How social networks influence human behavior has been an interesting topic in applied research. Existing methods often utilized scale-level behavioral data (e.g., total number of positive responses) to estimate the influence of a social network on human behavior. This study proposes a novel approach to studying social influence that utilizes item-level behavioral measures. Under the latent space modeling framework, we integrate the two latent spaces for respondents' social network data and item-level behavior measures into a single space we call 'interaction map'. The interaction map visualizes the association between the latent homophily among respondents and their item-level behaviors, revealing differential social influence effects across item-level behaviors. We also measure overall social influence by assessing the impact of the interaction map. We evaluate the properties of the proposed approach via extensive simulation studies and demonstrate the proposed approach with a real data in the context of studying how students' friendship network influences their participation in school activities.
Abbe, E. (2018). Community detection and stochastic block models: Recent developments. Journal of Machine Learning Research, 18(177), 1–86.
Barber, B. L., Eccles, J. S., & Stone, M. R. (2001). Whatever happened to the jock, the brain, and the princess? Journal of Adolescent Research, 16(5), 429–455.
Block, P., Stadtfeld, C., & Snijders, T. (2019). Forms of dependence: Comparing SAOMs and ERGMs from basic principles. Sociological Methods & Research, 48(1), 202–239.
Carr, C. T., & Zube, P. (2015). Network autocorrelation of task performance via informal communication within a virtual world. Journal of Media Psychology, 27(1), 33–44.
Cheng, L. A., Mendonça, G., & Júnior, JCd Farias. (2014). Physical activity in adolescents: analysis of the social influence of parents and friends. Jornal de Pediatria, 90(1), 35–41.
[PMID: 24156835]
D’Angelo, S., Murphy, T. B., & Alfo, M. (2019). Latent space modelling of multidimensional networks with application to the exchange of votes in Eurovision song contest. Annals of Applied Statistics, 13(2), 900–930.
Daraganova, G., & Robins, G. (2013). Autologistic actor attribute models. Exponential Random Graph Models for Social Networks: Theory, Methods and Applications, pp. 102–114
Decelle, A., Krzakala, F., Moore, C., & Zdeborová, L. (2011). Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications. Physical Review E, 84(6), 066106.
Dittrich, D., Leenders, R. T. A. J., & Mulder, J. (2019). Network autocorrelation modeling: A bayes factor approach for testing (multiple) precise and interval hypotheses. Sociological Methods & Research, 48(3), 642–676.
Doreian, P. (1989). Network autocorrelation models: Problems and prospects. Spatial statistics: Past, present, future. pp. 369–389.
Eccles, J., Barber, B., Stone, M., & Hunt, J. (2003). Extracurricular activities and adolescent development. Journal of Social Issues, 59(4), 865–889.
Erdős, P., & Rényi, A. (1960). On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 5, 17–61.
Feldman, A. F., & Matjasko, J. L. (2005). The role of school-based extracurricular activities in adolescent development: A comprehensive review and future directions. Review of Educational Research, 75(2), 159–210.
Fienberg, S. E. (2012). A brief history of statistical models for network analysis and open challenges. Journal of Computational and Graphical Statistics, 21(4), 825–839.
Fosdick, B. K., & Hoff, P. D. (2015). Testing and modeling dependencies between a network and nodal attributes. Journal of the American Statistical Association, 110(511), 1047–1056.
[PMID: 26848204]
Frank, K. A., & Xu, R. (2021). Causal inference for social network analysis. The oxford handbook of social networksOxford University Press.
Frank, K. A., Zhao, Y., & Borman, K. (2004). Social capital and the diffusion of innovations within organizations: The case of computer technology in schools. Sociology of Education, 77(2), 148–171.
Frank, O., & Strauss, D. (1986). Markov graphs. Journal of the American Statistical Association, 81(395), 832–842.
Fredricks, J. A., & Eccles, J. S. (2006). Is extracurricular participation associated with beneficial outcomes? concurrent and longitudinal relations. Developmental Psychology, 42(4), 698–713.
[PMID: 16802902]
Fujimoto, K., Wang, P., & Valente, T. W. (2013). The decomposed affiliation exposure model: A network approach to segregating peer influences from crowds and organized sports. Network Science, 1(2), 154–169.
[PMID: 24349718]
Gardner, M., Roth, J., & Brooks-Gunn, J. (2008). Adolescents’ participation in organized activities and developmental success 2 and 8 years after high school: Do sponsorship, duration, and intensity matter? Developmental Psychology, 44(3), 814–30.
[PMID: 18473646]
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis (Edition, Vol. 3). New York, NY: Chapman and Hall/CRC.
Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7(4), 457–472.
Goldsmith-Pinkham, P., & Imbens, G. W. (2013). Social networks and the identification of peer effects. Journal of Business & Economic Statistics, 31(3), 253–264.
Gollini, I., & Murphy, T. B. (2016). Joint modeling of multiple network views. Journal of Computational and Graphical Statistics, 25(1), 246–265.
Gower, J. C. (1975). Generalized procrustes analysis. Psychometrika, 40(1), 33–51.
Handcock, M. S., Raftery, A. E., & Tantrum, J. M. (2007). Model-based clustering for social network. Journal of the Royal Statistical Society, Series A, 170, 301–354.
Hoff, P., Raftery, A., & Handcock, M. S. (2002). Latent space approaches to social network analysis. Journal of the American Statistical Association, 97(460), 1090–1098.
Holland, P. W., Laskey, K. B., & Leinhardt, S. (1983). Stochastic blockmodels: First steps. Social Networks, 5(2), 109–137.
Holland, P. W., & Leinhardt, S. (1981). An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association, 76(373), 33–50.
Hunter, D. (2007). Curved exponential family models for social networks. Social Networks, 29(2), 216–230.
[PMID: 18311321]
Hunter, D. R., Goodreau, S. M., & Handcock, M. S. (2008). Goodness of fit of social network models. Journal of the American Statistical Association, 103(481), 248–258.
Jeon, M., Jin, I. H., Schweinberger, M., & Baugh, S. (2021). Mapping unobserved item-respondent interactions: A latent space item response model with interaction map. Psychometrika, 86(2), 378–403.
[PMID: 33939062]
Knifsend, C. A., & Graham, S. (2011). Too much of a good thing? how breadth of extracurricular participation relates to school-related affect and academic outcomes during adolescence. Journal of Youth and Adolescence, 41(3), 379–389.
[PMID: 22160442]
Krivitsky, P. N., Handcock, M. S., Raftery, A. E., & Hoff, P. D. (2009). Representing degree distributions, clustering, and homophily in social networks with latent cluster random network models. Social Networks, 31, 204–213.
[PMID: 20191087]
Larson, R., Hansen, D., & Moneta, G. (2006). Differing profiles of developmental experiences across types of organized youth activities. Developmental Psychology, 42(5), 849–63.
[PMID: 16953691]
Lauritzen, S., Rinaldo, A., & Sadeghi, K. (2017). Random networks, graphical models, and exchangeability. Journal of the Royal Statistical Society, Series B, 80(3), 481–508.
Lee, C., & Wilkinson, D. J. (2019). A review of stochastic block models and extensions for graph clustering. Applied Network Science, 4, 122.
Leenders, R. T. (2002). Modeling social influence through network autocorrelation: Constructing the weight matrix. Social Networks, 24(1), 21–47.
Lei, J., & Rinaldo, A. (2015). Consistency of spectral clustering in stochastic block models. The Annals of Statistics, 43(1), 215–237.
Lu, X., & Szymanski, B. K. (2019). A regularized stochastic block model for the robust community detection in complex networks. Scientific Reports, 9, 13247.
[PMID: 31519944]
Mahoney, J. L., Cairns, B. D., & Farmer, T. W. (2003). Promoting interpersonal competence and educational success through extracurricular activity participation. Journal of Educational Psychology, 95(2), 409–418.
Manski, C. F. (1993). Identification of endogenous social effects: The reflection problem. The Review of Economic Studies, 60(3), 531.
Matias, N. C. F. (2019). Elaboración de una escala de participación en actividades extracurriculares para niños. Ciencias Psicológicas, 235–248.
McCabe, K., Modecki, K., & Barber, B. (2016). Participation in organized activities protects against adolescents’ risky substance use, even beyond development in conscientiousness. Journal of Youth and Adolescence, 45(11), 2292–2306.
[PMID: 26979446]
Mercken, L., Snijders, T. A., Steglich, C., Vertiainen, E., & Vries, H. D. (2010). Smoking-based selection and influence in gender-segregated friendship networks: A social network analysis of adolescent smoking. Addiction, 105(7), 1280–1289.
[PMID: 20456296]
Ord, K. (1975). Estimation methods for models of spatial interaction. Journal of the American Statistical Association, 70(349), 120–126.
Paluck, E. L., Shepherd, H., & Aronow, P. M. (2016). Changing climates of conflict: A social network experiment in 56 schools. Proceedings of the National Academy of Sciences of the United States of America, 113(3), 566–571.
[PMID: 26729884]
Paluck, E. L., H. Shepherd, & P. M. Aronow (2020). Changing climates of conflict: A social network experiment in 56 schools, new jersey, 2012–2013. Inter-university Consortium for Political and Social Research.
Parker, A., Pallotti, F., & Lomi, A. (2021). New network models for the analysis of social contagion in organizations: An introduction to autologistic actor attribute models. Organizational Research Methods, 25(3), 513–540.
Raftery, A., Niu, X., Hoff, P., & Yeung, K. (2012). Fast inference for the latent space network model using a case-control approximate likelihood. Journal of Computational and Graphical Statistics, 21(4), 909–919.
Rastelli, R., Friel, N., & Raftery, A. (2016). Properties of latent variable network models. Network Science, 4, 407–432.
Ripley, R. M., Snijders, T. A. B., B’oda, Z., V"or"os, A., & Preciado, P. (2022). Manual for Siena version 4.0. Technical report, Oxford: University of Oxford, Department of Statistics; Nuffield College. R package version 1.3.14. https://www.cran.r-project.org/web/packages/RSiena/ .
Robins, G., Pattison, P., & Elliott, P. (2001). Network models for social influence processes. Psychometrika, 66(2), 161–189.
Robins, G., Snijders, T., Wang, P., Handcock, M., & Pattison, P. (2007). Recent developments in exponential random graph (p*) models for social networks. Social Networks, 29(2), 192–215.
Rohe, K., Chatterjee, S., & Yu, B. (2011). Spectral clustering and the high-dimensional stochastic blockmodel. The Annals of Statistics, 39(4), 1878–1915.
Salter-Townshend, M., & McCormick, T. H. (2017). Latent space models for multiview network data. The Annals of Applied Statistics, 11(3), 1217–1244.
[PMID: 29721127]
Scott, D., Dam, I., & Wilton, R. (2012). Investigating the effects of social influence on the choice to telework. Environment and Planning A, 44(5), 1016–1031.
Sewell, D. K. (2017). Network autocorrelation models with egocentric data. Social Networks, 49, 113–123.
Sewell, D. K., & Chen, Y. (2015). Latent space models for dynamic networks. Journal of the American Statistical Association, 110(512), 1646–1657.
Shakarian, P., Bhatnagar, A., Aleali, A., Shaabani, E., & Guo, R. (2015). The Independent Cascade and Linear Threshold Models (pp. 35–48). Springer.
Sijtsema, J. J., Ojanen, T., Veenstra, R., Lindenberg, S., Hawley, P. H., & Little, T. D. (2010). Forms and functions of aggression in adolescent friendship selection and influence: A longitudinal social network analysis. Social Development, 19(3), 515–534.
Simpkins, S. D., Schaefer, D. R., Price, C. D., & Vest, A. E. (2013). Adolescent friendships, bmi, and physical activity: Untangling selection and influence through longitudinal social network analysis. Journal of Research on Adolescence, 23(3), 537–549.
Snijders, T. (2001). The statistical evaluation of social network dynamics. Sociological Methodology, 31(1), 361–395.
Snijders, T. (2017). Stochastic actor-oriented models for network dynamics. Annual Review of Statistics and Its Application, 4, 343–363.
Snijders, T., Bunt, G. G., & Steglich, C. (2010). Introduction to actor-based models for network dynamics. Social Networks, 32(1), 44–60.
Steglich, C., Snijders, T. A. B., & Pearson, M. (2010). Dynamic networks and behavior: Separating selection from influence. Sociological Methodology, 40(1), 329–393.
Sun, J., & Tang, J. (2011). A survey of models and algorithms for social influence analysis. In C. C. Aggarwal (Ed.), Social network data analytics (pp. 177–214). Springer.
Sweet, T., & Adhikari, S. (2020). A latent space network model for social influence. Psychometrika, 85(2), 251–274.
[PMID: 32221792]
Urberg, K. A., Değirmencioğlu, S. M., & Pilgrim, C. (1997). Close friend and group influence on adolescent cigarette smoking and alcohol use. Developmental Psychology, 33(5), 834–844.
[PMID: 9300216]
Valente, T.W. (2005). Network models and methods for studying the diffusion of innovations. In Models and methods in social network analysis, (pp. 98–116). Cambridge University Press.
Vitale, M. P., Porzio, G. C., & Doreian, P. (2016). Examining the effect of social influence on student performance through network autocorrelation models. Journal of Applied Statistics, 43(1), 115–127.
Wang, S. S., Paul, S., & De Boeck, P. (2019). Joint latent space model for social networks with multivariate attributes. arXiv:1910.12128 .
Zhang, A. Y., & Zhou, H. H. (2016). Minimax rates of community detection in stochastic block models. The Annals of Statistics, 44(5), 2252–2280.
Zheng, K., Padman, R., Krackhardt, D., Johnson, M. P., & Diamond, H. S. (2010). Social networks and physician adoption of electronic health records: Insights from an empirical study. Journal of the American Medical Informatics Association, 17(3), 328–336.
[PMID: 20442152]
Grants
2022-22-0439/Yonsei University
NRF2020R1A2C1A01009881 and RS-2023-00217705/National Research Foundation of Korea