Adolescent friendship as a dynamic system: entropy and deviance in the etiology and course of male antisocial behavior.

Considerable evidence and theoretical support exist for the idea that adolescent friendships have a unique and significant impact on long-term patterns of social development (Hartup, 1983; Piaget, 1954; Sullivan, 1953). Indeed, the last 20 years are marked by a growing literature on the positive effects of friends (e.g., Berndt, 1996; Bukowski & Hoza, 1989; Cauce, 1986; Furman, 1996; Newcomb & Brady, 1982; Parker & Asher, 1993; Youniss, 1983). Unfortunately, there is also a dark side to friendships, contributing, sometimes dramatically, to social maladaptations and problem behavior (Hartup, 1996).

The study of negative peer influence is especially relevant to understanding the development and course of antisocial behavior (Dishion, French, & Patterson, 1995). Psychologists (e.g., Quay, 1993), psychiatrists (e.g., Robins, 1966), and sociologists (Burgess & Akers, 1966; Elliott, Huizinga, & Ageton, 1985; Giordano, Cernkovich, & Pugh, 1986; Gold, 1970; Short & Strodbeck, 1965) have placed peer influence as central to classification, etiology, and the course of deviance. Healy (1927), one of the earliest psychological scholars of adolescent deviance, observed:

 
      ... bad companions play an immense part in the production of 
      criminalism. To be sure there are quite solitary individuals who 
      have developed an anti-social grudge, or who have deliberately 
      entered upon a professional criminalistic career, but the majority 
      work up their impulses gregariously. Bad companions may be 
      considered as part of the psychical environment, and may exert 
      influence under many varying conditions. (p. 293) 

Over 75 years later, we continue to work on understanding the dynamics through which "bad companions" contribute to the motivation to commit deviant acts (Bagwell, Newcomb, & Bukowski, 1998; Dishion, Spracklen, Andrews, & Patterson, 1996; Fergusson & Horwood, 1999; Vitaro, Gendreau, Tremblay, & Oligny, 1998). Not only is the understanding of the dynamic of negative peer influence important for designing realistic intervention strategies that reduce problem behavior, but also for clarifying the role of friendships in normative development (Cicchetti & Toth, 1992).

The study of influence in close relationships is as complicated as it is informative. Much of the work on influence has been generated from a learning paradigm, in which there is a focus on studying and identifying contingent action-reaction patterns. For example, we tested the proposition that friends' contingent, positive reactions to deviant talk influence the development of adolescent problem behavior (Dishion et al., 1996). Formal testing of this idea requires the collection of direct observations of friendship interactions, such as deviant talk and laughter, that capture antecedents and consequences. Contingencies between two proximal events (i.e., lag 1 contingencies: [t.sub.n] and [t.sub.n+1]) can be quantified by a Z score (Bakeman & Gottman, 1986; Bakeman & Quera, 1995; Gottman & Roy, 1990; Sackett, 1979). When two events reliably covary in time, the Z score index is above 1.96.

Using this approach, we found support for the hypothesis that friends mutually influence one another through laughter contingent upon deviant talk. We also discovered that not only did antisocial boys respond more positively to deviant talk, they also did not reinforce normative talk. In general, adolescents tended to match their level of deviant talk to the relative rate of reinforcement, a principle referred to as matching law (for a review, see McDowell, 1988). The relative rate of reinforcement can only be understood by studying dyadic reactions to both deviant and normative talk.

Despite the promise of the sequential approach for understanding friendship influence, the quantitative framework of contingency analysis has its limitations. Bakeman and Quera (1995) proposed several limitations to the use of Z scores in the analysis of interaction sequences. Both the manner in which codes are defined (on a dyadic or individual level) and the number of events within a sequence affect the magnitude of the Z score.

Another approach to studying friendship influence is to think of the relationships as a dynamic system (Abraham, Abraham, Shaw, & Garfinkel, 1990; Dumas, Lemay, & Dauwalder, 2001; Lewis, 2000). In contrast to sequential analyses, a dynamic approach is not concerned just with contingencies among proximal events, but also considers the overall temporal organization of the dyadic exchange. In this sense, a dynamic-systems analysis is a general methodological framework for studying relationship process (Granic, Hollenstein, Dishion, & Patterson, 2003). A key strategy within this approach for studying the organization of relationship exchanges is the use of a state-space grid (Duncan, 1991; Lewis, 2000). Figure 1(a) and (b) are the interaction state-space grids for two friendship dyads in the Oregon Youth Study (OYS). These grids display the interactions of each friendship dyad over the entire observation session. In our previous research (Dishion, Andrews, & Crosby, 1995), the interpersonal dynamics of friendship interaction were coded as Positive Engagement (compliment, praise), Directives (command, requests), Negative Engagement (criticism, blame), and Converse (calm talk, discussions). These categories are used in the state-space grids shown in Fig. 1(a) and (b).

[FIGURE 1 OMITTED]

A visual inspection of these two friendship interactions using state-space grids reveals many possible comparisons of possible theoretical interest. One obvious difference between these two friendship interactions is the level of order and organization in the dyadic exchange. Even though both friendship interactions have approximately the same number of events, one dyad restricts interactions to one area of the state-space grid, while the other appears more disorganized and complex.

Information theory provided an important quantitative and conceptual framework for defining and understanding this particular dynamic structure (Attneave, 1959; Campbell, 1982; Krippendorff, 1986). Using this framework, transitions in events are conceptualized as units of information. Information systems can range between being organized and predictable (Fig. 1(a)), or complex and uncertain (Fig. 1(b)).

The general idea is that less information is needed to predict the reactions from actions in a low entropy dyad [Fig. 1(a)], compared to a high entropy dyad [Fig. 1(b)]. Entropy (H) is computed simply by considering the distribution of conditional probabilities within an action-reaction transition matrix. Therefore, a transition matrix low in entropy (H) would have many zero cells in a statespace grid (see Fig. 1(a) and one or two transition cells that were heavily used by a dyad. Conversely, a high entropy transition matrix would be one in which all conditional cells were equiprobable (see Fig. 1(b)).

Note that a low entropy dyadic exchange does not tell us anything about the content of the exchange, just the dynamic interpersonal structure. One of the most common low entropy patterns is one in which both adolescents engage in extended discussions, represented by the Converse-Converse area of the grid. Friends who have long, uninterrupted conversations are those most likely to be quantified as a low entropy exchange. However, we have no idea what the boys in such a friendship are talking about. To understand negative peer influence, it is important to study the content of the interaction, and more importantly, the interplay between the content and the dynamic structure of the friendship interaction.

An important methodological detail is worth noting at this juncture. In order to study the interface between the structural dynamics and the content of a friendship interaction, it is important to code for these dimensions independently. If the same coding system is used to define both, there is a numerical confound. For example, it would be true by definition that dyads who engage in high levels of deviant talk would be those that are low in entropy, if entropy was quantified using a coding system for deviant talk. In this study, we consider the structural dynamics of the interpersonal process in relation to the content of the boys' interactions, each measured by independent coding systems.

How might the computation of entropy on adolescent friendship interactions further our understanding of adolescent friendships on antisocial behavior? Some expectations can be derived from the literature on the development of antisocial behavior, deviant peer relationships, and peer relationships, in general.

Several researchers propose that antisocial children exhibit arrested socialization (Coie, Dodge, Terry, & Wright, 1991; Dodge & Coie, 1987; Patterson, 1982; Patterson, …