A Co-Evolution Model for Dynamic Social Network and Behavior
Affiliation(s)
Department of Public Health Sciences, Loyola University Medical School, Maywood, USA.
Department of Public Health Sciences, Loyola University Medical School, Maywood, USA.
ABSTRACT
Individual behaviors, such as drinking, smoking, screen time, and physical activity, can be strongly influenced by the behavior of friends. At the same time, the choice of friends can be influenced by shared behavioral preferences. The actor-based stochastic models (ABSM) are developed to study the interdependence of social networks and behavior. These methods are efficient and useful for analysis of discrete behaviors, such as drinking and smoking; however, since the behavior evolution function is in an exponential format, the ABSM can generate inconsistent and unrealistic results when the behavior variable is continuous or has a large range, such as hours of television watched or body mass index. To more realistically model continuous behavior variables, we propose a co-evolution process based on a linear model which is consistent over time and has an intuitive interpretation. In the simulation study, we applied the expectation maximization (EM) and Markov chain Monte Carlo (MCMC) algorithms to find the maximum likelihood estimate (MLE) of parameter values. Additionally, we show that our assumptions are reasonable using data from the National Longitudinal Study of Adolescent Health (Add Health).
Individual behaviors, such as drinking, smoking, screen time, and physical activity, can be strongly influenced by the behavior of friends. At the same time, the choice of friends can be influenced by shared behavioral preferences. The actor-based stochastic models (ABSM) are developed to study the interdependence of social networks and behavior. These methods are efficient and useful for analysis of discrete behaviors, such as drinking and smoking; however, since the behavior evolution function is in an exponential format, the ABSM can generate inconsistent and unrealistic results when the behavior variable is continuous or has a large range, such as hours of television watched or body mass index. To more realistically model continuous behavior variables, we propose a co-evolution process based on a linear model which is consistent over time and has an intuitive interpretation. In the simulation study, we applied the expectation maximization (EM) and Markov chain Monte Carlo (MCMC) algorithms to find the maximum likelihood estimate (MLE) of parameter values. Additionally, we show that our assumptions are reasonable using data from the National Longitudinal Study of Adolescent Health (Add Health).
Cite this paper
Tong, L. , Shoham, D. and Cooper, R. (2014) A Co-Evolution Model for Dynamic Social Network and Behavior. Open Journal of Statistics, 4, 765-775. doi: 10.4236/ojs.2014.49072.
Tong, L. , Shoham, D. and Cooper, R. (2014) A Co-Evolution Model for Dynamic Social Network and Behavior. Open Journal of Statistics, 4, 765-775. doi: 10.4236/ojs.2014.49072.
References
[1] Christakis, N.A. and Fowler, J.H. (2007) The Spread of Obesity in a Large Social Network over 32 Years. New England Journal of Medicine, 357, 370-379.
http://dx.doi.org/10.1056/NEJMsa066082 [2] Fowler, J.H. and Christakis, N.A. (2008) Dynamic Spread of Happiness in a Large Social Network: Longitudinal Analysis over 20 Years in the Framingham Heart Study. British Medical Journal, 337, 1-9.
http://dx.doi.org/10.1136/bmj.a2338 [3] Fowler, J.H. and Christakis, N.A. (2008) Estimating Peer Effects on Health in Social Networks: A Response to Cohen-Cole and Fletcher; and Trogdon, Nonnemaker, and Pais. Journal of Health Economics, 27, 1400-1405.
http://dx.doi.org/10.1016/j.jhealeco.2008.07.001 [4] Alexander, C., Piazza, M., Mekos, D. and Valente, T. (2001) Peers Schools and Adolescent Cigarette Smoking. Journal of Adolescent Health, 29, 22-30.
http://dx.doi.org/10.1016/S1054-139X(01)00210-5 [5] Trogdon, J.G., Finkelstein, E.A., Hylands, T., Dellea, P.S. and Kamal-Bahl, S.J. (2008) Indirect Costs of Obesity: A Review of the Current Literature. Obesity Reviews, 9, 489-500.
http://dx.doi.org/10.1111/j.1467-789X.2008.00472.x [6] De La Haye, K., Robins, G., Mohr, P. and Wilson, C. (2010) Obesity-Related Behaviors in Adolescent Friendship Networks. Social Networks, 32, 161-167.
http://dx.doi.org/10.1016/j.socnet.2009.09.001 [7] De La Haye, K., Robins, G., Mohr, P. and Wilson, C. (2011) How Physical Activity Shapes, and Is Shaped by, Adolescent Friendships. Social Science & Medicine, 73, 719-728.
http://dx.doi.org/10.1016/j.socscimed.2011.06.023 [8] De La Haye, K., Robins, G., Mohr, P. and Wilson, C. (2011) Homophily and Contagion as Explanations for Weight Similarities among Adolescent Friends. Journal of Adolescent Health, 49, 421-427.
http://dx.doi.org/10.1016/j.jadohealth.2011.02.008 [9] Salvy, S.J., De La Haye, K., Bowker, J.C. and Hermans, R.C.J. (2012) Influence of Peers and Friends on Children’s and Adolescents’ Eating and Activity Behaviors. Physiology & Behavior, 106, 369-378.
http://dx.doi.org/10.1016/j.physbeh.2012.03.022 [10] Cohen-Cole, E. and Fletcher, J.M. (2008) Is Obesity Contagious? Social Network vs. Environmental Factors in the Obesity Epidemic. Journal of Health Economics, 27, 1382-1387.
http://dx.doi.org/10.1016/j.jhealeco.2008.04.005 [11] Shalizi, C. and Thomas, A. (2011) Homophily and Contagion Are Generically Confounded in Observational Social Network Studies. Sociological Methods and Research, 40, 211-239.
http://dx.doi.org/10.1177/0049124111404820 [12] Snijders, T.A.B., Pattison, P.E., Robins, G.L. and Handcock, M.S. (2006) New Specifications for Exponential Random Graph Models. Sociological Methodology, 36, 99-153.
http://dx.doi.org/10.1111/j.1467-9531.2006.00176.x [13] Snijders, T.A.B., van de Bunt, G.G. and Steglich, C.E.G. (2010) Introduction to Actor-Based Models for Network Dynamics. Social Networks, 32, 44-60.
http://dx.doi.org/10.1016/j.socnet.2009.02.004 [14] Train, K. (2009) Discrete Choice Methods with Simulation. Cambridge University Press, New York.
http://dx.doi.org/10.1017/CBO9780511805271 [15] Robins, G., Pattison, P., Kalish, Y. and Lusher, D. (2007) An Introduction to Exponential Random Graph (p*) Models for Social Networks. Social Networks, 29, 173-191.
http://dx.doi.org/10.1016/j.socnet.2006.08.002 [16] Bearman, P.S. and Moody, J. (2004) Suicide and Friendships among American Adolescents. American Journal of Public Health, 94, 89-95.
http://dx.doi.org/10.2105/AJPH.94.1.89 [17] Bearman, P.S., Moody, J. and Stovel, K. (2004) Chains of Affection: The Structure of Adolescent Romantic and Sexual Networks. American Journal of Sociology, 110, 44-91.
http://dx.doi.org/10.1086/386272 [18] Gordon-Larsen, P., The, N.S. and Adair, L.S. (2010) Longitudinal Trends in Obesity in the United States from Adolescence to the Third Decade of Life. Obesity, 18, 1801-1804.
http://dx.doi.org/10.1038/oby.2009.451 [19] Wright, C.M., Emmett, P.M., Ness, A.R., et al. (2010) Tracking of Obesity and Body Fatness through Mid-Childhood. Archives of Disease in Childhood, 95, 612-617.
http://dx.doi.org/10.1136/adc.2009.164491 [20] Smith, K.P. and Christakis, N.A. (2008) Social Networks and Health. Annual Review of Sociology, 34, 405-429.
http://dx.doi.org/10.1146/annurev.soc.34.040507.134601 [21] Apicella, C.L., Marlowe, F.W., et al. (2012) Social Networks and Cooperation in Hunter-Gatherers. Nature, 481, 497-501.
http://dx.doi.org/10.1038/nature10736
[1] Christakis, N.A. and Fowler, J.H. (2007) The Spread of Obesity in a Large Social Network over 32 Years. New England Journal of Medicine, 357, 370-379.
http://dx.doi.org/10.1056/NEJMsa066082 [2] Fowler, J.H. and Christakis, N.A. (2008) Dynamic Spread of Happiness in a Large Social Network: Longitudinal Analysis over 20 Years in the Framingham Heart Study. British Medical Journal, 337, 1-9.
http://dx.doi.org/10.1136/bmj.a2338 [3] Fowler, J.H. and Christakis, N.A. (2008) Estimating Peer Effects on Health in Social Networks: A Response to Cohen-Cole and Fletcher; and Trogdon, Nonnemaker, and Pais. Journal of Health Economics, 27, 1400-1405.
http://dx.doi.org/10.1016/j.jhealeco.2008.07.001 [4] Alexander, C., Piazza, M., Mekos, D. and Valente, T. (2001) Peers Schools and Adolescent Cigarette Smoking. Journal of Adolescent Health, 29, 22-30.
http://dx.doi.org/10.1016/S1054-139X(01)00210-5 [5] Trogdon, J.G., Finkelstein, E.A., Hylands, T., Dellea, P.S. and Kamal-Bahl, S.J. (2008) Indirect Costs of Obesity: A Review of the Current Literature. Obesity Reviews, 9, 489-500.
http://dx.doi.org/10.1111/j.1467-789X.2008.00472.x [6] De La Haye, K., Robins, G., Mohr, P. and Wilson, C. (2010) Obesity-Related Behaviors in Adolescent Friendship Networks. Social Networks, 32, 161-167.
http://dx.doi.org/10.1016/j.socnet.2009.09.001 [7] De La Haye, K., Robins, G., Mohr, P. and Wilson, C. (2011) How Physical Activity Shapes, and Is Shaped by, Adolescent Friendships. Social Science & Medicine, 73, 719-728.
http://dx.doi.org/10.1016/j.socscimed.2011.06.023 [8] De La Haye, K., Robins, G., Mohr, P. and Wilson, C. (2011) Homophily and Contagion as Explanations for Weight Similarities among Adolescent Friends. Journal of Adolescent Health, 49, 421-427.
http://dx.doi.org/10.1016/j.jadohealth.2011.02.008 [9] Salvy, S.J., De La Haye, K., Bowker, J.C. and Hermans, R.C.J. (2012) Influence of Peers and Friends on Children’s and Adolescents’ Eating and Activity Behaviors. Physiology & Behavior, 106, 369-378.
http://dx.doi.org/10.1016/j.physbeh.2012.03.022 [10] Cohen-Cole, E. and Fletcher, J.M. (2008) Is Obesity Contagious? Social Network vs. Environmental Factors in the Obesity Epidemic. Journal of Health Economics, 27, 1382-1387.
http://dx.doi.org/10.1016/j.jhealeco.2008.04.005 [11] Shalizi, C. and Thomas, A. (2011) Homophily and Contagion Are Generically Confounded in Observational Social Network Studies. Sociological Methods and Research, 40, 211-239.
http://dx.doi.org/10.1177/0049124111404820 [12] Snijders, T.A.B., Pattison, P.E., Robins, G.L. and Handcock, M.S. (2006) New Specifications for Exponential Random Graph Models. Sociological Methodology, 36, 99-153.
http://dx.doi.org/10.1111/j.1467-9531.2006.00176.x [13] Snijders, T.A.B., van de Bunt, G.G. and Steglich, C.E.G. (2010) Introduction to Actor-Based Models for Network Dynamics. Social Networks, 32, 44-60.
http://dx.doi.org/10.1016/j.socnet.2009.02.004 [14] Train, K. (2009) Discrete Choice Methods with Simulation. Cambridge University Press, New York.
http://dx.doi.org/10.1017/CBO9780511805271 [15] Robins, G., Pattison, P., Kalish, Y. and Lusher, D. (2007) An Introduction to Exponential Random Graph (p*) Models for Social Networks. Social Networks, 29, 173-191.
http://dx.doi.org/10.1016/j.socnet.2006.08.002 [16] Bearman, P.S. and Moody, J. (2004) Suicide and Friendships among American Adolescents. American Journal of Public Health, 94, 89-95.
http://dx.doi.org/10.2105/AJPH.94.1.89 [17] Bearman, P.S., Moody, J. and Stovel, K. (2004) Chains of Affection: The Structure of Adolescent Romantic and Sexual Networks. American Journal of Sociology, 110, 44-91.
http://dx.doi.org/10.1086/386272 [18] Gordon-Larsen, P., The, N.S. and Adair, L.S. (2010) Longitudinal Trends in Obesity in the United States from Adolescence to the Third Decade of Life. Obesity, 18, 1801-1804.
http://dx.doi.org/10.1038/oby.2009.451 [19] Wright, C.M., Emmett, P.M., Ness, A.R., et al. (2010) Tracking of Obesity and Body Fatness through Mid-Childhood. Archives of Disease in Childhood, 95, 612-617.
http://dx.doi.org/10.1136/adc.2009.164491 [20] Smith, K.P. and Christakis, N.A. (2008) Social Networks and Health. Annual Review of Sociology, 34, 405-429.
http://dx.doi.org/10.1146/annurev.soc.34.040507.134601 [21] Apicella, C.L., Marlowe, F.W., et al. (2012) Social Networks and Cooperation in Hunter-Gatherers. Nature, 481, 497-501.
http://dx.doi.org/10.1038/nature10736