International Journal of Behavioral Development 2005 The International Society for the [624176]

International Journal of Behavioral Development #2005 The International Society for the
2005, 29 (2), 101–109 Study of Behavioural Development
http://www.tandf.co.uk/journals/pp/01650244.html DOI: 10.1080/01650250444000405
The Actor–Partner Interdependence Model: A model of
bidirectional effects in developmental studies
William L. Cook
Maine Medical Center, Portland, ME, USADavid A. Kenny
University of Connecticut, Storrs, CT, USA
The actor–partner interdependence model (APIM) is a model of dyadic relationships that integrates
a conceptual view of interdependence with the appropriate statistical techniques for measuring and
testing it. In this article we present the APIM as a general, longitudinal model for measuring
bidirectional effects in interpersonal relationships. We also present three different approaches totesting the model. The statistical analysis of the APIM is illustrated using longitudinal data on
relationship specific attachment security from 203 mother–adolescent dyads. The results support the
view that interpersonal influence on attachment security is bidirectional. Moreover, consistent with ahypothesis from attachment theory, the degree to which a child’s attachment security is influenced byhis or her primary caregiver is found to diminish with age.
The Actor–Partner Interdependence Model (APIM: Kashy &
Kenny, 1999; Kenny, 1996a) is a model of dyadic relationshipsthat integrates a conceptual view of interdependence in two-
person relationships with the appropriate statistical techniques
for measuring and testing it. The APIM is being increasinglyused in the social sciences; for example, in studies of emotion(Butler, Egloff, Wilhelm, Smith, Erickson, & Gross, 2003),
health (Butterfield, 2001), leisure activities (Berg, Trost,
Schneider, & Allison, 2001), communication competence(Lakey & Canary, 2002), personality (Robins, Caspi, &
Moffitt, 2000), and attachment style (Campbell, Simpson,
Kashy, & Rholes, 2001). Additionally, the model has beenrecommended in the area of the study of families (Rayens &
Svavardottir, 2003), close relationships (Campbell & Kashy,
2002), small groups (Bonito, 2002), and as a framework forevaluating treatment outcomes in couple therapy (Cook, 1998;Cook & Snyder, in press). The purpose of this article is to
describe the APIM and discuss one key use of the model: to
assess bidirectional effects within longitudinal designs. Webegin with an explication of interdependence in relationships
from conceptual and statistical perspectives. This necessarily
involves a discussion of measurement issues in relationshipresearch. Next we use a path diagram to elucidate the
components of APIM. Three different statistical approaches
for testing the parameters of this path diagram are providedand the advantages and disadvantages of each are discussed.
We then illustrate the application of the APIM by investigating
processes of interpersonal influence in the attachment securityof mothers and their adolescent children.
Interdependence and the assumption of
independent observations
As the name suggests, the APIM is designed to measure
interdependence within interpersonal relationships. There isinterdependence in a relationship when one person’s emotion,
cognition, or behaviour affects the emotion, cognition, orbehaviour of a partner (Kelley & Thibaut, 1978; Kelley,
Holmes, Kerr, Reis, Rusbult, & Van Lange, 2003). A
consequence of interdependence is that observations of twoindividuals are linked or correlated such that knowledge of oneperson’s score provides information about the other person’s
score. For example, the marital satisfaction scores of husbands
and wives tend to be positively correlated. This linkage ofscores is more generally referred to as nonindependence of
observations . Other processes by which nonindependent ob-
servations may arise in dyad scores are discussed elsewhere(Cook, 1998; Kenny, 1996a; Kenny & Cook, 1999). Com-
monly used statistical procedures (e.g., ANOVA and multiple
regression) assume independent (uncorrelated) observations inthe dependent variable. Consequently, the scores of two‘‘linked’’ individuals would be treated as if they were
completely independent observations, when in fact the
correlation would indicate that they are not independentobservations. When the assumption of independence is
violated, the test statistic (e.g., torF) and the degrees of
freedom for the test statistic are inaccurate, and its statisticalsignificance (i.e., the pvalue) is biased (Kenny, 1995; Kenny &
Judd, 1986; Kenny, Kashy, & Bolger, 1998). Thus, whenever
there are nonindependent observations, it is necessary to treatthe dyad (or group) rather than the individual as the unit of
analysis (see Kenny, 1995; Kenny & Judd, 1986).
The presence of nonindependence is determined by
measuring the association between the scores of the dyadmembers. Different measures are used depending on the type
of dyad. For dyads with distinguishable members (e.g.,
husbands and wives or older and younger siblings), noninde-pendence can be measured with the Pearson product–moment
correlation. For indistinguishable dyad members (e.g., iden-
tical twins or same-sex couples), nonindependence is measuredwith the intraclass correlation (Kenny, 1995). According to
Correspondence should be sent to William L. Cook, Center for
Psychiatric Research, Maine Medical Center, 22 Bramhall Street,
Portland, ME 04102-3175, USA; e-mail: cookw@mmc.org.The research was supported in part by a grant from the National
Science Foundation (DBS-9307949).

102 COOK AND KENNY / ACTOR–PARTNER INTERDEPENDENCE
Myers (1979), a liberal test ( p¼.20, two-tailed) should be
used in testing whether there is nonindependence because the
failure to detect nonindependence could lead to bias in
significance tests. If the independence of observations issupported statistically, then one could, in principal, treat the
individual rather than the dyad as the unit of analysis. The
larger Nwould generally result in greater power for testing
hypotheses. Additional information on the measurement of
nonindependence as well as the effects on power of using the
dyad rather than the individual as the unit of analysis can befound in Kenny et al. (1998) and Gonzalez and Griffin (2001).
Measurement and the meaning of
interdependence
What does it mean to treat the dyad rather than the individual
as the unit of analysis? It means that the sample size for the
analysis is based on the number of pairs of participants(parent–child, siblings, or married couples), rather than thenumber of individuals. This requirement begs another ques-
tion. How can the scores of two individuals be analysed as if
they are one? One of the early solutions to this problem was totake the sum or the average of the two individual scores and
treat it as a ‘‘dyad score’’ in the analysis. This solution had
some appeal because it seemed, on the surface at least, to implythat a ‘‘higher-order’’ phenomenon was being measured,
something truly ‘‘dyadic’’. Baucom (1983) recognised that
there are conceptual problems with such measures when hecriticised the practice of summing husband and wife scores on
marital satisfaction measures to create a dyad-level variable.
Christensen and Arrington (1987) have re-articulated thiscomplaint:
For instance, a summing (or averaging) procedure could
produce results that would equate a couple in which one spouse
is very satisfied and the other unsatisfied with a couple in which
both partners are moderately satisfied (the average maritalsatisfaction score would be the same). Most clinicians andresearchers would conceptualize these two cases in very
different ways, and the unit resulting from an averaging
procedure would not capture these distinctions (pp. 268–269).
Thus, regardless of the type of dyad (e.g., husband–wife,
father–child, brother–sister), summed or averaged scores maywell create a mis-measure of the dyad. This may also be the
case when ratings are made of dyadic or group characteristics
such as cohesion (Cook & Kenny, 2004).
The actor–partner interdependence model
As an alternative to combining the scores of dyad members to
manage nonindependent observations, a generally moreinformative approach is to retain the individual unit measures
but treat them as being nested within the dyad. As will be seen,
this approach allows for the estimation of both individual anddyadic factors. For purposes of illustration, suppose we areinterested in the development of relationship-specific attach-
ment security in mother–adolescent relationships (Cook,
2000). By relationship-specific attachment security, we meanhow secure each person feels in relationship to the other and
not the more global measure of attachment style. For brevity,
these measures are referred to as attachment security .A
unidirectional, social-mould theory would predict that theadolescent’s attachment security would be predicted by
characteristics of the mother. A more contemporary, bidirec-
tional view would predict that each person influences the other(Kobak & Hazan, 1991; Lollis & Kuczinski, 1997; Kuczinski,2003).
Figure 1 presents the path diagram for the essential version
of the APIM. There are four variables in this model. The twodependent or outcome variables are labelled Yand Y
0and
stand for the outcomes for persons A (e.g., mother’s attach-
ment security or Y) and B (e.g., child’s attachment security or
Y0), respectively. The XandX0variables are the measures of
Person A and Person B, respectively, that are expected to
predict YandY0. In the most basic longitudinal model, the
model of focus in this article, they would be based on the same
measurement instrument as the Yvariables but measured at
some earlier point in time. For example, earlier measures of themother’s attachment security ( X) and the child’s attachment
security ( X
0) are expected to predict mother’s ( Y) and child’s
(Y0) attachment security at a later point in time.
The two most central components of the APIM are the
actor effects and the partner effects. In longitudinal terms, an
actor effect measures how much a person’s current behaviour is
predicted by his or her own past behaviour. In Figure 1, theactor effects are represented by the two paths labelled a. The
actor effect is a measure of the stability of mother’s attachment
security in relationship to the child ( XtoY) and the stability of
the child’s attachment security in relationship to the mother
(X
0toY0). Developmental researchers have long understood
that the prediction of development (i.e., change) must occurwithin the context of having statistically controlled for thestability of the outcome variable. Thus, the inclusion of actor
effects in longitudinal models has a long history, although these
stability effects have not been typically labelled as actor effectsuntil recently (Cook, 1998). What may not be as well
understood is that actor effects, to be measured accurately,
should be estimated while controlling for partner effects.Partner effects measure how much one person is influenced by a
partner and are represented in Figure 1 by the diagonal paths
labelled p.
1For example, the path from XtoY0might measure
the mother to adolescent partner effect (how much her priorattachment security predicts her child’s later attachment
security) and the path from X
0toYwould measure the
Figure 1. The actor–partner interdependence model (APIM). X¼
data for person A, Time 1; X0data for person B, Time 1; Y¼data for
person A, Time 2; Y0¼data for person B, Time 2; U¼residual
(unexplained) portion of person A’s Time 2 score; U0¼residual for
person B’s Time 2 score. Single-headed arrows indicate causal or
predictive paths. Double-headed arrows indicate correlated variables.
Paths labelled as aindicate actor effects and paths labelled as pindicate
partner effects.
1Although we use the term influence , an actor or partner path in the model
may simply indicate a predictive relation, not necessarily a causal one.

adolescent to mother partner effect (i.e., how much the child’s
prior attachment security predicts his or her mother’s later
attachment security). Partner effects measure a form of
interdependence. Consequently, they cannot be measuredwithin individuals; they are by definition dyadic. Because the
APIM is not limited to longitudinal designs, actor effects can
more generally be defined as the effects of a person’s owncharacteristics on his or her own outcomes, and partner effects
are defined as the effects of a partner’s characteristics on a
person’s outcome.
There are two additional features of the APIM to consider,
correlations between the independent variables and correla-
tions between residual variables: The correlation between the
independent variables is indicated by the curved, double-headed arrow between Xand X
0.There is an important
statistical role for this correlation. It ensures that if either of the
Xvariables predicts a Yvariable, it is done while controlling for
the other Xvariable. Thus, actor effects are estimated
controlling for partner effects, and partner effects are estimated
controlling for actor effects.
It is unlikely that the Xvariables explain all the variance in
the dependent variables. The extent to which the Yvariables
are not explained by either of the Xvariables is represented in
Figure 1 by UandU0; the residual or error terms for YandY0,
respectively. If the actor and partner effects are the only reason
for the correlation between YandY0(i.e., the only source of
nonindependence), when the variance in Yand Y0due to
partner effects is removed, Yand Y0should no longer be
correlated. However, there may be other reasons for the
correlation between Yand Y0.For example, if the two
individuals come from the same family, a family-level factor
may cause their scores to covary. The curved, double-headed
arrow connecting Uand U0indicates that the unexplainedvariance in the dependent variables is correlated, even after the
covariance due to partner effects has been removed. Specifica-
tion of a correlation between the residuals controls for
additional sources of nonindependence such as family effects.
It should be clear from Figure 1 that when one tests for
bidirectionality, one is not testing a single hypothesis but rather
two hypotheses. Bidirectionality is supported only if Xpredicts
Y0and X0predicts Y(i.e., both partner effects are statistically
significant). Typically, theory would suggest the inclusion of
additional variables into the model. If the added variablesmeasure characteristics of the individuals in the dyad, theireffects on the dependent variables would also be either actor or
partner effects. For example, in Figure 2 child age and gender
have been added to the model for mother’s and child’sattachment security. If child age or child gender predicts the
child’s own attachment security, it is a child actor effect. If
child age or child gender predicts the mother’s security inrelationship to the child, it is a partner effect. Note that there
would be bidirectional effects if mothers feel more secure in
relationship to older children (a child partner effect for age)and if children feel more secure if they have been raised bysecure mothers (a partner effect for mother’s attachment
security). Thus, the two partner effects do not have to be
defined over the same variable to conclude that there isbidirectional influence.
Interaction effects
In the language of the analysis of variance (ANOVA), actor and
partner effects are main effects, i.e., the direct effects of the
independent variables on the dependent variables. Thestandard ANOVA model also tests whether combinations ofINTERNATIONAL JOURNAL OF BEHAVIORAL DEVELOPMENT, 2005, 29 (2), 101–109 103
Figure 2. The actor–partner interdependence model including child age and gender variables. Child age, child gender, security of child’s
attachment to mother, and security of mother’s attachment to child at time t 1predict security in child’s attachment to mother and security in the
mother’s attachment to child at time t 2. Single-headed arrows indicate causal or predictive paths. Double-headed arrows indicate correlated
variables.

104 COOK AND KENNY / ACTOR–PARTNER INTERDEPENDENCE
the independent variables have an effect on the outcome,
interaction effects. In terms of parent–child relationships,
interaction effects can be important determinants of child
outcomes. Sameroff (1975; Sameroff & Chandler, 1975)coined the term interactional model to describe the investigation
of child outcomes that are affected by the crossing of parent
and child characteristics. The interactional model has alsobeen referred to as the ‘‘goodness of fit’’ model because it
assumes that developmental outcomes depend on the extent to
which parent and child characteristics match or fit together(Lerner, 1993; Thomas & Chess, 1977).
In an interactional model, one of the independent variables,
called the moderator variable, affects the size of the effect of
another independent variable on the outcome variable. Ofparticular importance are partner characteristics that moderate
the effect of actor characteristics, or actor–partner interactions.
As an example of actor–partner interaction, suppose thattemperamentally easy children are relatively compliant to low
power-oriented parental demands and temperamentally diffi-
cult children are relatively compliant to high power-orientedparental demands. In this case, the main effects (parentalpower orientation and child temperament) would not be
predictive of child compliance. Rather, it is the combination or
goodness-of-fit of parent and child characteristics that deter-mines child compliance. The interaction of actor and partner
characteristics can also be used to model synergy or reciprocity.
If reciprocity of negativity is characteristic of their relationship,the product of parent and child negativity scores at one point in
time would be predictive of their negativity scores at a later
point in time, independent of the main effects (i.e., actor orpartner effects). That there is often conceptual overlap in the
nature of the data (i.e., interpersonal interactions) and analytic
terminology (i.e., statistical interaction) no doubt has led to
confusion in the use of the term interactional in research
studies.
Sometimes the size of an actor or partner effect can be
different depending on the value of a third variable. Forexample, if a parent has been very responsive to the child, the
probability that the child will comply with a subsequent
parental request (a partner effect) may be greater than inparent–child relationships of unresponsive parents (Parpal &
Maccoby, 1985). This would constitute a partner-moderated
partner effect because parental responsiveness (a partner
characteristic) moderates a partner effect (i.e., the probability
that the child will comply with a parental request). If we look
for a more proximal cause, we may find that children in apositive mood or who, more generally, have warm feelings fortheir parents, are more compliant (see Lay, Waters, & Park,
1989). This would constitute an actor-moderated partner effect
because the child’s attitude toward the parent (a childcharacteristic) moderates the probability of his or her being
compliant with a parental request (a partner effect). An
interaction like this is what is meant when it is said thatrelationships are contexts for interaction (Hinde & Stevenson-
Hinde, 1987; Lollis & Kuczinski, 1997). The relationship as
constituted by the enduring attitudes and expectations of oneperson toward another (e.g., the child’s positive attitudetoward the parent) moderates how that person responds to
the other at any given moment.
Age as a moderator of actor and partner effects. In the previous
example, relationships (and attitudes toward others) were
proposed as moderators of interpersonal processes affectingchild compliance. Given the importance of parent–child
relationships to child development, developmental researchers
are naturally interested in the development of relationships. In
this regard, we do not simply mean the processes of influencethat unfold over time, but how the age and development of the
participants affects these processes (Hartup & Laursen, 1999).
Stated differently, the interest is in how development mayaffect actor and partner effects.
As noted earlier, one type of actor effect is that the person’s
past score on a variable will predict his or her future score onthe same variable. For example, a child’s attachment securityat age 15 would tend to be a strong predictor of his or her
attachment security at age 16. According to attachment theory
(Bowlby, 1973), the strength of this relationship should changeover time. As the child ages, working models of relationships
(i.e., over-learned expectations or schemas) should become
increasingly stable and influential psychological factors. Con-sequently, the degree to which an 11-year-old’s attachment
security predicts his or her attachment security at age 12
should not be as strong as the degree to which a 17-year-old’sattachment security predicts his or her attachment security atage 18. In other words, the child’s age moderates the child’s
actor effect, revealing that the stability of internal working
models of relationships is developmental. Such would con-stitute an actor-moderated actor effect .
The child’s age might also moderate the parent partner
effect in this example. It could be that the more the child’sexpectations are predicted by intrapersonal processes (i.e., by
internal working models), the less they would be predicted by
interpersonal processes (i.e., the parent’s actual behaviour). Iftrue, we may find that the older the child, the less the influence
of the parent’s attachment security on the child’s attachment
security. Such would constitute an actor-moderated partner
effect.
The statistical analysis of the APIM
In this section, we provide general guidance for the analysis of
the APIM using three statistical techniques: ordinary regres-sion analysis, structural equation modelling (SEM), and
multilevel modelling (MLM). The methods presented here
apply to dyads in which two persons are distinguishable bytheir role (e.g., mother and child) or some other characteristic
(e.g., birth order of siblings). The methods for the analysis of
dyads in which the members are indistinguishable (e.g.,identical twins, gay couples) are detailed elsewhere (Griffin &
Gonzalez, 1995; Kenny 1996a; Kenny, Kashy, & Cook, in
press).
Ordinary regression analysis
The simplest, but least general approach to the assessment of
bidirectional influence in longitudinal research with dyads is
via a pair of separate multiple regression analyses, one each forpredicting the outcome of the two partners. In one analysis, themother outcome variable (i.e., the variable measured at time
t
2) would be regressed on the child and mother predictor
variables measured at time t 1. In the other analysis, the child
outcome variable would be regressed on the child and mother
predictor variables measured at time t 1. (The order of these
two analyses does not matter.) Couple is the unit of analysis(i.e., the Nbeing the number of dyads, not the number of

individuals), so the independence assumption is not violated.
The interests are the magnitude of actor and partner effects in
each analysis and their statistical significance. The actor effect
estimating the stability of the variable over time would almostalways be present, but other actor effects (e.g., age or other
measures of actor characteristics) may not be. If any of the
partner effects are present, the inference can be that there isinterpersonal influence or interdependence. A partner effect
for each partner must be statistically significant to support the
hypothesis that influence is bidirectional. Additionally, themodel may also include contextual variables or other factorsthat are not personal characteristics of either partner.
There are drawbacks to this ordinary least squares
approach. First, this method of analysis does not allow a testof differences between the two actor effects or between the two
partner effects of the dyad members. So if a researcher were
interested, for example, in whether children influence theirmothers more than mothers influence their children, this
approach cannot address the question. Second, it cannot
address the question of whether for either individual the actoror partner effect is the larger effect. Third, it also does notallow one to pool effects across dyad members. For example, it
may be that the partner effect for neither mothers nor children
is statistically significant when evaluated separately, but whenthe two partner effects are pooled, the combined partner effect
is significantly different from zero. Thus, one would conclude
that there is interdependence, but it is not role-specific. Testsof pooled effects generally have more power than do tests of
separate effects (Kenny & Cook, 1999).
Structural equation modelling (SEM)
The SEM approach has several advantages over the ordinary
regression analysis approach to testing the APIM. With respect
to the APIM, key features of SEM are (1) that more than one
equation can be estimated and tested simultaneously and (2)the relations between parameters in different equations can be
specified. This allows a direct translation of the model in
Figure 1 into one model to be estimated and tested using aSEM statistical program (e.g., LISREL, EQS, AMOS). The
dyad is the unit of analysis (i.e., the Nis equal to the number of
dyads) and the model is estimated from the covariance matrixof all the independent and dependent variables. Unless latentvariables are used, the sample size requirements are no
different than for ordinary regression analysis (Kenny & Cook,
1999).
Different SEM software programs have different languages
and procedures for estimating the components in the model,
but all require the same general specifications. In the basicmodel, there are two equations, one for each of the dependent
variables. So for an analysis of mother–child dyads, there
would be one equation written for the mother outcome at timet
2and another for the child outcome at t 2. The mother and
child variables at time t 1would be the predictor variables in
this equation. The regression coefficient for the mother’s timet
1variable would estimate the actor effect for mothers and the
regression coefficient for the child’s time t 1variable would
estimate the partner effect for the child on the mother. The
child outcome at time t 2would be the dependent variable in
the second equation and, again, the predictor variables would
be the mother and child variables measured at time t 1. In this
case, the regression coefficient for the mother variable wouldestimate the partner effect of the mother on the child and theregression coefficient for the child variable would estimate the
child actor effect. There is a residual variance for each
equation, representing the effect of all the other predictor
variables that have not been included in the equation pluserrors of measurement. The residual effects from the mother
and child equations would be allowed to correlate, as noted
earlier, to control for other sources of nonindependence. Theindependent variables (mother’s and child’s scores at time t
1)
would also be allowed to correlate so that partner effects would
be estimated while controlling for actor effects and vice versa.Some software programs now have graphical interface toolsthat can be used to draw a path model like that of Figure 1.
The software translates the drawing into the corresponding
specifications.
A powerful feature of SEM is that it is possible to compare
and statistically evaluate the size of parameters within the
model, something that cannot be done within least squares.For example, one can test whether the mother partner effect is
equal to the child partner effect, which answers the question of
who has more influence in the relationship. One can testwhether actor effects, partner effects, and residual variances areequal across time, thus testing whether the data have
stationarity. Finally, one can compare parameters within a
given role (e.g., just the mothers); for example, whether theactor effect for mothers is equal to the partner effect for
mothers. To compare the size of two parameters, one
compares the chi-square goodness-of-fit value for a modelwith the two parameters forced to be equal to the chi-square
goodness-of-fit value for the same model but without the
parameters set to be equal. If the difference between the twochi-square values is statistically significant, then forcing the
parameters to be equal has significantly worsened the fit of the
model. Thus, it is inferred that the parameters are not equal.This procedure, referred to as the chi-square difference test, isdescribed in any text or manual for structural equation
modelling.
Multilevel modelling (MLM)
The analysis of the APIM using multilevel modelling proce-dures, compared to SEM methods, requires a considerable
shift in thinking about the organisation of data and theestimation of effects. Whereas there are two equations in theSEM version of the APIM, one for each member of the dyad,
MLM estimates all the parameters of the model within a single
equation and so implies a very different data structure. Table 1presents an example of the data for three dyads organised for a
MLM analysis. There are several ways to model dyadic
processes within MLM. We illustrate what is called the‘‘two-intercept’’ approach that was introduced by Rauden-
bush, Brennan, and Barnett (1995).
The first two variables in Table 1 are dyad ID and the
person number. Note that for every dyad there is a record for
person 1 (e.g., mother) and a record for person 2 (e.g., child)
and always in that order (or always in the order of childfollowed by the mother). This ordering reflects the nestedstructure of the data; person nested within dyad. The data
must be organised according to the appropriate nesting
structure for most MLM programs. The next variable in Table1 is the dependent variable (DV) or outcome score. The value
of the dependent variable is typically different for each member
of the dyad. That each person occupies a separate record givesthe appearance that the individual is the unit of analysis, butINTERNATIONAL JOURNAL OF BEHAVIORAL DEVELOPMENT, 2005, 29 (2), 101–109 105

this is not the case. MLM programs take into account the
nesting of individuals within dyads and the concomitantnonindependence of observations this entails.
As in any regression analysis, the predictor variables must be
on the same record as the outcome variable. This introduces acomplexity into the data organisation, because the identity ofthe actor and the identity of the partner shift with each record.
For record 1, the actor is mother (her outcome is the Y
variable) and the partner is child. For record 2, the actor is thechild (his or her outcome is the Yvariable) and the partner is
mother. To ensure that the appropriate actor and partner
variables are used in predicting a particular outcome, thefollowing procedure can be used.
First, in the two-intercept approach, two dummy variables
are created to identify whose outcome the Yvariable refers to
for that particular record. The mother dummy variable,
labelled M_dum in Table 1, is scored as 1 for records in which
mother’s outcome is the Yvariable and 0 if the child’s outcome
is the Yvariable. The child dummy variable, labelled C_dum in
Table 1, is scored as 1 for records in which the child’s outcome
is the Yvariable and 0 if the mother’s outcome is the Y
variable. These dummy codes are used to create the predictorvariables that measure and test for actor and partner effects.
Recall that the original predictor variables are the mother and
child scores at time t
1. These two scores are multiplied by the
two dummy variables, as if to create moderator variables.
Multiplying the mother dummy variable by the mother time t 1
variable reproduces the mother’s time t 1variable for records
where the mother’s outcome is the Yvariable and she is the
actor, but it produces a zero for records where the child’s
outcome is the Y variable. This new variable is the motheractor variable ( M_act ). Multiplying the mother dummy
variable by the child’s time t
1variable reproduces the child’s
time t 1score for records where the mother’s outcome is the Y
variable (and so the child is the partner) and a zero otherwise.This new variable is therefore the child partner variable
(C_part ). Now, for all the records in which the mother’s
outcome is the Yvariable, the mother’s time t
1score is the
mother actor variable and the child’s time t 1score is the child’s
partner variable. Otherwise, these variables are scored with
zeros.
Creation of the child actor variable and the mother partner
variable uses the same procedure as above, but now the
predictor variables are multiplied by the child dummy variable.
When the child dummy variable is multiplied by the child’stime t
1score, this creates the child actor variable ( C_act ),
which will be the child’s time t 1score for records where the
child’s outcome is the Yvariable and the child is the actor.When the child dummy variable is multiplied by the mother’s
time t 1score, it reproduces the mother’s time t 1score on
records where the child’s outcome is the Yvariable and the
mother is in the partner role ( M_prt ). In summary, four
variables are created; a mother actor variable, a mother partnervariable, a child actor variable and a child partner variable.These variables have values for every record, but they have
non-zero values only for those records where the appropriate
dyad member’s outcome is the Yvariable. Thus, they are
predictor variables only for the outcomes that they are
supposed to predict.
Specifications
After the data file has been created and read into the multilevel
modelling program, the details of the analysis must bespecified. It is necessary to indicate number of levels (of
nesting) in the data. For the APIM, the outcome variable (e.g.,
attachment security at time t
2) has two levels; dyad and
individual. The dyadic level is identified by the ID variable,and the individual level is identified by the person variable.
Next, one specifies the independent variables, indicating for
each whether it has fixed and/or random components, and if ithas a random component, at what level (individual or dyadic)
it varies. There are a total of six independent variables in the
simplest version of the APIM. The model has no ordinary errorterm. Rather M_dum andC_dum variables are used as intercept
variables for mother and child, respectively, instead of the
usual common intercept. The intercept variables will each havea fixed component, which is the intercept, and a random
component. The correlation between random components for
M_dum andC_dum models the residual covariance in Figure 1.
Not all MLM programs (e.g., SAS and SPSS
2) allow for the
multiple intercepts and zero error variance needed to replicate
precisely the SEM approach, but several programs do (e.g.,
HLM and MLwiN).
The other four variables in the model are the two actor
variables and the two partner variables. Estimation of these
coefficients is the primary goal of the analysis. Most multilevelmodelling programs also allow for the comparison of effects
(e.g., whether mother or child has the larger partner effect)
using a procedure comparable to the chi-square difference test.Thus, it shares an important advantage with SEM.106 COOK AND KENNY / ACTOR–PARTNER INTERDEPENDENCE
Table 1Organisation of data for multilevel modelling
ID Person DV M_dum C_dum M_act C_act M_prt C_prt
3 1 3.8 1 0 5.0 0 0 3.5
3 2 3.7 0 1 0 3.5 5.0 0
5 1 4.4 1 0 3.7 0 0 3.5
5 2 3.4 0 1 0 3.5 3.7 06 1 4.7 1 0 4.3 0 0 2.8
6 2 3.0 0 1 0 2.8 4.3 0
DV¼dependent variable; M_dum ¼dummy code identifying records where mother is the actor; C_dum ¼
dummy code identifying records where child is the actor; M_act ¼mother actor variable; C_act ¼child actor
variable; M_prt ¼mother partner variable; and C_prt ¼child partner variable.
2SPSS and SAS can be used to estimate a version of the two-intercept model
but space precludes a complete description of these models.

Illustration
Returning to the example of attachment security in mother–
adolescent dyads, we said that the bidirectional view wouldpredict that each person influences the other. We can test this
using the APIM. Our outcome variables are mother’s comfort
depending on the adolescent ( Y) and the adolescent’s comfort
depending on the mother ( Y
0), both obtained at time t 2. Our
predictor variables are mother’s comfort depending on the
adolescent ( X) and the adolescent’s comfort depending on
mother ( X0)at time t 1, approximately a year earlier. These data
are from a larger study of attachment security in family
relationships (Cook, 2000). That study investigated the
interdependence of attachment security using the socialrelations model (SRM: Cook, 1994; Kenny & La Voie,
1984). The SRM analysis (Cook, 2000) was cross-sectional,
but provided information on whether one person’s attachmentsecurity in relationship to another family member was due to
family, actor, partner, or unique relationship effects.
3We will
focus here only on the variable ‘‘relationship specific comfortdepending on others’’, which we refer to as attachment security .
Participants
The data involve 203 mother–adolescent pairs who provided
data at both of two waves of sampling, approximately 1 year
apart. The average age at time 1 of the mothers was 46 years
(SD¼3.36), and the average age of the adolescent was 16
years ( SD¼2.15). There were 96 boys and 106 girls in the
adolescent sample.
Analysis and results
We first examine the APIM with only main effects included,which corresponds to the path diagram presented in Figure 2.
We also test for the equality of the actor and partner effectswithin each role; that is, whether a person’s actor effect is equal
to his or her own partner effect. The purpose of this test is
primarily to illustrate the technique of testing equalityconstraints. Finally, we test whether age of the adolescent
moderates the actor or partner effects of the mothers and
adolescents. We performed all tests using the SEM approachbecause for distinguishable dyads it offers the simplest andmost direct way to perform the analysis. The EQS program is
used for all SEM analyses.
Actor effects. The question of whether characteristics of the
person predict his or her own outcome over time is measured
and tested by the actor effects. The results are presented in thefirst four rows of Table 2. For both mothers and adolescents,
the actor effects for attachment security are large, positive, and
statistically significant, indicating that there is reliable stabilityin the degree to which they feel comfortable depending on each
other. We do note that as predicted, the actor effect for the
mother is more stable than it is for the child. Two additionalactor effects were tested for the child; whether the child’sgender and age predict changes in the child’s attachment
security. Neither of these actor effects was statistically
significant.
Partner effects. The question of whether characteristics of the
mother or the child predict each other’s attachment security ismeasured and tested by the partner effects. The results arepresented in the middle section of Table 2. Both of the partner
effects for attachment security are positive and statistically
significant. These results indicate that the mother’s prior levelof attachment security influences the child’s later level of
attachment security, and that the child’s prior level of
attachment security influences the mother’s later level ofattachment security. In other words, the influence process is
bidirectional.
In many cases an interesting question might be: Who has
more influence on whom? As seen in Table 2, the effect of
child on the mother is slightly larger than the effect of the
mother on the child, but the difference is very small and notvery meaningful theoretically. For these data, a more interest-ing comparison is between the actor and the partner effects
predicting a given person’s outcomes. For the adolescent the
comparison is between the adolescent actor effect (anintrapsychic variable) and the mother partner effect (an
interpersonal variable). For mother outcomes, this comparison
is between the mother actor effect and the adolescent partnereffect. These comparisons are made using the chi-square
difference test, which was described earlier. Because the basic
APIM is a saturated model and so has zero degrees of freedom,the chi-square for goodness of fit for the model is zero. If weconstrain the adolescent’s actor effect ( b¼.663) and the
mother partner effect ( b¼.127) to be equal, we gain a degree
of freedom and the chi-square will be non-zero. If the chi-square were statistically significant, we would reject the null
hypothesis that the two covariances are equal. For this test, we
findw
2(N¼203, df ¼1)¼33.23, p5.001, indicating thatINTERNATIONAL JOURNAL OF BEHAVIORAL DEVELOPMENT, 2005, 29 (2), 101–109 107
3The actor and partner effects of the APIM should not be confused with
similarly named effects from the social relations model (Kenny & La Voie, 1984).
In the social relations model analysis, actor and partner effects are components ina measurement model (i.e., latent variables or factors) rather than causal
variables. In the APIM the actor and partner effects reflect causal or predictive
effects.Table 2
APIM of mother–child dynamics (N ¼203 dyads)
APIM parameters Estimate Z
Actor effects
C1!C2 .663* 11.40
M1!M2 .789* 16.18
Child age 1!C2 .037 1.86
Child gender 1!C2 –.045 –0.51
Partner effects
C1!M2 .155* 3.07
M1!C2 .127* 2.26
Child age 1!M2 .013 0.77
Child gender 1!M2 .139+ 1.82
Interaction effects
Child age* M1!M2 –.017 –0.827
Child age* C1!C2 .056+ 1.891
Child age*M 1!C2 –.052* –2.167
Child age* C1!M2 –.027 –1.043
The estimates are unstandardised regression coefficients. M1¼
mother’s attachment security, time t1;C1¼child’s attachment
security, time t 1;M2¼mother’s attachment security, time t2;C2¼
child’s attachment security, time t 2. An asterisk between two variables
indicates an interaction effect. Interaction effects were tested within amodel that included all the main effects.
*p5.05; + p5.10.

108 COOK AND KENNY / ACTOR–PARTNER INTERDEPENDENCE
the two effects cannot be treated as equal without seriously
worsening the fit of the model. The adolescent’s outcome is
affected more by his or her own prior level of attachment
security than by the mother’s influence over the course of ayear. The comparison of the predictors of mother’s outcomes
yields a similar result. The mother actor effect ( b¼.789) is
significantly larger than the child partner effect ( b¼.155),
w
2(1,N¼203)¼58.27, p5.001.
Interaction effects. Lastly we tested whether child age moder-
ated the actor and partner effects for attachment security inmother–adolescent dyads. This involved creating two interac-
tion variables; (1) the product of mother’s attachment security
by child age, and (2) the product of child’s attachment securityby child age. Prior to performing these multiplications, we
centred each of the variables (Aiken & West, 1991). Centring
involves subtracting out the mean of each variable in theinteraction. It has the important role of reducing multi-
collinearity due to high correlations between interaction terms
and the independent variables from which they are created,and it increases the interpretability of the main effects. In thecase of dyadic measures, the centring variable (or mean) that is
subtracted out should be the mean of the partners’ scores taken
together (Kenny & Cook, 1999; Kenny et al., in press). Inother words, one does not subtract the mean for mothers from
the mother score and the mean for adolescents from the
adolescent score; rather, one subtracts the mean of theircombined score from both of their scores.
The interaction terms were included as independent
variables, along with the actor and partner main effects, in anew model predicting mother and child attachment security
(time t
2) outcomes. The results of this analysis are presented in
the bottom third of Table 2. The first two rows of the tablepresent the effects of child’s age as a moderator of the actoreffects. Age does not moderate the mother actor effect or the
child actor effect at conventionally accepted levels of statistical
significance. The last two rows in Table 2 present the effects ofchild’s age as a moderator of the partner effects. The results
indicate that the child’s age moderates the mother partner
effect, but not the child partner effect. The attachment securityof younger adolescents is affected more by their mothers than
that of older adolescents, b¼/C0.052, Z¼/C02.167, p5.05.
This result is consistent with the hypothesis from attachmenttheory that the internal working models of younger adoles-
cents, compared to older adolescents, are affected more by
recent relationships with significant others (Bowlby, 1973). Italso demonstrates how the APIM can be used to testhypotheses on the development of relationships.
4
Conclusion
This article has presented and illustrated the APIM as a means
of conceptualising and measuring interdependence in close
relationships, with a special focus on the assessment ofbidirectional effects. Interdependence is measured by theAPIM partner effect, the extent to which one person’s
thoughts, feelings, or behaviour influence the thoughts,feelings, or behaviour of another person. Bidirectional effects
are present when the partner effects for both members of a
dyad are present and statistically significant. Although the
APIM has often been presented within the context of cross-sectional data analysis (Berg et al., 2001; Butler et al., 2003;
Butterfield, 2001; Campbell et al., 2001; Lakey & Canary,
2002), we hope we have demonstrated that it is equallyapplicable to longitudinal data analysis.
There are other models of dyadic relationships that
correspond to other forms of dyadic nonindependence. Theseinclude the common fate model, in which group effects (orcouple effects) are distinguished from individual effects, and
the dyadic feedback or mutual influence model, in which each
person’s outcomes affect the other’s outcomes (Cook, 1998;Kenny, 1996a). Of all these models, the APIM has been—and
is likely to continue to be—favoured by researchers. As we
hope this article has shown, the APIM corresponds to patternsof interpersonal processes that are of considerable interest to
family and developmental researchers.
As a conceptual model of interdependence, the APIM is
applicable to a variety of analytic situations. For example, intime-series analyses of dyadic interaction such as sequential
analysis and cross-lagged regression analysis, the conceptuali-
sation of actor–partner interdependence is the same aspresented in Figure 1. The only difference is that the unit of
analysis is time (or event) rather than dyad. In this context, the
autocontingency or autocorrelation effects are actor effects andthe measures of reciprocity (i.e., cross-lagged contingencies)
are partner effects (Cook, 2002). The APIM has also been
used in complex analyses of growth in relationships. Forinstance, Raudenbush et al. (1995) tested whether growth (or
decline) in a partner’s job-role quality predicted growth (or
decline) in own or partner’s marital satisfaction. Kurdek(1998) has also published analyses that integrate the APIMwith growth curve modelling. He found that growth in a
person’s depressive symptoms was associated with decline in
own marital satisfaction (an actor effect) but was not associatedwith decline in partner’s marital satisfaction.
In summary, the APIM is a method of estimating
interdependence in naturalistic studies of close relationships.It is particularly well-suited to developmental research in areas
where experimentation is not appropriate. Finally, the APIM is
not a model that is in competition with other methods ofanalysis such as sequential analysis or growth curve analysis.
Rather, it is a general model that is complementary to these
other methods. The integration of the APIM with otheranalytic methods has the potential to address important andcomplex questions about human development.
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