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Sensitivity analysis for network observations with applications to inferences of social influence effects

Published online by Cambridge University Press:  19 October 2020

Ran Xu Open the ORCID record for Ran Xu [Opens in a new window]  and
Kenneth A. Frank
Ran Xu*
Affiliation:
Department of Allied Health Sciences, University of Connecticut, Storrs, CT 06269, USA
Kenneth A. Frank
Affiliation:
Department of Counseling, Educational Psychology and Special Education, Michigan State University, East Lansing, MI 48824, USA (email: kenfrank@msu.edu)
*
*Corresponding author. Email: ran.2.xu@uconn.edu
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Abstract

The validity of network observations is sometimes of concern in empirical studies, since observed networks are prone to error and may not represent the population of interest. This lack of validity is not just a result of random measurement error, but often due to systematic bias that can lead to the misinterpretation of actors’ preferences of network selections. These issues in network observations could bias the estimation of common network models (such as those pertaining to influence and selection) and lead to erroneous statistical inferences. In this study, we proposed a simulation-based sensitivity analysis method that can evaluate the robustness of inferences made in social network analysis to six forms of selection mechanisms that can cause biases in network observations—random, homophily, anti-homophily, transitivity, reciprocity, and preferential attachment. We then applied this sensitivity analysis to test the robustness of inferences for social influence effects, and we derived two sets of analytical solutions that can account for biases in network observations due to random, homophily, and anti-homophily selection.

Keywords

sensitivity analysisnetwork observationsselection mechanismssocial influence

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Type
Research Article
Information
Network Science , Volume 9 , Issue 1 , March 2021 , pp. 73 - 98
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

Action Editor: Stanley Wasserman

References

An, W. (2011). Models and methods to identify peer effects. In J. Scott & Peter J. Carrington (Eds.), The Sage handbook of social network analysis (pp. 515–532). London: Sage.Google Scholar
An, W. (2015). Instrumental variables estimates of peer effects in social networks. Social Science Research, 50, 382–394.CrossRefGoogle Scholar
Aral, S., Muchnik, L., & Sundararajan, A. (2009). Distinguishing influence-based contagion from homophily-driven diffusion in dynamic networks. Proceedings of the National Academy of Sciences, 106(51), 21544–21549.CrossRefGoogle Scholar
Backman, C. W., & Secord, P. F. (1959). The effect of perceived liking on interpersonal attraction. Human Relations, 12, 379–84.CrossRefGoogle Scholar
Barabási, A. L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509–512.Google Scholar
Bernard, H. R., & Killworth, P. D. (1977). Informant accuracy in social network data II. Human Communication Research, 4(1), 3–18.CrossRefGoogle Scholar
Bernard, H. R., Killworth, P. D., & Sailer, L. (1982). Informant accuracy in social-network data V. An experimental attempt to predict actual communication from recall data. Social Science Research, 11(1), 30–66.Google Scholar
Bernard, H. R., Killworth, P., & Sailer, L. (1981). Summary of research on informant accuracy in network data and the reverse small world problem. Connections, 4(2), 11–25.Google Scholar
Berndt, T. J., & Murphy, L. M. (2002). Influences of friends and friendships: Myths, truths, and research recommendations. Advances in child development and behavior, 30, 275–310.Google Scholar
Blau, P. M. (1977). Inequality and heterogeneity: A primitive theory of social structure (Vol. 7). New York: Free Press.Google Scholar
Borgatti, S. P., & Everett, M. G. (2000). Models of core/periphery structures. Social Networks, 21(4), 375–395.CrossRefGoogle Scholar
Burt, R. S., & Knez, M. (1995). Kinds of third-party effects on trust. Rationality and Society, 7(3), 255–292.CrossRefGoogle Scholar
Byrne, D. E. (1971). The attraction paradigm (Vol. 11). Cambridge, MA: Academic Press.Google Scholar
Carley, K. M. (1991). Designing organizational structures to cope with communication breakdowns: A simulation model. Organization & Environment, 5(1), 19–57.CrossRefGoogle Scholar
Casciaro, T. (1998). Seeing things clearly: Social structure, personality, and accuracy in social network perception. Social Networks, 20(4), 331–351.CrossRefGoogle Scholar
Christakis, N. A., & Fowler, J. H. (2007). The spread of obesity in a large social network over 32 years. New England Journal of Medicine, 357(4), 370–379.CrossRefGoogle Scholar
Christakis, N. A., & Fowler, J. H. (2008). The collective dynamics of smoking in a large social network. New England Journal of Medicine, 358(21), 2249–2258.CrossRefGoogle Scholar
Davis, G. F., Yoo, M., & Baker, W. E. (2003). The small world of the American corporate elite, 1982–2001. Strategic Organization, 1(3), 301–326.CrossRefGoogle Scholar
Davis, J. A. and Leinhardt, S. (1972): The structure of positive interpersonal relations in small groups. In J. Berger, M. Zeldith Jr., & B. Anderson (Eds.), Sociological Theories in Progress (Vol. 2, pp. 218–251). Boston: Houghton Mifflin.Google Scholar
Doreian, P. (2001). Causality in social network analysis. Sociological Methods & Research, 30(1), 81–114.CrossRefGoogle Scholar
Emirbayer, M., & Goodwin, J. (1994). Network analysis, culture, and the problem of agency. American Journal of Sociology, 1411–1454.CrossRefGoogle Scholar
Feld, S. L. (1981). The focused organization of social ties. American Journal of Sociology, 1015–1035.CrossRefGoogle Scholar
Feld, S. L., & Carter, W. C. (2002). Detecting measurement bias in respondent reports of personal networks. Social Networks, 24(4), 365–383.CrossRefGoogle Scholar
Fleming, L., King III, C., & Juda, A. I. (2007). Small worlds and regional innovation. Organization Science, 18(6), 938–954.CrossRefGoogle Scholar
Frank, K. A. (2000). Impact of a confounding variable on a regression coefficient. Sociological Methods & Research, 29(2), 147–194.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Frank, K. A., Zhao, Y., Penuel, W. R., Ellefson, N., & Porter, S. (2011). Focus, fiddle, and friends: Experiences that transform knowledge for the implementation of innovations. Sociology of education, 84(2), 137–156.CrossRefGoogle Scholar
Frank, K. A., Maroulis, S. J., Duong, M. Q., & Kelcey, B. M. (2013). What would it take to change an inference? Using Rubin’s causal model to interpret the robustness of causal inferences. Educational Evaluation and Policy Analysis, 35(4), 437–460.CrossRefGoogle Scholar
Frank, K. & Min, K. S. (2007). 10. Indices of Robustness for Sample Representation. Sociological Methodology, 37(1), 349–392.Google Scholar
Frank, K. A. & Xu, R. (2020). Causal Inference for Social Network Analysis. In R. Light & J. Moody (Eds.), The Oxford Handbook of Social Networks. 288–310. New York, Oxford: Oxford University Press.Google Scholar
Freeman, L. C. (1977). A set of measures of centrality based on betweenness. Sociometry, 40(1), 35–41.CrossRefGoogle Scholar
Freeman, L. C., Romney, A. K., & Freeman, S. C. (1987). Cognitive structure and informant accuracy. American Anthropologist, 89(2), 310–325.CrossRefGoogle Scholar
Friedkin, N. E., & Johnsen, E. C. (1990). Social influence and opinions. Journal of Mathematical Sociology, 15(3–4), 193–206.CrossRefGoogle Scholar
Friedkin, N. E., & Johnsen, E. C. (1999). Social influence networks and opinion change. Advances in Group Processes, 16(1), 1–29.Google Scholar
Girvan, M., & Newman, M. E. (2002). Community structure in social and biological networks. Proceedings of the National Academy of Sciences, 99(12), 7821–7826.CrossRefGoogle Scholar
Goffman, E. (1963). Behavior in public places: Notes on the social organization of gatherings. New York: Free Press Glencoe. 248 pp.Google Scholar
Golder, S. A., Wilkinson, D. M., & Huberman, B. A. (2007). Rhythms of social interaction: Messaging within a massive online network. In C. Steinfield, B. T. Pentland, M. Ackerman, & N. Contractor (Eds.), Communities and technologies 2007 (pp. 41-66). London: Springer.Google Scholar
Granovetter, M. S. (1973). The strength of weak ties. American Journal of Sociology, 1360–1380.CrossRefGoogle Scholar
Guimerà, R., & Sales-Pardo, M. (2009). Missing and spurious interactions and the reconstruction of complex networks. Proceedings of the National Academy of Sciences, 106(52), 22073–22078.CrossRefGoogle Scholar
Handcock, M. S., & Gile, K. J. (2010). Modeling social networks from sampled data. The Annals of Applied Statistics, 4(1), 5.CrossRefGoogle Scholar
Hoff, P. D., Raftery, A. E., & Handcock, M. S. (2002). Latent space approaches to social network analysis. Journal of the American Statistical Association, 97(460), 1090–1098.CrossRefGoogle Scholar
Huisman, M. (2009). Imputation of missing network data: Some simple procedures. Journal of Social Structure, 10(1), 1–29.Google Scholar
Iyengar, R., Van den Bulte, C., & Valente, T. W. (2011). Opinion leadership and social contagion in new product diffusion. Marketing Science, 30, 195–212.CrossRefGoogle Scholar
Jin, E. M., Girvan, M., & Newman, M. E. (2001). Structure of growing social networks. Physical Review E, 64(4), 046132.CrossRefGoogle Scholar
Kandel, D. B. (1978). Homophily, selection, and socialization in adolescent friendships. American Journal of Sociology, 84(2), 427–436.CrossRefGoogle Scholar
Killworth, P., & Bernard, H. (1976). Informant accuracy in social network data. Human Organization, 35(3), 269–286.CrossRefGoogle Scholar
Kossinets, G. (2006). Effects of missing data in social networks. Social Networks, 28(3), 247–268.CrossRefGoogle Scholar
Kossinets, G., & Watts, D. J. (2009). Origins of homophily in an evolving social network. American Journal of Sociology, 115(2), 405–450.CrossRefGoogle Scholar
Krackhardt, D. (1987). QAP partialling as a test of spuriousness. Social Networks, 9(2), 171–186.CrossRefGoogle Scholar
Leenders, R. T. A. (2002). Modeling social influence through network autocorrelation: constructing the weight matrix. Social networks, 24(1), 21–47.CrossRefGoogle Scholar
Leifer, E. M. (1988). Interaction preludes to role setting: Exploratory local action. American Sociological Review, 53(6), 865.CrossRefGoogle Scholar
Liljeros, F., Edling, C. R., Amaral, L. A. N., Stanley, H. E., & Åberg, Y. (2001). The web of human sexual contacts. Nature, 411(6840), 907–908.Google Scholar
Lyons, R. (2011). The spread of evidence-poor medicine via flawed social-network analysis. Statistics, Politics, and Policy, 2(1).CrossRefGoogle Scholar
Manski, C. F. (1993). Identification of endogenous social effects: The reflection problem. The Review of Economic Studies, 60(3), 531–542.CrossRefGoogle Scholar
Mark, N. (1998). Beyond individual differences: Social differentiation from first principles. American Sociological Review, 309–330.CrossRefGoogle Scholar
Marsden, P. V. (1990). Network data and measurement. Annual Review of Sociology, 435–463.CrossRefGoogle Scholar
Marsden, P. V., & Friedkin, N. E. (1993). Network studies of social influence. Sociological Methods & Research, 22(1), 127–151.CrossRefGoogle Scholar
Marsden, P. V. (2005). Recent developments in network measurement. Models and Methods in Social Network Analysis, 8, 30.CrossRefGoogle Scholar
Martin, C., & Niemeyer, P. (2019). Influence of measurement errors on networks: Estimating the robustness of centrality measures. Network Science, 7(2), 180–195.CrossRefGoogle Scholar
Mayhew, B. H. (1980). Structuralism versus individualism: Part 1, shadowboxing in the dark. Social Forces, 59(2), 335–375.CrossRefGoogle Scholar
McPherson, M., Smith-Lovin, L., & Cook, J. M. (2001). Birds of a feather: Homophily in social networks. Annual Review of Sociology, 415–444.CrossRefGoogle Scholar
Merton, R. K. (1968). The Matthew effect in science. Science, 159(3810), 56–63.Google Scholar
Mollica, K. A., Gray, B., & Trevino, L. K. (2003). Racial homophily and its persistence in newcomers’ social networks. Organization Science, 14(2), 123–136.CrossRefGoogle Scholar
Montoya, R. M., & Insko, C. A. (2008). Toward a more complete understanding of the reciprocity of liking effect. European Journal of Social Psychology, 38(3), 477–498.CrossRefGoogle Scholar
Moffitt, R. A. (2001). Policy interventions, low-level equilibria, and social interactions. Social Dynamics, 4(45–82), 6–17.Google Scholar
Moody, J. (2004). The structure of a social science collaboration network: Disciplinary cohesion from 1963 to 1999. American Sociological Review, 69(2), 213–238.CrossRefGoogle Scholar
Newcomb, T. M. (1956). The prediction of interpersonal attraction. American psychologist, 11(11), 575.CrossRefGoogle Scholar
Newman, M. E. (2001). The structure of scientific collaboration networks. Proceedings of the National Academy of Sciences, 98(2), 404–409.CrossRefGoogle Scholar
Page, S. E. (2007). The difference: How the power of diversity creates better groups, firms, schools, and societies. Princeton, NJ: Princeton Univ. Press.Google Scholar
Pan, W., & Frank, K. A. (2004). An approximation to the distribution of the product of two dependent correlation coefficients. Journal of Statistical Computation and Simulation, 74(6), 419–443.CrossRefGoogle Scholar
Penuel, W. R., Sun, M., Frank, K. A., & Gallagher, H. A. (2012). Using social network analysis to study how collegial interactions can augment teacher learning from external professional development. American Journal of Education, 119(1), 103–136.CrossRefGoogle Scholar
Pitts, V. M., & Spillane, J. P. (2009). Using social network methods to study school leadership. International Journal of Research & Method in Education, 32(2), 185–207.CrossRefGoogle Scholar
Platt, J. R. (1964). Strong inference. Science, 146(3642), 347–353.Google Scholar
Pustejovsky, J. E., & Spillane, J. P. (2009). Question-order effects in social network name generators. Social networks, 31(4), 221–229.CrossRefGoogle Scholar
Rivera, M. T., Soderstrom, S. B., & Uzzi, B. (2010). Dynamics of dyads in social networks: Assortative, relational, and proximity mechanisms. Annual Review of Sociology, 36, 91–115.CrossRefGoogle Scholar
Robins, G., Pattison, P., & Woolcock, J. (2004). Missing data in networks: Exponential random graph (p*) models for networks with non-respondents. Social Networks, 26(3), 257–283.CrossRefGoogle Scholar
Robins, G., Pattison, P., Kalish, Y., & Lusher, D. (2007). An introduction to exponential random graph (p*) models for social networks. Social Networks, 29(2), 173–191.CrossRefGoogle Scholar
Rosenbaum, P. R., & Rubin, D. B. (1983). Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. Journal of the Royal Statistical Society. Series B (Methodological), 212–218.CrossRefGoogle Scholar
Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41–55.CrossRefGoogle Scholar
Runger, G., & Wasserman, S. (1980). Longitudinal analysis of friendship networks. Social Networks, 2(2), 143–154.CrossRefGoogle Scholar
Schelling, T. C. (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1(2), 143–186.CrossRefGoogle Scholar
Shalizi, C. R., & Thomas, A. C. (2011). Homophily and contagion are generically confounded in observational social network studies. Sociological Methods & Research, 40(2), 211–239.CrossRefGoogle Scholar
Snijders, T. A., Steglich, C. E., & Schweinberger, M. (2007). Modeling the co-evolution of networks and behavior. Longitudinal models in the behavioral and related sciences, 31(4), 41–71.Google Scholar
Sprecher, S. (1998). Insiders’ perspectives on reasons for attraction to a close other. Social Psychology Quarterly, 287–300.CrossRefGoogle Scholar
Steglich, C., Snijders, T. A., & Pearson, M. (2010). Dynamic networks and behavior: Separating selection from influence. Sociological Methodology, 40(1), 329–393.CrossRefGoogle Scholar
Sun, M., Penuel, W. R., Frank, K. A., Gallagher, H. A., & Youngs, P. (2013). Shaping professional development to promote the diffusion of instructional expertise among teachers. Educational Evaluation and Policy Analysis, 35, 344–369.CrossRefGoogle Scholar
Sweet, T., & Adhikari, S. (2020). A Latent Space Network Model for Social Influence. Psychometrika, 1–24.CrossRefGoogle Scholar
Uzzi, B., & Spiro, J. (2005). Collaboration and creativity: The small world Problem1. American Journal of Sociology, 111(2), 447–504.CrossRefGoogle Scholar
Valente, T. W. (1996). Social network thresholds in the diffusion of innovations. Social networks, 18(1), 69–89.CrossRefGoogle Scholar
Valente, T. W. (2005). Network models and methods for studying the diffusion of innovations. In P. J. Carrington, J. Scott, & Stanley (Eds.), Models and methods in social network analysis, 28, 98. Cambridge: Cambridge university press.Google Scholar
Valente, T. W., Pitts, S., Wipfli, H., & Yon, G. G. V. (2019). Network influences on policy implementation: Evidence from a global health treaty. Social Science & Medicine, 222, 188–197.CrossRefGoogle Scholar
VanderWeele, T. J. (2011). Sensitivity analysis for contagion effects in social networks. Sociological Methods & Research, 40(2), 240–255.CrossRefGoogle Scholar
VanderWeele, T. J., & An, W. (2013). Social networks and causal inference. In Handbook of causal analysis for social research (pp. 353–374). Springer, Dordrecht. Edited by Stephen L. Morgan.CrossRefGoogle Scholar
Van Duijn, M. A., Snijders, T. A., & Zijlstra, B. J. (2004). p2: A random effects model with covariates for directed graphs. Statistica Neerlandica, 58(2), 234–254.CrossRefGoogle Scholar
Wasserman, S. & Faust, K. (1994). Social network analysis: Methods and applications (Vol. 8). Cambridge university press, Cambridge.CrossRefGoogle Scholar
Watts, D. J. (1999). Networks, dynamics, and the small-world phenomenon. American Journal of sociology, 105(2), 493–527.CrossRefGoogle Scholar
Xu, R. (2018). Alternative estimation methods for identifying contagion effects in dynamic social networks: A latent-space adjusted approach. Social Networks, 54, 101–117.CrossRefGoogle Scholar
Zerubavel, N., Bearman, P. S., Weber, J., & Ochsner, K. N. (2015). tracking popularity in real-world social networks. Proceedings of the National Academy of Sciences, 112(49), 15072–15077.CrossRefGoogle Scholar
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, 328–336.CrossRefGoogle Scholar
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