Small n Evolving Structures: Dyadic Interaction between Intimates
William A. Griffin
Shana Schmidt
Family & Human Development
Arizona State University
There are numerous ways to test and refine models of social processes. The most common
is the “statistical approach” (Gilbert & Troitzsch, 1999); it uses inductive or deductive reasoning
or both to pair the observed behavior with some quantitative assessment of the system (e.g.,
correlations, variance, covariance) measured at a single point in time (Gilbert & Troitzsch, 1999;
Kohler, 2000). Another recently developed method of testing models of social dynamics is
computer simulation (Axelrod, 1997; Hannon & Ruth, 1997; Gilbert & Troitzsch, 1999; Kohler
& Gumerman, 2000; Morrison, 1991). Axelrod (1997) refers to this latter method as the third
way of doing science (inductive and deductive being the first two). Like deduction, it starts with
a set of explicit assumptions -- but it does not prove theorems. This method instead generates
simulated data that can be analyzed inductively. But unlike the inductive method, the simulated
data come from a rigorously specified set of rules rather than direct measurement of the real
world. Induction seeks to find patterns while deductive methods want to determine the
consequences of assumptions -- whereas computer simulations allow experimentation and aid
intuition (Axelrod, 1997; Hannon & Ruth, 1997). Kohler (2000) views simulations as generators
of a phenomenon that demonstrate possible casual pathways, and Axelrod (1997) views
simulations as tools to enrich our understanding of fundamental processes. Either of these
complimentary positions clearly states the need and value of computer simulations of social
processes (Kohler & Gumerman, 2000; Belew & Mitchell, 1996).
The core of our work is an attempt to understand and model the reciprocal evolutionary
dynamics ubiquitous to all social processes (Conti et al., 1998). As such, the research is informed
by multiple scientific disciplines ranging from economics (Arthur, 1994), political science
(Cederman, 1997; 2002) and sociology (Gilbert & Troitzsch, 1999) to computer science (Feber,
1999), physics (Rocha, 1999) and applied mathematics (Newman, 2003). During the last decade
the traditional boundaries between these disciplines have been broached by a general scientific
methodology -- agent based modeling (ABM). ABM is a common language, and with it, comes
common assumptions (Axelrod, 1997; Casti, 1997). Among the relevant assumptions, one is
most pertinent to this research: social processes are complex continuously evolving entities that
adaptively configure themselves according to basic rules that, in turn, modify the environment
housing the agents that comprise the entities. This assumption lays the foundation for our study;
at the general level, we investigate social processes, and at the specific level, we want to know
how dyads – ranging from adult couples to child peers -- form and change. From this foundation
we have several broad questions that focus our work:
 How do dyads emerge? That is, how is the state of a dyadic relationship not obtainable
from simply examining two individuals interacting?
 What is the utility of maintaining an extended relationship?
 Relationships derive from multiscale interactions – ranging from second-to-second to
day-by-day, and eventually, extending into years. What is the morphological
correspondence over these scales?
As evident from these questions, our research objectives extend beyond merely studying
dyads: we address questions about social processes that are germane to all human interactions
involving micro-exchanges of social rewards and the diversity of shifting reinforcers – and how
these crucial processes change over time.
Agent Based Models in Small n Dynamics
An agent based model is one that has agents implementing social interactions according to a
set of rules constructed by the investigator consistent with either theory or observed data. Agents
are processes implemented on a computer that have autonomy and the ability to interact with
other agents and their environment, their actions are goal directed, and they evolve. These
characteristics permit the agents to engage in complex social interactions unguided by the
investigator. A model usually contains many agents, ranging from tens to thousands, with each
being slightly different from the other on the attributes considered relevant by the investigator.
This ensemble of autonomous heterogeneous agents allows social interaction to be
computationally constructed and its outcomes observed based on internalized social norms,
internal behavioral rules, and data acquired on the basis of agent experience (Macy & Willer,
2002). Using a basic complex systems paradigm, the analyst is able to explore the possible
generative mechanisms underlying the observed phenomena (Holland, 1995). Most importantly,
this creation of complex adaptive systems in an artificial world permits the analyst to explore
emergent macro phenomena -- structural patterns not reducible to or evident in the properties of
the micro-level agents (Rocha, 1999). It is the recursive agent-to-agent and agent-toenvironment interaction over time, each modifying and co-adapting to the other, that creates the
critical and continuously evolving macro patterns that social and behavioral scientists study.
For example, over the past two years we have been developing PlayMate, an agent based
modeling program that simulates playgroup formation in children ages 4 to 6 years (Griffin,
Hanish, Martin, & Fabes, 2004). In the fall of each year, new and returning children come
together in our child development lab where many eventually settle into groups of semi-stable
play partners. Factors contributing to the formation of these playgroups are currently unknown.
The children’s social environment differs slightly each year because of variation in playgroup
formations, and these formations derive from the stability of who plays with whom. Both the
groupings and the resulting structures evolve as the year progresses. To keep the model simple
and results tractable, PlayMate uses static (e.g., sex) and dynamic (e.g., sociability) child
attributes to modify the likelihood of interacting with another child. The effects modeled for
these traits or attributes can be modified to represent postulated developmental shifts. Agent
based modeling provides a mechanism for simulating this type of evolution (Griffin, 2003). In
modeling the emergent behavior, we assume that individual child attributes influence the quality
and subsequent likelihood of peer interactions. It is framed around a state transition model,
where a child is always in one of four states: (1) playing with another child; (2) playing with an
adult (a teacher); (3) playing alone after (1); or (4) playing alone after (2). Early in our work it
became obvious that solitary play, either (3) or (4), occupies about 20-25% of a child’s time, and
the propensity to enter and exit this state varies according to (1) or (2). Analyses comparing the
simulated and the realized data indicate that the current implementation of PlayMate effectively
captures the general formation of specific groups within the classroom (Griffin et al., 2004).
Our investigation of children forming playgroups incorporates the key assumptions,
objectives, and goals of agent based models. These fundamental features of an ABM are:
 Abduction, rather than induction or deduction, is used to infer the plausible relationship
between the artificial world created by rule generated agent behavior and the real world.

Putative theoretical assumptions are converted to a set of rules – a computer program –
outlining the behavior of the agents to each other and the environment.
 Each agent possesses a strategy set that is invoked during the interaction with another
agent; agent-to-agent interaction determines and is reciprocally influenced by the
emergence of structure as agent and structure co-evolve within the environment.
 Multiple interactions among heterogeneous agents are studied to examine the emerging
structures that evolve for the particular set of rules implemented by the agents.
 As exchanges and interactions occur in the simulation, agents and the rules they carry
evolve, producing complex social processes analogous to those found in the real world.
In their simplest form, agents represent discrete entities that interact with other agents and
their environment via algorithms; in essence, sets of if-then statements configured to behave in a
putative manner consistent with theory or investigator intuition. In their more complex form,
agents socialize, aggregate, and evolve into embodiments of phenomena (i.e., cultures, mobs,
flocks, economies), and collectively act as a singularity. And most complex of all: the agency of
the collective modifies the base set of if-then rules residing in the individual agents. These
evolving dynamical processes with hierarchical levels of reciprocal influence are the bane and
the blessing of agent based modeling. Shifting alignments and evolving aggregated forms
generate behavioral compositions reminiscent of reality (Horgan, 1995). These displays of
dynamism represent credible arguments for using computational science to capture interorganism interdependencies, sociality, evolution, and population level propensities; in effect,
agent based models provide a mechanism for depicting complex adaptive systems (Bankes,
2002), and yet, to date, no models have been forwarded that examine dyadic processes.
Moreover, a model usually contains many agents, ranging from tens to thousands, with each
being slightly different from the other on the attributes considered relevant by the investigator.
In fact, Page (2002) has argued that agent diversity is a key component for developing realistic
models of social complexity and population level uncertainty.
Modeling the dynamics of children playing was our initial focus because we assumed that it
would be simpler to model than dyads; multiple independent agents, each assessed on a variety
of attributes, and the probability of playing is determined by the similarity of attribute level,
recency of play, and gender preference. Preliminary findings are robust and closely replicate
realized data (Griffin, Hanish, Martin, & Fabes, 2004). Married adults (and other configurations
of established dyads), on the other hand, bring into an interaction a history bound by emotion,
where an action at each time point is inherently linked to individual cognitions and attributions
(Bradbury & Fincham, 1990) and distal and proximal goals that reciprocally intermingle between
spouses. This forms a unique dynamic system that is difficult to simulate (Axelrod, 1997;
Pearson & Boudarel, 2001; Thomas & Malone, 1979), owing to its absence in the literature.
Work in our lab over the past several years has shown that it is possible to create salient
indices of dyadic interaction (Griffin, 2000), and from the indices, pattern recognition software
can be used to classify distressed from nondistressed couples (Griffin, 2002). We have laid the
foundation for determining what is important in a couple’s interaction. From the extracted
features, the final benefit arises – the identification of the behavioral and affect tendencies that
need to be simulated to regenerate the process. We are presently developing a prototype
simulation for the dyadic interaction.
The Critical Dyad: Data Collection and Coding of Marital Interaction
At the Marital Interaction Lab at Arizona State University we began collecting couple and
family interactional data fifteen years ago. During that period we have conducted numerous
studies examining affect and behavioral expression in marital and post-marital interaction, and
the role of disease in marital (e.g., Parkinson’s) and family (e.g., Asthma) interactions (Griffin,
2002; see Griffin, Greene, & Decker-Haas, 2003 for an overview). Across studies, the general
methodology for collecting adult dyadic data has remained the same; a brief overview is given
below.
Procedure.
Couples were seated in a room constructed to resemble a small living area containing prints,
curtains, plants, and two chairs in the center of the room. Two unobtrusive, partially concealed,
remotely controlled cameras were mounted on the walls at head level behind each chair. All
audio-visual and mixing equipment was controlled from a room adjacent to the interaction.
Video signals were combined producing a split screen image with audio being obtained from
lavaliere microphones worn by each spouse.
Interaction Task.
For married couples, the task is always the same. Couples initially are given the Areas of
Disagreement questionnaire (i.e., standard Strodbeck’s revealed differences task; see Gottman,
1979). Each marital partner selects a list of potential disagreement areas typically associated with
marital relationships and ranks the items according to the level and duration of disagreement.
Couples are then instructed on how to use the Affect Generation computers in the lab. After they
become familiar with the procedure, they return to their chairs. With the lab assistant's help, the
couple selects the three most common topics from the list of problem areas, ranks them from
most to least distressing, and agrees to discuss them. The lab assistant then instructs the couple to
engage in a 12- or 15-minute discussion (depends on the study) and attempt to resolve the issues
according to their rankings. The assistant leaves the room and uses a visual or audio signal to
tell the couple to commence their discussion. After the allotted time expires, each dyad member
immediately and independently rates his or her affect.
Affect Ratings.
Spouses were separated immediately after each conversation, and then simultaneously
reviewed the videotaped splitscreen playback, and rated his or her own affect during the
interaction. The videotape was played back through a specially configured microcomputer using
software that overlays a 9-level, color-coded, vertical bar on the 19” color video monitor. This
overlay was positioned beside the face on the monitor of the individual reviewing the tape. The
affect rating ranges from extreme negative (red), through neutral (gray) to extreme positive
(blue), and is controlled by a pc mouse. Extreme negative is at the monitor bottom, neutral is at
mid-monitor, and positive is at the top of the monitor. The width of the bar varies at each affect
level (5 pixel increments) corresponding to the intensity of the affect, neutral being the thinnest.
The widest affect level is 28 pixels wide (1.5 cm). As the reviewer moves the mouse, the affect
bar is high-lighted corresponding to the degree and direction of the affect. For example, as the
individual's affect rating becomes more negative (positive), the mouse is pulled back (pushed
forward) and the appropriate affect level becomes high-lighted, and as the high-lighted area
moves further from neutral, the width of the level expands to reflect intensity. During the review
of the tape, and viewing only his or her own rating, each spouse was asked to move the mouse to
reflect affect experience during the interaction (i.e., "How were you feeling at each moment?").
Software recorded the location of the bar position every second, providing a continuous measure
of affect throughout the interaction. Prior to the first interaction task each couple was taught
how to use the rating system. Additional information about this data acquisition technique and
assumptions about validity is in Griffin (1993).
Coding.
We initially code Talk Turn; reliability is in the mid-.9s (kappa). These delineate the
conversational structure at each turn into the roles of speaker or listener. Nonverbals are then
coded for each talk turn. This is a listener category containing three positive attending behaviors
(i.e., eye gaze, head nod, and back channel) and one negative contemptuous behavior, eye roll.
(We also code gaze for the speaker to examine if the speaker is looking when talking.)
Basically, we include this category to determine if the speaker has reason to perceive the listener
as not listening, being disrespectful, or worse, being contemptuous. This impression by the
speaker may or may not be evident by his or her action, but it usually influences the affect rating,
which then provides an opportunity to compare (e.g., ratio) the speaker versus listener values in
either real time or averaged across the talk turn.
Similarly, by using the Verbal codes, we add additional dimensionality by assessing whether
the speaker is being generally helpful or facilitating (i.e., Problem Solution, Agree) or destructive
(i.e., Negative (e.g., Hostile statement expressing unambiguous dislike or disapproval of a
specific behavior engaged in by the partner. A comment intended to demean or embarrass the
other person.). These are also compared to the listener attending behavior, or examined for
internally consistency with the self-reported affect. In effect, at each unitized time point, either a
talk turn or in real-time, we have knowledge of how each person was feeling, the presence or
absence of constructive or destructive statements, and attending behavior by the listener. In
composite form, these coded behaviors form an index of the process at time tx that permit the
reconstruction, visualization, and pattern classification of dyadic interactions (see Griffin, 2000;
2002). Estimates of these dynamic processes are summarized as multi-dimensional vectors
representing a real-time multivariate index conveying relevant information about the system -ranging from its size, complexity, uniqueness, evolution, and possible trajectory.
Reconstructing the dynamics of dyadic interaction
As evident from the brief discussion above, agent based models typically consist of a huge
number of simple agents implementing rules that, through their collective action, generate
emergent phenomena. With dyadic behavior however, the generation of phenomena derives
from the interaction of only two agents; consequently, the question becomes: How can agent
based modeling methodology be used to generate realistic, and theoretically defensible,
simulations?
If we assume that the feelings of one spouse toward the other spouse is generated by an
attribution set (Bradbury 2002) – a cognitive structure that evolved during the couple’s history
and that is maintained by current events -- and that the internal feelings generated by the
attribution set are expressed as observable verbal statements and nonverbal behaviors, then it
could be argued that such overt behaviors accurately and fully reflect internal affect states or
that, at minimum, they reflect some leakage of those emotions. More importantly, especially for
the modeler of a dynamic system, is that behaviors and emotions in a couple are inexorably
interrelated, each reflecting the same phenomena – the quality of the relationship.
We assume, based on ample evidence, that happily married couples interact differently than
unhappily married couples (see, e.g., Heyman, 2001). This suggests that dyads, of any type or
configuration, can be categorized by their qualitative state, and the criteria for categorization
would be based on measurable characteristics observable during interactions with each other.
The critical decision in developing a simulation of dyadic interaction is determining the
generating process that is reflective of, and yet simultaneously modifies, the quality of the dyadic
state. Our current model presupposes that at each turn in an interaction – either as clearly
demarcated talk turns (constructed from lab tasks), or the more fluid exchanges seen in
interactions between two people – the mechanism driving the behavior in the next small
increment of time is the reduction of state ambiguity. In effect, we assume that all dyadic
interaction has as its objective the disambiguation of the state of the dyad. We assume that each
affective or behavioral nuance expressed during each moment-to-moment exchange
simultaneously reflects and generates the dyadic state and that each participant directs these
features to minimize the ambiguity. By assuming that state disambiguation is the generating
process of dyadic interaction, we can focus on developing algorithms that reduce state ambiguity
between the members of a dyad at each moment in the interaction. However the uncertainty
inherent in an evolving system containing encoding and decoding errors, attributional biases,
differential interests and goals for the dyad insure that some amount of ambiguity always
remains. This supposition invokes two additional assumptions that are necessary to model a
dyad in real time: (1) a state, as defined by the composite behaviors generated by the dyad
members at each moment in the interaction, has Markov properties (i.e., the history of the system
is encapsulated in the present state), and (2) transitions of individual affective and behavioral
responses embedded in the state are stochastic and not deterministic. Consequently, if we allow
the individual’s response set (e.g., verbal, nonverbal, affect) to represent attributes, then an agent
based model can be implemented as an extended interaction of multiple agents, two at a time.
From these extended interactions, the state of the dyadic system continuously evolves in
response to the ambiguity generated by the exchanges.
We are currently developing several methods of modeling this process. Among these, we
describe one below that successfully combines the prerequisite characteristics of agent based
modeling with a mechanism that can potentially generate the behavior patterns seen in married
couples. We define an agent as an individually generated code index A where e.g., A={Affect,
Gaze, Verbal} for the speaker, and A = {Affect, Gaze, Nonverbal} for the listener. Each code
comprising the index is assigned a numerical value (see Griffin 2000; 2002 for details), and in
composite, this set forms a string (or vector, depending on its usage). Agents representing
possible combinations of responses are stored in a large n-dimensional matrix, where n refers to
the number of codes being used to describe the interaction of each person. Each participant in
the dyad can be thought of as being composed of a landscape of agents. An initial startup
response for each person is selected based on known interaction propensities as a function of
marital quality. These response sets, one from each interactant, are compared and the
information is inserted back into the matrix where a new response set is generated. This
represents one interaction episode (i.e., a talk turn) containing a speaker and a listener. Each
iteration attempts to reduce state ambiguity by generating a new response set that is closer to the
response set displayed by the other person in the previous iteration (e.g., gaze longer with higher
affect rating); each response set however is not optimally derived, and by design, contains
heterogeneity. Moreover, the response generated is inserted back into the matrix, increasing its
likelihood of future selection. In effect, the response to the ambiguity modifies the likelihood
that generated it. This allows the agents and the system to evolve over time in response to
environmental information. This “exchange and modify” procedure is iterated several hundred
times to simulate the interaction of a couple. These synthetic data are then compared to realized
data collected in the laboratory.
More colloquially, think of two sentries from opposing camps meeting and exchanging
information about ideas held in their respective camps – the more similar the information
exchanged, the less ambiguous the situation. After the meeting, the sentries return to their
respective camps with information about two factors that describe and summarize the
relationship between camps: (1) how far apart the two camps are (assessed via string edit
distance (Levenshtein)); and (2) the direction of the difference (e.g., sentry 1 has a higher value
message than sentry 2; this are assessed by vector length). After returning to the camp a large
number of agents are polled from sections of the camp that are known to understand the position
held by the opposing camp; an aggregate response is generated from this polling and a new
sentry is sent out to convey the position of the camp. The number of agents polled is a function
of the ambiguity levels -- higher levels result in a larger, more heterogeneous, catchment area of
the camp.
We are currently developing the algorithms and code that implement the iterative process
described above. Our objective is to generate data of dyadic interaction that is indistinguishable
from actual data observed in couples across a wide range of reported martial satisfaction levels.
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