standard deviation below the mean on Need for Cognitive Closure (-.538) is equal to .282 (p = .002)
with a large effect size (r = .545); the effect of Noise Sensitivity for persons who are one standard
deviation above the mean on Need for Cognitive Closure (.536) is equal to .020 (p = .823), with a
less than small effect size (r = .038). The effect of Noise Sensitivity equals zero when Need for
Cognitive Closure equals .617. (See Table 3 and the graph or table as the end of the SPSS output.)
Test of Nonlinearity
The tests of nonlinearity were as follows: The quadratic interaction effect of Need for
Cognitive Closure with Noise Sensitivity is .106 and is not statistically significant (p = .594). The
quadratic interaction effect of Noise Sensitivity with Need for Cognitive Closure is .122 and is not
statistically significant (p = .437). There is then no evidence of nonlinear effects.
Regions of Statistical Significance
Considered here are regions of Need for Cognitive Closure in which the effect of Noise
Sensitivity on Stress are statistically significant (Aiken & West, 1991). The negative effect of
Noise Sensitivity is statistically significant when Need for Cognitive Closure is in the region
(Johnson-Neyman) from -1.510 to .151. The negative effect of Noise Sensitivity has a statistically
significant region (Potthoff extension) when Need for Cognitive Closure is in the range of from
-1.510 to .062.
Table 1: Descriptive Statistics
Variable
Mean
Standard Deviation
------------------------------------------------------------------------Noise Sensitivity
-.004
.788
Need for Cognitive Closure
-.001
.537
Stress
1.781
.411
Table 2: Moderated Regression Coefficients
Predictor
Estimate Effect Size p
------------------------------------------------------------------------------------------Intercept
1.794
<.001
Noise Sensitivity
.151
.291
.006
Need for Cognitive Closure
.034
.044
.686
Noise Sensitivity x Need for Cognitive Closure -.244
.0405
.061
(Note that the effect size measure in Table 2 is r for Noise Sensitivity, r for Need for Cognitive
Closure, and f squared for the interaction.)
davidakenny.net/dtt/moderate.htm and davidakenny.net/dtt/apimd.htm
David A. Kenny
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APS Boston May 29, 2010
Table 3: Predicted Means for the Causal Variable (-1 and +1 sd) and the Moderator (+1 and -1 sd)
Need for Cognitive Closure
Noise Sensitivity
-.538
.536
------------------------------------------------.792
1.552
1.797
.784
1.997
1.828
References
Aguinis, H. (2004). Moderated regression. New York: Guilford.
Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting
interactions. Thousand Oaks, CA: Sage.
Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social
psychological research: Conceptual, strategic and statistical considerations. Journal of Personality
and Social Psychology, 51, 1173-1182.
davidakenny.net/dtt/moderate.htm and davidakenny.net/dtt/apimd.htm
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APS Boston May 29, 2010
davidakenny.net/dtt/moderate.htm and davidakenny.net/dtt/apimd.htm
David A. Kenny
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APS Boston May 29, 2010
Example 2: APIM Distinguishable Dyads Example
The Actor-Partner Interdependence Model (APIM; Gonzalez & Griffin, 1999; Kenny,
Kashy, & Cook, 2006) a model of dyadic data and it uses characteristics of the person and the
person’s partner to predict a person’s response. As an example, I use data collected by Linda
Acitelli (1997). Dyad members are said to be distinguishable because in this case one member is
the husband and the other member is the wife. The equations are
YH = bH + aHXH + pHWXW + EH
YW = bW + aWXW + pWHXH + EW
where EH and EW are correlated. I use positivity of perceptions of the partner to predict relationship
satisfaction. The key question is the following: Does seeing your partner positively lead to
relationship satisfaction both for yourself and your partner? The one covariate included in the
analysis is the number of years married. In an APIM analysis, we regress both husband’s and
wife’s satisfaction on both husband’s and wife’s positivity.
There is a macro written in SPSS (soon to be available at davidakenny.net\dtt\apimd.htm)
that accomplishes these analyses:
ApimDText a = RSpouse/p = PSpouse /y = RSatisfied /distvar=RGender
/dyadid = coupleid xn = 'Other Positivity' yn = 'Satisfaction' clist= yearsmarried.
Actor-Partner Interdependence Model for Husband and Wife
The focus of this study is the investigation of the effect of Other Positivity on Satisfaction
and how that effect differs for Husband and Wife. Both the effect of own Other Positivity (actor)
and the effect of partner's Other Positivity (partner) on Husband's and Wife's Satisfaction are
studied. There is a total of 148 dyads with no missing data, each with one Husband and one Wife.
The total number of individuals is 296. The means and standard deviations for Husband and Wife
are presented in Table 1. There is one covariate that is controlled in all analyses. The covariate
explains a statistically significant amount of variance of Satisfaction controlling for actor and
partner effects (.035 proportion of the total variance for the Husband and .011 proportion for the
Wife), chi square test with 1 degree of freedom equal to 6.126 (p = .013).
RESULTS
Actor Effects
The actor effect for Husband is equal to .374 and is statistically significant (p < .001), with a
small effect size (beta = .289), and the actor effect for Wife is equal to .523 and is statistically
significant (p < .001), with a medium effect size (beta = .404). The difference between these two
actor effects is not statistically significant (p = .312).
Partner Effects
The partner effect from Wife to Husband is equal to .372 and is statistically significant (p <
.001), with a small effect size (beta = .242). The partner effect from Husband to Wife is equal to
davidakenny.net/dtt/moderate.htm and davidakenny.net/dtt/apimd.htm
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APS Boston May 29, 2010
.261 and is statistically significant (p = .005), with a small effect size (beta = .201). The difference
between these two partner effects is not statistically significant (p = .454).
Actor-Partner Interactions
The actor-partner interaction for Husband Satisfaction is equal to -.214 and is not statistically
significant (p = .322). The partner effect for persons who are one standard deviation above the
mean on Other Positivity is .261 and for persons who are one standard deviation below the mean on
Other Positivity is .485. Additionally, the actor-partner interaction Wife Satisfaction is equal to
-.134 and is not statistically significant (p = .523). The partner effect for persons who are one
standard deviation above the mean on Other Positivity is .202 and for persons who are one standard
deviation below the mean on Other Positivity is .324. The difference between these two interaction
effects is not statistically significant (p = .711).
The effect of the absolute difference of the two members on Other Positivity for Husband's
Satisfaction is equal to -.095 and is not statistically significant (p = .491). Thus, if two members
have the same score on Other Positivity, their score on Husband's Satisfaction is .095 units higher
than it is for a dyad whose scores on Satisfaction differ by one unit. The effect of the absolute
difference of the two members on Other Positivity for Wife's Satisfaction is equal to -.073 and is not
statistically significant (p = .585). Thus, if two members have the same score on Other Positivity,
their score on Wife's Satisfaction is .073 units higher than it is for a dyad whose scores on
Satisfaction differ by one unit. The difference between these two discrepancy effects is not
statistically significant (p = .876).
Effect of the Distinguishing Variable
The predicted score on Satisfaction for those who score zero on Other Positivity is 3.608 for
Husband and 3.583 for Wife and that difference is not statistically significant (p = .620), with a less
than small effect size (d = .043).
Relation of Actor and Partner Effects
An analysis was made of the relative size of actor and partner effects. For Husband, there is
evidence for "couple model" (Kenny & Cook, 1999) in that the actor and partner effects are not
statistically significantly different. It may make sense to sum or average the two Other Positivity
scores for Husband. For Wife, there is evidence for "couple model" (Kenny & Cook, 1999) in that
the actor and partner effects are not statistically significantly different. It may make sense to sum or
average the two Other Positivity scores for Wife.
Error Variances and Correlation
The correlation between Husband errors with Wife errors is equal to .444. Thus, the two
members of the dyad are similar to one another. The error variance for Husband is equal to .346 and
for Wife is .323. The R squared (Kenny, Kashy, & Cook, 2006), controlling for the covariate, for
the Husband is equal to .189 and for the Wife is equal to .211.
Test of Distinguishability
The test of distinguishability yields a chi square test with four degrees of freedom that equals
1.561 with a p value of .816. Because the test of distinguishability is not statistically significant, we
conclude that members are statistically indistinguishable. The test of the effect of the distinguishing
davidakenny.net/dtt/moderate.htm and davidakenny.net/dtt/apimd.htm
David A. Kenny
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APS Boston May 29, 2010
variable is not statistically significant (p = .620). The test of the interaction of the distinguishing
variable with the actor effect is not statistically significant (p = .312), and the test interaction of the
distinguishing variable with the partner effect is not statistically significant (p = .454). Finally, the
test that error variances are different is not statistically significant (p = .632).
Treating Dyad Members as Indistinguishable
The overall actor effect is equal to .441 and is statistically significant (p < .001), with a
medium effect size (beta = .340). The overall partner effect is equal to .313 and is statistically
significant (p < .001), with a small effect size (beta = .242). The intraclass correlation treating dyad
members as indistinguishable is equal to .448. If we treat the dyad members as indistinguishable,
the R squared is equal to .185. Treating the dyad members as indistinguishable, there is evidence
for "couple model" (Kenny & Cook, 1999) in that the actor and partner effects are not statistically
significantly different. It may make sense to sum or average the two Other Positivity scores.
The actor-partner interaction is equal to -.181 and is not statistically significant (p = .322).
The partner effect for persons who are one standard deviation above the mean on Other Positivity is
.224 and for persons who are one standard deviation below the mean on Other Positivity is .404.
Alternatively, the effect of the absolute difference of the two members on Other Positivity is equal
to -.073 and is not statistically significant (p = .527). Thus, if two members have the same score on
Other Positivity, their score on Satisfaction is .073 units higher than it is for a dyad whose scores on
Satisfaction differ by one unit. Treating dyad members as indistinguishable, there is not evidence of
an actor-partner interaction.
Table 1: Descriptive Statistics
Variable
Mean
Standard Deviation
--------------------------------------------------------Other Positivity
Husband
-.018
.523
Wife
.018
.474
Satisfaction
Husband
3.608
.656
Wife
3.588
.638
Table 2: Effect Estimates
Effect
Coefficient
p value
Beta
---------------------------------------------------------------Actor (Husband)
.374
<.001
.289
Actor (Wife)
.523
<.001
.404
Partner (Wife to Husband)
.372
<.001
.242
Partner (Husband to Wife)
.261
.005
.201
davidakenny.net/dtt/moderate.htm and davidakenny.net/dtt/apimd.htm
David A. Kenny
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APS Boston May 29, 2010
Figure 1
APIM Diagram
.374*
Husband
______________________> Husband
Other Positivity
Satisfaction
/\
\
/\
/\
/
\
/
\
(
\
/
\
(
\
/
\
(
\
/
E1
(
\
/
)
.925*[
X
]1.328
(
/
\
)
(
.372* /
\ .261*
E2
(
/
\
/
(
/
\
/
\
/
\
/
\/
/
\/
\/
Wife
.523*
Wife
Other Positivity ____________________> Satisfaction
* p < .05
References
Kenny, D. A., & Cook, W. (1999). Partner effects in relationship research: Conceptual
issues, analytic difficulties, and illustrations. Personal Relationships, 6, 433-448.
Kenny, D. A., Kashy, D. A., & Cook, W. (2006). Dyadic data analysis. New York:
Guilford.
davidakenny.net/dtt/moderate.htm and davidakenny.net/dtt/apimd.htm