Developmental Psychopathology: Maladaptive and Adaptive Attractors in Children's Close Relationships

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9 Developmental Psychopathology: Maladaptive andAdaptive Attractors in Children’s Close Relationships

erika s. lunkenheimer and thomas j. dishion

Introduction

Routine, day-to-day interactions form the fabric of our interpersonal experi-ence. A mother and her toddler, for example, might have a number of difficultmoments in any given day as they jointly navigate the child’s newly developingautonomy (e.g., the child wants to play with a forbidden toy). On the other hand,the majority of the day will typically be spent speaking about more neutral topicssuch as eating, cleaning up, and getting dressed. Historically, clinical researchershave focused on more atypical, maladaptive interactions between children andtheir parents or peers, with the goal of reducing these aversive interactions.These maladaptive interactions are important. For example, negative interper-sonal interchanges, in moderation, may allow for reflection and insight, offeringimportant opportunities for adaptive change in relationships (Dunn & Brown,1994; Lunkenheimer, Shields, & Cortina, 2007). However, they are also rare:Even with the most problematic children, observational researchers code onlyabout 5% to 10% of family and peer interactions as aversive (Dishion, Duncan,Eddy, & Fagot, 1994). In contrast, adaptive neutral or positive interactions arenot only more common, but we are more likely to observe them in the homeand laboratory contexts. Further, an important goal of preventive interventionprograms is to promote and build on existing adaptive interaction patternsin close personal relationships. Thus both adaptive and maladaptive interac-tions in close relationships should be of interest to clinical and developmentalpsychopathology researchers.

In this chapter, we argue that a nonlinear dynamical systems (NDS) frame-work offers an efficient and theoretically sound analysis of both adaptive andmaladaptive interactions in children’s close relationships, thereby improvingour understanding of the development of psychopathology in children and ado-lescents. Moreover, NDS analysis of close relationships informs the design ofefficient and effective preventive and clinical interventions, which most oftentarget children’s relationships. We first briefly review the study of maladaptive

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relationship influence in developmental psychopathology, focusing on coercionand peer deviancy research with regard to parent–child and child–peer relation-ships, respectively. We then address how NDS theory and principles (attractorsin particular) add to the field of developmental psychopathology by informingresearch on relationship influence. Next, we address NDS methods and reviewempirical research that has used NDS methods to analyze maladaptive attrac-tors to date. Subsequently, we offer new directions for the study of attractors indevelopmental psychopathology, proposing the notions that adaptive attractorsand the study of attractors across contexts may hold untapped value for develop-mental and intervention scientists. Finally, we suggest some implications of NDStheory and methods for clinical interventions with children and their parentsand peers.

Developmental Psychopathology

According to the principles of developmental psychopathology, human behav-ior is determined by multiple influences at various layers of the ecology (e.g.,self, family, neighborhood, culture) that interact continually and dynamically(Cicchetti, 1993; Garmezy & Rutter, 1983; Sameroff, 1995). Developmentalphenomena are thus conceptualized systemically because they are contextuallydependent and organized hierarchically through integrated intrapersonal, inter-personal, and higher-order systemic processes. For example, one could imaginethe process of a parent dealing with her child’s behavior problem at school asembedded within many potential historical and environmental contexts, such asher own school involvement when she was a child, the culture of teacher−parentinteractions at that particular school, and how she and her partner coparent indisciplining the child’s behavior. In conceptualizing these sorts of contextualfactors and their interrelations, the systemic approach to developmental psy-chopathology has been shaped by many theories, including general systemstheory (Sameroff, 1995; von Bertalanffy, 1968), developmental systems theory(Ford & Lerner, 1992), the ecological framework (Bronfenbrenner, 1986), thetransactional model (Sameroff & Chandler, 1975), the organizational approach(Cicchetti & Schneider-Rosen, 1986; Sroufe & Rutter, 1984), and the epigeneticview (Gottlieb, 1991).

A primary aim in developmental psychopathology is the study of individ-ual differences in children’s adaptive and maladaptive developmental trajecto-ries, and the mechanisms that produce continuity and discontinuity in thosetrajectories. Therefore, when studying relationship influences, developmentalpsychopathologists examine how interactions in interpersonal relationships actas the mechanisms that contribute to children’s adaptive versus maladaptivedevelopment. Research targeting these mechanisms has often involved the studyof negative, aversive interactions in family and peer relationships, because theserelationships act as the primary contexts for child development.


284 Erika S. Lunkenheimer and Thomas J. Dishion

A prominent example of this research is the study of parent−child coercion.Coercion theory (Patterson & Reid, 1970) originated in the study of reciprocallyaversive behaviors between mother and child and is based on a social learningperspective. Early analyses of parent−child interactions revealed that both par-ticipants were being mutually shaped to engage in aversive behavior througha combination of classical and operant conditioning. For example, a motherscolding a child for misbehavior can lead to the child’s angry shouting. If themother backs out of the interaction to stop the child’s shouting, both partici-pants are shaped by this behavior. The mother has been shaped to “give up” whenthe child becomes aversive, and the child has been shaped to become aversiveagain the next time the mother scolds or nags. The parent’s negative reinforce-ment contributes to a positive feedback cycle whereby parent−child interactionsbecome increasingly aversive and difficult to manage, leading to the escalationof children’s underregulated, aggressive behaviors and the elevation of parentalrejection over time (Patterson & Bank, 1989). This reciprocal causality betweenparent and child must be understood to inform how children emerge from suchfamily interactions with serious antisocial behavior problems (Patterson, Reid,& Dishion, 1992) and effectively intervene with families to solve these problems(Patterson, 1982). According to coercion theory, these maladaptive interactionpatterns between parents and children can also generalize across contexts tochildren’s relationships with siblings, teachers, and peers.

Research linking parent–child coercion and children’s problem behaviorsover time (Patterson, 1986; Patterson, Capaldi, & Bank, 1991) has illustrated theimportance of relationship influence on children’s developmental psychopathol-ogy. Global ratings of parent–child relationship quality have predicted the devel-opment of disruptive behavior problems in early and middle childhood (Criss,Shaw, & Ingoldsby, 2003; Deater-Deckard, Atzaba-Poria, & Pike, 2004; Harrist,Pettit, Dodge, & Bates, 1994; Mize & Pettit, 1997). Aversive transactions ofmutually negative affect have been observed across adolescence (Conger & Ge,1999), with parents’ and adolescents’ expressed negativity predicting increasesin the other’s negativity in subsequent assessments (Kim, Conger, Lorenz, &Elder, 2001). In fact, experimental research has shown that mothers of conduct-disordered children express more negative affect with their own children thanwith unfamiliar conduct-disordered children, indicating that emotions andbehaviors are entrenched in past relationship history (Anderson, Lytton, &Romney, 1986).

The social learning perspective and the role of negative reinforcement incoercion theory originally prompted a methodological focus on contingency(i.e., action–reaction) patterns in microsocial interaction. Thus developmentalpsychopathologists have also studied relationship influence by examining con-tingency patterns in real time (in seconds or minutes) in relation to child develop-ment. For example, Dumas, LaFreniere, and Serketich (1995) examined groupdifferences in sequential chains of affect and behavior in early mother–child



interactions involving socially competent, anxious, or aggressive children (2.5–6years). Competent children and their mothers showed more positive, recipro-cal chains, with firm limit setting in the face of coercive attempts. Aggressivechildren made more coercive control attempts, and their mothers respondedwith indiscriminant affect and failures in limit setting, as coercion theory wouldpredict. Cole, Teti, and Zahn-Waxler (2003) examined self-initiated and con-tingent affect in mother−child interactions at age 5 in relation to change inchildren’s conduct problems between 5 and 7 years of age. Mothers’ contingentangry emotional responses were uncommon but still contributed to stability inchildren’s behavior problems over time, whereas mothers’ positive contingentresponses predicted reduced levels of child problems.

Research on peer relationships in adolescence has also illustrated the effects ofmaladaptive, real-time interactions in close relationships on developmental out-comes. Dishion, Andrews, and Crosby (1995) examined adolescent friendshipinteractions and their influence on adolescents’ problem behavior. Initial codingof hundreds of interaction patterns with a topographic coding system (e.g., con-verse, negative engagement, positive engagement, and directives) revealed thata vast majority (more than 70%) could be described as simply “converse,” orneutral verbal conversation. This pattern was not particularly useful for under-standing individual differences in the development of serious antisocial behaviorin adolescence (Dishion, Andrews, et al., 1995). Thus a new coding system wasdesigned that captured the salient features of the conversation topics used in ado-lescent friendships. Two topics were identified, deviant talk and normative talk,and two reactions were also identified, “laugh” and “pause.” With only thesefour codes, Dishion and colleagues explained considerable variation in ado-lescent outcomes such as drug use (Dishion, Capaldi, Spracklen, & Li, 1995),delinquency (Dishion, Spracklen, Andrews, & Patterson, 1996), and violence(Dishion, Eddy, Haas, & Li, 1997) with a process they called deviancy training.

For example, in testing the peer deviancy training model of how adolescents’involvement with deviant peers affects their development, Dishion et al. (1996)examined whether friends’ contingent, positive reactions (e.g., laughter) to thetarget child’s deviant talk influenced the development of problem behavior.Contingencies between two proximal behaviors (i.e., lag 1 contingencies fromtn to tn+1) across the interaction can be quantified by a Z score (Gottman &Roy, 1990). When two behaviors reliably covary in time, the Z score indexis greater than 1.96. Using this approach, findings supported the hypothesisthat friends mutually influenced one another through laughter contingent ondeviant talk (Dishion et al., 1996). In general, adolescents tended to match theirlevel of deviant talk to the relative rate of reinforcement, a principle referredto as matching law (see McDowell, 1988). These deviant interactions predictedincreases in adolescents’ self-reported delinquent behavior over a 2-year period,providing support for the ongoing importance of proximal interactions intoadolescence.



As these examples illustrate, we have learned a good deal about the role ofmaladaptive relationship influence in developmental psychopathology to date,and we have the theories to guide further research in the realms of coercivefamily process and deviant peer interactions. This is fitting, because interven-tion programs target the reduction of aggressive, antisocial behaviors, and thusa comprehensive model for the development of such behaviors is essential.However, interventions also aim to increase adaptive relationship patterns, andthus developmental psychopathology research also relies on an understanding ofadaptive and normative developmental processes. The field’s predominant focuson the continuity of maladaptive processes has diverted needed attention awayfrom its emphasis on change, discontinuity, and adaptation for the purposes ofprevention (Granic & Patterson, 2006).

Despite the evidence that contingent, dyadic interaction sequences play a rolein the development of child psychopathology, there are also methodological lim-itations in the sequential analysis of microsocial interactions. First, as previouslystated, the low base rate of negative behaviors expressed during observationalassessments (Dishion et al., 1994) makes the study of positive and neutral behav-iors a needed complement to this research. Second, the quantitative frameworkof sequential analysis may be limited by the manner in which codes are defined(e.g., on a dyadic or individual level), and the number of events within a sequencewill affect the magnitude of the Z score representing relationships among theseevents (Bakeman & Quera, 1995). Third and most important, sequential analysismisses some important properties of a relationship as an evolving and changingsystem. An operative assumption in sequential analysis is that the contingencybetween partners’ behaviors is stationary or linear, meaning that it remains thesame during the course of an observation. However, it is the changing patterns ofinteraction over time that are of interest when studying a close relationship as asystem. For instance, subtle, gradual adjustments such as a wink, smile, or roll ofthe eyes can lead to the emergence of a new interaction pattern that repeats itselfand can have meaning for a close relationship that goes far beyond the tit-for-tat details. It is precisely these sorts of nonlinear interaction patterns that mayhelp illuminate the individual differences in development that developmentalpsychopathologists study.

Finally, there is a vital, overarching feature of relationship processes thatdevelopmental psychopathologists have not yet fully captured: the interrelationsamong different developmental scales (Granic & Hollenstein, 2003; Granic &Patterson, 2006; Lewis, 2000), whether they are time scales (from real timein seconds to developmental time in years) or nested scales of the ecologicalcontext (from the molecular to the cultural). These scales are interdependent;for instance, more macroscopic patterns in the family such as family routines(e.g., a mother working the night shift) might shape more microscopic parent–child dynamics (e.g., the child’s behavior problems with his father at bedtime),which in turn might contribute to changes at the macroscopic level (e.g., marital



discussion that results in new parental work schedules). If we then analyzeparental work status and child behavior problems as two separate variables witha linear relationship, we have missed this fluid interdependency across time andrelational context. Although extant research has provided evidence for a linkbetween processes on different scales (e.g., real and developmental time), weneed to move beyond representing these scales as separate entities and worktoward the direct analysis of their interrelationship.

Application of NDS Theory to Developmental Psychopathology

The application of NDS theory to the study of relationship influence in develop-mental psychopathology allows for the direct analysis of dynamic interrelationsacross scales of time and context. This is because NDS theory conceptualizesdevelopmental phenomena as dynamic systems governed by the principle ofself-organization (discussed in detail later). By treating a close relationship asa dynamic system that self-organizes, we have a theoretical foundation withwhich to understand the structure, organization, and patterning of the relation-ship within and across time and context. An NDS approach also offers corre-sponding empirical tools for researchers to analyze more effectively the wholeof the relationship as a system. These tools allow for the direct study of theinterrelations between real and developmental time, for example, or the study ofnonlinear pattern shifts during the course of a given interaction. Consequently,a major benefit of an NDS approach to developmental psychopathology is thatit provides researchers with the opportunity to study individual differences inthese structural and organizational patterns to determine how these facets of therelationship influence trajectories of child development.

The application of NDS theory to developmental phenomena draws ondynamic and nonlinear systems theories in disciplines such as biology, physics,and mathematics. Many developmental theorists and scientists have paved theway for the application of NDS to developmental psychopathology by arguingfor related systemic and process-based accounts of developmental phenomena(Gottlieb, 1997; Kantor & Smith, 1975; Sameroff & Chandler, 1975; Schneirla,1957; Werner, 1948, 1957). Thus, in many respects, an NDS approach to devel-opment builds on a body of successful interdisciplinary behavioral scienceapproaches.

In describing developmental phenomena from an NDS perspective, The-len and Smith (1994, 1998) argued that developmental changes are, at theircore, qualitatively discontinuous or novel and that such novelty emerges fromwithin the system itself through processes of self-organization. In other words,the interactions within a complex system produce pattern and order withoutexplicit instruction to do so. A system may be bound at various levels; for exam-ple, the self is a system that encompasses multiple intrapersonal processes (e.g.,emotional, cognitive, biological) geared toward development. Any given dyad



(e.g., parent and child) is also a system, as are broader ecological contexts (e.g., aschool district) and more microscopic internal processes (e.g., the neurologicalsubstrates of language production). Although self-organizing, these develop-mental systems are also open systems because they draw in information from thesurrounding environment to increase this internal order or organization. Thisis in contrast to a closed system in which information is not absorbed from thesurrounding environment.

Many different components make up a dynamic, developmental system, andthey operate interdependently and continually on scales of both ecology (i.e.,from the molecular to the cultural) and time (i.e., from milliseconds to years;Thelen & Smith, 1998). Although theoretically these diverse components couldinteract in millions of potential ways, the actual number of ways in which theyrelate to one another is constrained. Through self-organization, hierarchicalintegration emerges, with certain integrative variables (termed order parameters)organizing the behavior of the system into a small number of preferred states oradaptive modes of behavior. These behavioral states that the system settles intoare called attractors, in that the system is “attracted to” a particular state undercertain conditions. In this way, microlevel components of the system organizeand constrain macrolevel organizational processes, and vice versa.

Initially, microlevel elements of the system couple and then attract behav-ior away from other potential states in real time. Therefore attractors are thesepatterns of interactions between elements of the system that become stable overdevelopmental time. Open, living systems are characterized by multistability,in which there are multiple possible attractors in the system, some deeper orshallower than others. The deeper or more stable the attractor, the more likelythat behavior will enter it, remain there, and prove resistant to perturbationsfrom the environment. By definition, attractors should represent relatively fre-quent events because they are the key dynamics underlying a developmentalprocess. Attractors are also contextually dependent (Granic & Patterson, 2006)because they are situated in a complex, multilayered ecology of developmentand are shaped by a history of prior interactions between the given elements.Therefore self-organization in real time and developmental time scales regulateand constrain each other: Individual elements and dyadic patterns between ele-ments are products of past recurring dyadic interactions, which then go on toconstrain future dyadic behavioral repertoires (Cicchetti & Toth, 1997; Dumas& LaFreniere, 1995).

Relationships as Nonlinear Dynamical Systems

Interpersonal relationships are self-organizing in that they produce ordered pat-terns that can be characterized using multiple NDS principles, as illustrated inthis volume and elsewhere (Dumas, Lemay, & Dauwalder, 2001; Lewis, 2000;Pincus & Guastello, 2005). At present, we focus specifically on how attractors



can be used to characterize relationship patterns. As applied to a relationship,an attractor is a systemic tendency for a dyad to get “stuck” in an exchangepattern that unfolds over time (Fogel, 1993; Fogel & Thelen, 1987). With repet-itive exposure, these interactions may become deeper and deeper behavioralattractors, in the context of which it becomes more difficult to induce or expe-rience change (Hollenstein, Granic, Stoolmiller & Snyder, 2004; Lewis, 2000).Individual and dyadic systems therefore become more entrenched and orga-nized, and less activation is needed to trigger these attractors over time (Granic,2000).

Correspondingly, the relationship system involves the coupling of elementswithin microsocial interactions, as in when a parent’s particular behavioral state(e.g., hostility) is coupled with a particular behavioral state of his or her child(e.g., withdrawal). For example, a father comes home from work exhausted andstressed, sees that his child’s room is a mess, and tells him in an irritated toneto clean it up. The child responds to this aversive tone by ignoring his fatherand continuing to play his video game. The father becomes angry and yells athis son that he never listens to him. The son becomes equally angry and lockshimself in his room for the rest of the night. These behaviors or elements ofthe system repeatedly interact to reproduce this sequence, which then serves asone of the attractor states that organizes the behavioral repertoire of this dyadover time. Another relevant example, as discussed previously, is the coupling ofdeviant talk and laughter in maladaptive adolescent peer interactions (Dishionet al., 1996). This attractor then shapes the available range of behaviors withinthe adolescent peer relationship in which deviant behavior is the preferred andrewarded state.

As illustrated by these examples, proximal, real-time microsocial interactionprocesses in interpersonal relationships are the engines of human develop-ment (Bronfenbrenner & Morris, 1998; Fogel & Thelen, 1987). In fact, manyresearchers have espoused the notion that development is essentially relationalin nature (Diamond & Aspinwall, 2003; Fogel, 1993; Laible & Thompson, 2000).The relationship between the child and his or her environment is an active, self-organizing system in which stability is found not only in the individual but alsoin the processes by which traits are upheld by transactions between the child andthe context (Sameroff & MacKenzie, 2003). A transaction between individualsinvolves a novel qualitative or quantitative change (Sameroff & Chandler, 1975),but subsequently this new dynamic between elements evolves into an attrac-tor over time (Thelen & Smith, 1994). Thus real-time, microlevel interactionprocesses drive the formation of attractors, which characterize the macrolevelorganization of the system, or the relationship within which the interaction lies(Dumas et al., 2001; Pincus, 2001).

Accordingly, one can see how the attractor principle is especially usefulfor our study of relationship influence in developmental psychopathology.Unfortunately, the lack of appropriate methodologies has caused these processes



to remain understudied in the field at large (Hinshaw, 2002). With this in mind,we now address some burgeoning NDS analytic methods and discuss how theyhave been applied to the study of attractors in developmental psychopathology.

NDS Analytic Methods in Developmental Psychopathology

An NDS approach provides an important methodological alternative to thestudy of microsocial interactions of relationship processes (Granic & Hollen-stein, 2003; Granic & Patterson, 2006). Thelen and Smith (1994, 1998) definedinterlinking steps in an NDS-based methodological strategy for the study ofdevelopmental phenomena:

1. Identify the collective variable of interest: An observable phenomenonthat captures the interrelatedness of diverse systemic elements must beidentified. For example, with regard to the development of self-regulat-ion, one might study the most prevalent exchange pattern in the inter-coordination of biological arousal, cognitive appraisal, and emotionalexpression.

2. Describe the attractors of the system: Look at how the system operateswith respect to the collective variable at a descriptive level. For example,map the real-time trajectory of parent–child coregulatory patterns tounderstand their relative stability and instability across various contextsand developmental stages. High stability across contexts or developmen-tal time would indicate an attractor.

3. Map the individual developmental trajectories of the collective variable:Determine whether individual variation in the collective variable overrepeated assessments (or in the case of dyadic research, between-dyadvariation in attractor states) is associated with developmental pathways.For example, consider whether a pattern of joint attention and engage-ment in parent–child interaction could contribute to individual differ-ences in children’s language development.

4. Identify phase transitions in development: Phase transitions occur whenthe underlying pattern of interaction shifts to another pattern underpredictable conditions. When one can predict phase transitions in socialinteraction, both the method with which an interaction dynamic canbe changed and the relevant control parameters become clearer. Forexample, if a talk–listen exchange pattern in a parent–adolescent dyadpredictably shifts into a hostile exchange attractor when discussing prob-lems within their relationship, it is a predictable phase transition, andappraised conflict is the control parameter.

5. Identify control parameters: As discussed in the previous step, the con-trol parameters are the nonlinear agents or mechanisms of change inthe system (see Thelen & Ulrich, 1991). Identification of the control



parameter is the critical step in determining whether a pattern can bechanged through intervention.

6. Manipulate control parameters to generate phase transitions experimen-tally: Following from the prior step, we must subsequently test whetherhypothesized mechanisms of change do, in fact, produce the expectedshift in behavior. For some time, it has been acknowledged that thebehavioral sciences lack rigor with respect to intervention experimentsthat test hypothesized relationships (Cook & Campbell, 1979; Dishion& Patterson, 1999).

These steps offer a research strategy with respect to NDS methods that, iffollowed, would facilitate great improvements over more traditional method-ologies. As illustrated in these guidelines, one aims first to identify an attractorwithin microlevel behaviors and then link this attractor to longer-term develop-mental trajectories. This necessarily involves the measurement of behaviors onat least two time scales: real time (e.g., in seconds or minutes) and developmen-tal time (e.g., over weeks or years). Several innovations in the visualization andmeasurement of microsocial interactions have been developed that allow for thestudy of developmental processes across different time scales. For example, onemay use Fourier analysis to illustrate cyclic patterns in time series data (Newtson,1994, 1998), Karnaugh maps to represent event frequencies of combinations ofbinary variables (Dumas et al., 2001), or dynamic growth modeling to matchsimulations derived from logistic difference equations to observed longitudinaldata (van der Maas & Molenaar, 1992; van Geert, 1994, 1995). In this chapter,we focus on one particular methodology, state space grids (SSGs; Lewis, Lamey,& Douglas, 1999) because it holds significant promise. For a broader review ofthe application of NDS methods to developmental psychopathology, see Granicand Hollenstein (2003).

According to NDS theory, a state space is a concept used to reflect the rangeof behaviors or possible states for a given system. Behavior moves along atrajectory in the state space in real time, and this trajectory is pulled towardcertain attractors (stable behavioral patterns) and away from others. Lewis etal. (1999) developed the SSG, a graphical approach that uses observational dataand quantifies the data according to two ordinal variables that define the statespace for any particular system (see Fig. 9.1 for an example). For instance, thesetwo behavioral variables might consist of parent positive affect on the x- axis andchild positive affect on the y axis, each coded at three levels (e.g., low, medium,and high), resulting in a 3 by 3– cell grid. Each point on the trajectory that movesthroughout the grid then represents dyadic information about the joint affect ofparent and child (e.g., parent is low positive, and child is high positive) in thatparticular time interval. Alternatively, instead of levels of a particular behavior,cells may represent different behaviors such as positive affect, negative affect,neutral conversation, and directives (see Fig. 9.2).



Figure 9.1. Example of a state space grid.

Figures 9.2. State space grids: High (upper) and low (lower) entropy friendship dyadsin adolescence.



Investigators working within a NDS framework have used SSGs to look atseveral structural features of relationship interactions to date, described in moredetail later in the chapter. For example, the analysis of behavioral rigidity and itsconverse, flexibility, is of interest to developmental psychopathologists becausethese features have been linked to mental health outcomes (Hollenstein, Granic,Stoolmiller, & Snyder, 2004). The extent to which the interaction is organized andpredictable versus chaotic and unpredictable is captured through an SSG-basedcomputation of entropy (Attneave, 1959; Dishion, Nelson, Winter, & Bullock,2004). Both rigidity and entropy are related to the concept of an attractor;for example, a dyadic attractor could consist of a rigid interaction patternduring which the dyad’s behavior remains in only one or two affective states.However, despite the advantages of using SSGs to study attractors, the field ofdevelopmental psychopathology has yet to converge on the exact nature of anattractor, its computation, or a formal stochastic test (Lewis, 2000).

Several researchers have successfully used SSGs to identify dynamic patternsof parent–child flexibility and rigidity as key factors in the early emergence ofpsychopathology in children and adolescents (Granic, 2000; Granic, Hollenstein,Dishion, & Patterson, 2003). For example, Hollenstein et al. (2004) examinedthe effect of dyadic parent–child rigidity at the beginning of the kindergartenyear on the development of children’s externalizing and internalizing behav-ior problems across kindergarten and first grade. Externalizing problems aredisruptive problems of underregulation such as hyperactivity, impulsivity, emo-tional lability, and aggression, whereas internalizing problems are problems ofmaladaptive overregulation such as anxiety, fear, and depression (Achenbach,1990). These researchers found that parent–child rigidity predicted the child’sinclusion in the “consistently high” and “increasing” externalizing groups andthe “consistently high” internalizing group of children during the course offour assessments. Further, the effect of rigidity remained after controlling forthe content of the interaction. These findings point to the utility of SSGs forilluminating the effects of real-time dynamic interaction structure on change inchild development over time.

Granic and Dishion (2003) were the first to apply SSGs to the analysis ofadolescent peer deviancy training. They used a time series approach to theidentification of attractors. That is, if two individuals become stuck in a devianttalk attractor, the amount of time they spent discussing that topic should getincreasingly longer during an observation session; thus the “duration of bouts”was used as an index of an attractor. These authors derived a slope score fromthe length of deviant talk bouts over the course of the session, with a positiveslope indicating that bout length increased throughout the session. This slopescore not only differentiated problem from nonproblem youth as measuredconcurrently but also predicted individual differences in adolescent outcomes3 years later, such as authority conflict (arrests, school expulsions, etc.) and drugabuse. This was the first study to link individual differences in the display of an



attractor to individual differences in adolescent development over the course ofseveral years.

Following up on this work, Dishion et al. (2004) applied SSGs to the analysisof adolescent friendship interactions in the Oregon Youth Study by examiningdeviant talk bouts and entropy in dyadic exchanges. The construct of entropyis drawn from Shannon’s work in information theory (Shannon & Weaver,1949). Transitions in events are conceptualized as units of information, and theinformation system can range from being organized and predictable to complexand uncertain. The general idea is that less information is needed to predictreactions from the actions in a low-entropy dyad compared with a high-entropydyad. Dishion et al. (2004) used Attneave’s (Attneave, 1959; Krippendorff, 1986)computation of Shannon entropy, in which entropy (H) is computed simplyby considering the distribution of conditional probabilities within an action–reaction transition matrix. Therefore, an organized dyad would have a transitionmatrix low in entropy (H), and its SSG would show a few cells that were heavilyused and many other cells that remained empty (see Fig. 9.2 upper). Conversely,an unpredictable dyad would have a transition matrix high in entropy where allconditional cells would be equivalently probable (see Figure 9.2 lower).

Dishion et al. (2004) attempted to explain variation in antisocial behavior of200 men at age 24 by observing 30 min of interaction with their friends whenstudy participants were age 13. After controlling for the boys’ prior antisocialbehavior, they found that the duration of deviant talk bouts significantly pre-dicted antisocial behavior 10 years later. Although entropy did not show a maineffect, the interaction term between entropy and deviant talk was significant.As one would expect, adolescents who were both organized in their interactionpatterns (low entropy) and engaged in high levels of deviant talk content werethose who showed the highest levels of antisocial behavior as young adults. Thus,as a result of a dyadic friendship system that was organized around deviance,individual outcomes were highly problematic.

Figure 9.2 shows the SSGs for two dyads from this study. Each grid displaysthe interactions of the friendship dyad throughout the 30-min observationsession, using the codes positive engagement (e.g., compliment, praise), directives(e.g., command, requests), negative engagement (e.g., criticism, blame), and con-verse (e.g., calm talk, discussions). A visual inspection of these SSGs reveals anobvious difference between the dyads in the organization of the dyadic exchange.Even though both interactions had approximately the same number of events,one dyad restricted interactions to one area of the grid, whereas the otherappeared more disorganized and complex. Friends who had long, uninterruptedconversations in the converse–converse area of the grid were the most likely tobe quantified as having a low-entropy interaction. However, it should be notedthat this dynamic structural facet of the interaction did not convey the contentof their exchange. These findings elucidate that to understand the influenceof close relationship interactions on development, it is important to study theinterplay between their content and their dynamic structure.



In summary, these studies demonstrate the possibilities available throughthe use of an NDS approach, and specifically, how important the study ofattractors in close personal relationships is to our understanding of children’smaladaptive developmental trajectories. Clearly, negative interactions appear tohave a distinct and powerful organizing function (Granic & Dishion, 2003),and both the content and structure of these interactions are important fordetermining future problem behaviors (Dishion et al., 2004). However, thesestudies also raise questions about how dynamic systems indices of positive andneutral aspects of microsocial interaction relate to individual differences inchildren’s developmental psychopathology In addition, the analysis of dynamicinteraction patterns as they evolve and change across relationship contexts isimplicated in the study of flexibility and rigidity, yet this research has rarely beenconducted. The remainder of this chapter addresses these issues by offering somenew directions for the study of attractors in developmental psychopathology andby examining the possible application of NDS principles and methods to thestudy of adaptive attractors for the purposes of intervention.

New Directions in the Study of Attractors

Adaptive Attractors

As previously described, there are multiple potential attractors in the behaviorallandscape of a relationship, as delineated by the NDS principle of multistability.Thus rather than focus on only aversive exchanges in family interactions, whichare low base rate by nature, one can look more broadly at all interactions in thefamily and how aversive interactions are related to positive, neutral, or othersignificant behaviors. This is an extremely important point. Considering thatthat negative interactions make up only about 5% to 10 of all coded family or peerinteractions even within clinical populations (Patterson, 1982), it is difficult tostudy repeated, aversive patterns except in the most dysfunctional family systems.

Researchers have been calling for closer study of positive parent–child inter-actions and their role in distinguishing children’s normative and atypical devel-opmental trajectories for some time (e.g., Gardner, 1987, 1992; Pettit, Bates, &Dodge, 1997). Research indicates that conduct-problem children spend less timein joint play and conversation with their parents than do nonproblem children(Gardner, 1987). However, when they do engage in contingent, positive inter-actions, these interactions are protective against the development of problembehaviors (Cole et al., 2003). For example, Lunkenheimer, Olson, and Kaciroti(2007) found that the time-lagged coregulation of positive affect between parentsand their 3-year-old children, specifically children’s positive responses to theirmothers and fathers, predicted lower levels of externalizing behavior problemsacross the transition to school.

We know even less about how more neutral attractors such as the converse–converse attractor mentioned previously contribute to individual differences



Figures 9.3. Parent–preschooler dyads that are high (upper) and low (lower) in theproportional duration of positive–neutral interaction.

in child development. Lunkenheimer, Dishion, and Winter (2008) have foundpreliminary evidence to support the notion that positive and neutral attractorsplay a role in children’s adaptive and maladaptive developmental outcomes. Ina study involving yearly assessments with parents and their children beginningat age 2 years, parent–child dyads were observed interacting in the home duringa variety of tasks (e.g., free play, clean-up, inhibition tasks) and were coded forpositive, neutral, negative, and directive behaviors. These behaviors were thenmapped onto an SSG. These researchers tested whether the proportional dura-tion of time the dyad spent engaged in joint positive and neutral affect at childage 2 years predicted child outcomes at age 4. Figure 9.3 provides examples of aparent–child dyad that spent a high proportion of the interaction in this quad-rant (upper panel) and another dyad that spent a proportionally low time there(lower panel). The proportional duration of dyadic positive–neutral interaction



predicted children’s language (�R2 = .03, p < .001), inhibitory control (�R2 =.03, p < .001), and externalizing behavior problems (�R2 = .01, p < .01) acrossthis formative developmental period (Lunkenheimer et al., 2008). Although pre-liminary, these findings point to the need for more NDS analysis of positive andneutral attractors and their role in children’s developmental psychopathology.

Attractors Across Contexts

Another important new direction for NDS approaches to the study of closerelationships and developmental psychopathology is to pursue a more com-prehensive overview of attractors across contexts. In other words, how do theparticular content or goal of the interaction (e.g., problem solving vs. play) andthe particular relationship in question (e.g., parent vs. peer vs. teacher) influencethe development of attractor patterns and their associated outcomes? AlthoughNDS theorists have argued for the importance of understanding attractors acrosscontexts (Thelen & Smith, 1994, 1998), we have little empirical evidence todate with which to answer these questions. Perhaps the predominant focus onmaladaptive attractors has made it difficult to assess the consistency and per-vasiveness of relationship dynamics across contexts in the child’s life becausewe typically see few of these interactions in observational research sessions. Thestudy of adaptive attractors in close relationships may offer a broader window forexamining how organizational properties of close relationships transfer acrossvarious relationship or environmental contexts in the child’s life.

The evidence that has been gathered thus far suggests that attractors may shiftdepending on the goal of an interpersonal interaction. Granic and Lamey (2002)introduced perturbations to mother–child problem-solving interactions andconsidered the change in interaction structure in reaction to the perturbationfor children defined as comorbid (having both externalizing and internalizingproblems) versus those who were “pure” externalizers. They found that whenthe interaction changed from a problem-solving interaction to one in which thedyad had to “wrap up” and produce a solution, dyads that included comorbidchildren shifted from a permissive to a mutually hostile attractor. This shift didnot occur for parents and children in the externalizing dyads, who remainedpermissive throughout the interaction despite the change in goal.

An NDS index of a relationship (e.g., entropy) may be significantly correlatedacross various interaction tasks, although from a conceptual perspective thesetasks may be quite different. Consider, for instance, that a parent and adolescentare asked to solve an interpersonal conflict regarding the time the youth comeshome in the evening. During this discussion, the dyad shifts in unison betweennegative and neutral bouts that are punctuated by humor. Indeed, humor func-tions as a release valve to promote a shift out of the negative–negative attractorto a more constructive discussion. Then, later, the dyad is asked to plan a familycelebration. This particular task results in circular positive–neutral exchanges,



with no negative bouts. The attractors derived from these two interactions lookquite different, the first being more flexible (as they engaged in a wider array ofaffective states) and the second relatively rigid. However, both interactions arelow in entropy in that even when the dyad shifted states, they did so in unison,much like two dancers shifting from the fox trot to the tango. More important,despite the fact that these interactions pull for different sorts of attractors, eachis appropriately tailored to the specific goal of the interaction.

Therefore, in the study of developmental psychopathology, it is crucial toassess attractors in the context of varying interaction goals, and similarly in thecontext of various relationships. This is especially important in light of the field’semphasis on the role of self-regulation in individual differences in children’s nor-mative and atypical developmental trajectories (Cicchetti & Toth, 1997; Cole,Michel, & Teti, 1994; National Institute of Child Health and Human Develop-ment (NICHD), 2004). Ultimately, individuals are considered flexible or “wellregulated” when they respond to changing interpersonal contexts in diverseways, and rigid when they apply the same interpersonal strategy across inter-personal contexts, regardless of whether it is optimal. For example, if we wereto learn that a child with behavior problems typically engages in a rigid, mal-adaptive attractor with her mother, but not with her father or teacher, it mightinform our basic understanding of the problem: the mechanism underlying herbehavior might be her relationship with her mother rather than generalizedself-regulatory difficulties. In an applied example, imagine if this maladaptiveattractor presents itself when the mother and child are discussing her academicperformance, but not her artwork or her peer relationships; a clinician’s aware-ness of these distinctions could offer points of entry in designing an interventionto improve their relationship. Incorporating these and other considerations, animproved relationship science would make sense of the contextual differencesin peer and family relationships and provide a comprehensive framework forstudying relationship influence within and across these contexts.

Implications for Intervention Science

A critical concern for developmental psychopathologists is the application ofknowledge of basic developmental processes toward intervention, in an effortto change developmental outcomes. Although relationship dynamics are notthe only cause of child psychopathology, they may be particularly critical tothe solution in the context of family treatment (Dishion & Patterson, 2006).Typical family intervention strategies often involve the treatment of multipleaspects of the family system simultaneously in an effort to alter or amelioratethe child’s difficulties. For instance, a family therapist might have a motherpractice her positive reinforcement skills with her child, while also addressinghow the father can support the mother’s efforts during that interaction. Thuseven though researchers often rely on linear approaches to test the effects of



family processes, an NDS framework comes closer to what therapists actuallydo in treatment sessions by more accurately representing the embedded natureof family relationships and the fluid, real-time interactions they attempt to alterin treatment.

One way NDS theory may be applied to improve interventions in children’sclose relationships is through the identification of “control parameters.” Aspreviously mentioned, in NDS theory, control parameters are the nonlinearagents or mechanisms of change in the system. With respect to intervention,control parameters are the constructs and dynamics we seek to identify thatboth predict salient developmental outcomes for children and serve as possibleintervention targets. A better understanding of both adaptive and maladaptiveinteraction dynamics through NDS research could lead to the identification ofcontrol parameters that both improve the treatment of maladaptive interactionsand promote adaptive interactions in prevention-oriented interventions.

Several treatment studies suggest that changing relationship dynamics infamilies reduces children’s problem behavior, thus providing evidence for howspecific aspects of intervention and family process may act as control parame-ters. Intervening systematically in parent–child relationships to improve parentmanagement practices has been shown to reduce child problem behavior (For-gatch & DeGarmo, 1999; Gardner, Burton, & Klimes, 2006; Gardner, Shaw,Dishion, Burton, & Supplee, 2007; Martinez & Forgatch, 2001). Research hasalso shown that reductions in parent–adolescent coercion (Dishion, Patterson,& Kavanagh, 1992) and improvements in parental monitoring (Dishion, Nelson,& Kavanagh, 2003) are associated with reductions in adolescent problem behav-ior. More impressively, therapists’ skills in guiding change in parenting practiceshave been linked to changes in observed parenting and reductions in childproblem behavior (Forgatch, Patterson, & DeGarmo, 2005).

Recent work has taken this a step further by examining the role of parents’positive behavioral support as a mediator of the effects of early interventionon children’s behavior problems (Dishion et al., 2007) and school readiness(Lunkenheimer, Dishion, Shaw, et al., 2008). These studies incorporated proac-tive parenting behaviors (e.g., praise, positive reinforcement) and neutral behav-iors that served to maintain interactive engagement such as conversation aboutroutine matters and verbal acknowledgments of another’s statement. In bothstudies, intervention had a modest but significant effect on child outcomesthrough its impact on parents’ positive behavior support. Successfully engagingparents in positive parenting practices may help increase the frequency of seem-ingly routine parent–child interactions such as conversation and play, which areformative to the development of school readiness factors such as language andself-regulation (Baldwin, 1995; Hart & Risley, 1995). This work illustrates theneed for more research on the role of adaptive dyadic attractors as potential con-trol parameters in preventive interventions, especially with respect to childrenin formative developmental periods.



Another important way an NDS perspective can be useful to interventionscience is its application to the technologies of change in actual clinical prac-tice. It became evident some time ago that simple knowledge of the behavioralprinciples underlying a clinical problem was not sufficient for helping peoplechange (Patterson, 1985). It is rare that clients arrive in clinics with a strongsense of how they want to change or a willingness to give up the interactiondynamics within which their troubles are embedded (DiClemente & Prochaska,1998). Thus an emerging trend in intervention science is to focus on strategiesto enhance motivation to change (Miller & Rollnick, 2002). Dishion and col-leagues developed the ecological approach to family intervention and treatment(EcoFIT) program, which is designed to both prevent and treat maladaptive out-comes in children and adolescents using motivational interviewing strategies.The core of the program is the Family Check-Up (Dishion & Stormshak, 2007),which begins with a videotaped microsocial observational assessment in thehome. In the subsequent feedback session, the therapist reviews the videotapedparent–child interactions with the parent and engages the parent in a discussionabout his or her motivation to change aspects of these interactions. The thera-pist builds on the parent’s existing strengths while also addressing maladaptiveparent–child interaction patterns. NDS-based visual stimuli such as the SSGcould be a powerful source of information for parents in this respect, enhancingmotivation and also providing directions for change. In this way, NDS couldhelp improve the efficiency of family interventions.

In conclusion, an NDS approach to the role of children’s close relationshipsin developmental psychopathology has proved beneficial for modeling promi-nent theories in the field. Additionally, this approach has spawned promisingmethodological techniques to test those theories, especially with respect to mal-adaptive interaction patterns. However, we have much farther to go. The inte-grated study of adaptive and maladaptive attractors in microsocial interactioncan inform basic research in children’s normative as well as atypical develop-mental pathways, and offer potential avenues for preventive intervention efforts.Understanding the roles of positive and neutral interaction attractors in childdevelopment, examining attractors across the contexts of varying interactiongoals and relationship types, and applying NDS principles to the analysis ofchange mechanisms in intervention will bolster the utility of NDS theory todevelopmental and intervention science.

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Developmental Psychopathology: Maladaptive and Adaptive Attractors in Children's Close Relationships

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