The First Delinquent Peers Are the Most Important: Examining Nonlinearity in the Peer Effect

Abstract

Criminologists have long recognized the importance of peers in the etiology of delinquency. Yet, the bulk of empirical studies on this topic make the implicit assumption that the peer effect to be conditioned is linear. With few notable exceptions, prior criminological research has not thought deeply about possible nonlinearity in the peer effect. To address this issue, the present study examines whether the functional form of the relationship between peer and respondent smoking, getting drunk, and fighting is nonlinear, and whether this nonlinearity is moderated by lagged respondent delinquency. Logistic regression models on adolescents from The National Longitudinal Study of Adolescent Health indicate that the marginal effect of peer delinquency on respondent delinquency decreases as the count of delinquent friends increases, consistent with a satiation effect. Moreover, the models indicate that the nonlinear effect of peer delinquency on respondent delinquency is moderated by prior respondent delinquency.

Keywords:

• influence
• nonlinear
• peers

Acknowledgements

Special acknowledgment is due Ronald R. Rindfuss and Barbara Entwisle for assistance in the original design. This research uses data from Add Health, a program project directed by Kathleen Mullan Harris and designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan Harris at the University of North Carolina at Chapel Hill, and funded by grant P01-HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development, with cooperative funding from 23 other federal agencies and foundations. Information on how to obtain the Add Health data files is available on the Add Health website (http://www.cpc.unc.edu/addhealth). No direct support was received from grant P01-HD31921 for this analysis.

Notes

¹ Note that Tanford and Penrod (1984) hypothesized the relationship between majority size and conformity as an S-shaped growth function, rather than as a uniformly decelerating curve.

² We thank a reviewer for pointing out that one can rarely be sure which actions are already in an individual’s repertoire. According to Hoppitt and Laland (2013, p. 72), “Even when a complete history of the individual’s behavior is available, it is difficult to exclude the possibility that an individual has an unlearned predisposition for an action they have never performed.” We, therefore, include the word naïve, which is commonly used in the social learning literature outside of criminology to acknowledge this possibility (see Hoppitt & Laland, 2013).

³ The Add Health data have two other options for identifying friends: the receive network, which consists of all individuals who named the respondent as a friend; and the nomination and receive network, which consists of all individuals who either the respondent named as a friend or who named the respondent as a friend. The ensuing analyses use the send nomination network.

⁴ In supplementary analyses, we also considered drinking alcohol. Since the results were consistent with those for getting drunk, we opted to present the results for getting drunk, which is a less normative, more delinquent act than drinking.

⁵ Very few respondents had networks with 8, 9, or 10 friends who reported smoking, getting drunk, or fighting. We, therefore, created a category representing seven or more friends reporting engagement in these acts. This affected 46, 74, and 17 cases in the smoking, getting drunk, and fighting models, respectively. We also estimated our models using the non-truncated measures with no substantive changes in the results.

⁶ To protect against model misspecification due to multi-collinearity concerns, we replicated the results using a centered measure of friend delinquency. We report that there were no substantive changes with the results. We also constructed and examined cubic network delinquency terms to investigate the possibility of more than one inflection point in the relationship between respondent and peer delinquency. These cubic terms were not significant in the models and are, therefore, not presented or discussed in this manuscript.

⁷ The interpretation of interaction (and, therefore, quadratic) terms through the use of marginal effects requires additional considerations in nonlinear models than in linear models (see Karaca-Mandic, Norton, & Dowd, 2012). In linear models, marginal effects of interactions can be accurately quantified by partial effect coefficients, holding all other covariates constant. In nonlinear models, however, the regression coefficients for the covariates change from additive to multiplicative when exponentiated (Ai & Norton, 2003; Norton, Wang, & Ai, 2004). We, therefore, calculate marginal effects at the means (MEMs).

Additional information

Notes on contributors

Carter Rees

Carter Rees received his doctorate in Criminal Justice from the University at Albany, SUNY. He is currently an assistant professor of Criminology and Criminal Justice at Arizona State University. His research applies the theoretical and statistical concepts of social network analysis to the longitudinal study of delinquency.

Gregory M. Zimmerman

Gregory M. Zimmerman received his doctorate in Criminal Justice from the University at Albany, SUNY. He is currently an Assistant Professor of Criminology and Criminal Justice at Northeastern University.