Birds of a feather, or friend of a friend? using exponential random graph models to investigate adolescent social networks*

In this article, we use newly developed statistical methods to examine the generative processes that give rise to widespread patterns in friendship networks. The methods incorporate both traditional demographic measures on individuals (age, sex, and race) and network measures for structural processes operating on individual, dyadic, and triadic levels. We apply the methods to adolescent friendship networks in 59 U.S. schools from the National Longitudinal Survey of Adolescent Health (Add Health). We model friendship formation as a selection process constrained by individuals’ sociality (propensity to make friends), selective mixing in dyads (friendships within race, grade, or sex categories are differentially likely relative to cross-category friendships), and closure in triads (a friend’s friends are more likely to become friends), given local population composition. Blacks are generally the most cohesive racial category, although when whites are in the minority, they display stronger selective mixing than do blacks when blacks are in the minority. Hispanics exhibit disassortative selective mixing under certain circumstances; in other cases, they exhibit assortative mixing but lack the higher-order cohesion common in other groups. Grade levels are always highly cohesive, while females form triangles more than males. We conclude with a discussion of how network analysis may contribute to our understanding of sociodemographic structure and the processes that create it.

[1]  Morroe Berger,et al.  Freedom and control in modern society , 1954 .

[2]  F. Harary,et al.  STRUCTURAL BALANCE: A GENERALIZATION OF HEIDER'S THEORY1 , 1977 .

[3]  A. Rapoport Contribution to the theory of random and biased nets , 1957 .

[4]  F. Heider The psychology of interpersonal relations , 1958 .

[5]  D. Dunphy The social structure of urban adolescent peer groups. , 1963 .

[6]  P. Lazarsfeld,et al.  Friendship as Social process: a substantive and methodological analysis , 1964 .

[7]  E. Rogers,et al.  HOMOPHILY-HETEROPHILY: RELATIONAL CONCEPTS FOR COMMUNICATION RESEARCH , 1970 .

[8]  D. Byrne The Attraction Paradigm , 1971 .

[9]  Mark S. Granovetter The Strength of Weak Ties , 1973, American Journal of Sociology.

[10]  J. Besag Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[11]  Stanley Wasserman,et al.  Random directed graph distributions and the triad census in social networks , 1977 .

[12]  P. Blau Inequality and Heterogeneity: A Primitive Theory of Social Structure , 1978 .

[13]  James A. Davis Clustering and Structural Balance in Graphs , 1977 .

[14]  D. Kandel Homophily, Selection, and Socialization in Adolescent Friendships , 1978, American Journal of Sociology.

[15]  S. Feld The Focused Organization of Social Ties , 1981, American Journal of Sociology.

[16]  Peter V. Marsden,et al.  Models and methods for characterizing the structural parameters of groups , 1981 .

[17]  P. Holland,et al.  An Exponential Family of Probability Distributions for Directed Graphs , 1981 .

[18]  S. Fienberg,et al.  Categorical Data Analysis of Single Sociometric Relations , 1981 .

[19]  S. Feld Social Structural Determinants of Similarity among Associates , 1982 .

[20]  S. Feld,et al.  Patterns of Sociometric Choices: Transitivity Reconsidered , 1982 .

[21]  Maureen T. Hallinan,et al.  Classroom Racial Composition and Children's Friendships , 1982 .

[22]  Meir Fershtman,et al.  Transitivity and the path census in sociometry , 1985 .

[23]  L. Smith-Lovin,et al.  Homophily in voluntary organizations: Status distance and the composition of face-to-face groups. , 1987 .

[24]  T. Snijders,et al.  Extensions of triad counts to networks with different subsets of points and testing underlying random graph distributions , 1987 .

[25]  D. Massey Economic Development and International Migration in Comparative Perspective , 1988 .

[26]  Roy M. Anderson,et al.  The Transmission Dynamics of Human Immunodeficiency Virus (HIV) , 1988 .

[27]  Maureen T. Hallinan,et al.  Interracial Friendship Choices in Secondary Schools. , 1989 .

[28]  D. J. Strauss,et al.  Pseudolikelihood Estimation for Social Networks , 1990 .

[29]  M. Morris,et al.  A log-linear modeling framework for selective mixing. , 1991, Mathematical biosciences.

[30]  Kathleen M. Carley A Theory of Group Stability , 1991 .

[31]  R. Mare Five decades of educational assortative mating. , 1991 .

[32]  C. Geyer,et al.  Constrained Monte Carlo Maximum Likelihood for Dependent Data , 1992 .

[33]  L. Dean,et al.  Effect of sexual behavior change on long-term human immunodeficiency virus prevalence among homosexual men. , 1994, American journal of epidemiology.

[34]  S. Watkins,et al.  WOMEN'S GOSSIP AND SOCIAL CHANGE , 1995 .

[35]  S. Wasserman,et al.  Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp , 1996 .

[36]  Trish,et al.  Protecting adolescents from harm. Findings from the National Longitudinal Study on Adolescent Health. , 1997, JAMA.

[37]  T. Valente,et al.  Social network associations with contraceptive use among Cameroonian women in voluntary associations. , 1997, Social science & medicine.

[38]  M. Kretzschmar,et al.  Concurrent partnerships and the spread of HIV , 1997, AIDS.

[39]  R. Jessor,et al.  New perspectives on adolescent risk behavior: Author index , 1998 .

[40]  Peter Shawn Bearman,et al.  New methods for new research on adolescent sexual behavior , 1998 .

[41]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[42]  M. Hojat,et al.  Protecting adolescents from harm. , 1998, JAMA.

[43]  S. Wasserman,et al.  Logit models and logistic regressions for social networks: II. Multivariate relations. , 1999, The British journal of mathematical and statistical psychology.

[44]  H. Kohler Fertility decline as a coordination problem , 2000 .

[45]  Martin G. Everett,et al.  Models of core/periphery structures , 2000, Soc. Networks.

[46]  M. McPherson,et al.  Birds of a Feather: Homophily in Social Networks , 2001 .

[47]  M. McPherson,et al.  BIRDS OF A FEATHER: Homophily , 2001 .

[48]  J. Moody Race, School Integration, and Friendship Segregation in America1 , 2001, American Journal of Sociology.

[49]  T. Valente,et al.  Peers, schools, and adolescent cigarette smoking. , 2001, The Journal of adolescent health : official publication of the Society for Adolescent Medicine.

[50]  Tom A. B. Snijders,et al.  Markov Chain Monte Carlo Estimation of Exponential Random Graph Models , 2002, J. Soc. Struct..

[51]  M. Handcock Center for Studies in Demography and Ecology Assessing Degeneracy in Statistical Models of Social Networks , 2005 .

[52]  Dana L Haynie,et al.  Friendship Networks of Mobile Adolescents , 2004 .

[53]  P. Bearman,et al.  Suicide and friendships among American adolescents. , 2004, American journal of public health.

[54]  Martina Morris,et al.  6. Exponential Family Models for Sampled and Census Network Data , 2004 .

[55]  Kathleen M. Carley,et al.  Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers , 2004 .

[56]  P. Pattison,et al.  New Specifications for Exponential Random Graph Models , 2006 .

[57]  D. Hunter,et al.  Inference in Curved Exponential Family Models for Networks , 2006 .

[58]  jimi adams,et al.  To tell the truth: Measuring concordance in multiply reported network data , 2007, Soc. Networks.

[59]  Mark S. Handcock,et al.  Center for Statistics and the Social Sciences University of Washington , 2007 .

[60]  Steven M. Goodreau,et al.  Advances in exponential random graph (p*) models applied to a large social network , 2007, Soc. Networks.

[61]  David R. Hunter,et al.  Curved exponential family models for social networks , 2007, Soc. Networks.

[62]  Martina Morris,et al.  ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. , 2008, Journal of statistical software.

[63]  Martina Morris,et al.  A statnet Tutorial. , 2008, Journal of statistical software.

[64]  D. Hunter,et al.  Goodness of Fit of Social Network Models , 2008 .

[65]  Return to Aztlan: The Social Process of International Migration from Western Mexico , 2009 .

[66]  Karl E. Bauman,et al.  Findings From the National Longitudinal Study on Adolescent Health , 2010 .

[67]  H. Kohler,et al.  Learning in social networks and contraceptive choice , 1997, Demography.

[68]  Jere R. Behrman,et al.  The density of social networks and fertility decisions: evidence from south nyanza district, kenya , 2001, Demography.