Inference of a universal social scale and segregation measures using social connectivity kernels

Hoffmann, Till and Jones, Nick S. (2020): Inference of a universal social scale and segregation measures using social connectivity kernels. Published in: Journal of the Royal Society Interface , Vol. 17, No. 171 (28 October 2020): p. 20200638.

Abstract

How people connect with one another is a fundamental question in the social sciences, and the resulting social networks can have a profound impact on our daily lives. Blau offered a powerful explanation: people connect with one another based on their positions in a social space. Yet a principled measure of social distance, allowing comparison within and between societies, remains elusive. We use the connectivity kernel of conditionally independent edge models to develop a family of segregation statistics with desirable properties: they offer an intuitive and universal characteristic scale on social space (facilitating comparison across datasets and societies), are applicable to multivariate and mixed node attributes, and capture segregation at the level of individuals, pairs of individuals and society as a whole. We show that the segregation statistics can induce a metric on Blau space (a space spanned by the attributes of the members of society) and provide maps of two societies. Under a Bayesian paradigm, we infer the parameters of the connectivity kernel from 11 ego-network datasets collected in four surveys in the UK and USA. The importance of different dimensions of Blau space is similar across time and location, suggesting a macroscopically stable social fabric. Physical separation and age differences have the most significant impact on segregation within friendship networks with implications for intergenerational mixing and isolation in later stages of life.

• Item Type: MPRA Paper
• Language: English
• Keywords: social networks; segregation; ego networks; inference
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; Z - Other Special Topics > Z1 - Cultural Economics ; Economic Sociology ; Economic Anthropology > Z13 - Economic Sociology ; Economic Anthropology ; Social and Economic Stratification

References

Blau PM. 1977 A macrosociological theory of social structure. Am. J. Sociol. 83, 26-54. (doi:10.1086/226505) McPherson M, Smith-Lovin L, Cook JM. 2001 Birds of a feather: homophily in social networks. Annu. Rev. Sociol. 27, 415-444. (doi:10.1146/annurev.soc.27.1.415) McPherson M, Smith-Lovin L, Brashears ME. 2006 Social isolation in America: changes in core discussion networks over two decades. Am. Sociol. Rev. 71, 353-375. (doi:10.1177/000312240607100301) Mossong J et al. 2008 Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS Med. 5, e74. (doi:10.1371/journal.pmed.0050074) Golub B, Jackson MO. 2012 How homophily affects the speed of learning and best-response dynamics. Q. J. Econ. 127, 1287-1338. (doi:10.1093/qje/qjs021) Boutyline A, Willer R. 2017 The social structure of political echo chambers: variation in ideological homophily in online networks. Polit. Psychol. 38, 551-569. (doi:10.1111/pops.12337) Bakshy E, Messing S, Adamic LA. 2015 Exposure to ideologically diverse news and opinion on facebook. Science 348, 1130-1132. (doi:10.1126/science.aaa1160) DeMarzo PM, Vayanos D, Zwiebel J. 2003 Persuasion bias, social influence, and unidimensional opinions. Q. J. Econ. 118, 909-968. (doi:10.1162/00335530360698469) Salathé M, Bonhoeffer S. 2008 The effect of opinion clustering on disease outbreaks. J. R. Soc. Interface 5, 1505-1508. (doi:10.1098/rsif.2008.0271) Currarini S, Jackson MO, Pin P. 2009 An economic model of friendship: homophily, minorities, and segregation. Econometrica 77, 1003-1045. (doi:10.3982/ECTA7528) Hipp JR, Perrin AJ. 2009 The simultaneous effect of social distance and physical distance on the formation of neighborhood ties. City Community 8, 5-25. (doi:10.1111/j.1540-6040.2009.01267.x) Wang Y, Zang H, Faloutsos M. 2013 Inferring cellular user demographic information using homophily on call graphs. In 2013 IEEE Conf. on Computer Communications Workshops (INFOCOM WKSHPS), Turin, Italy, pp. 211–216. See http://ieeexplore.ieee.org/document/6562897/. Leo Y, Fleury E, Alvarez-Hamelin JI, Sarraute C, Karsai M. 2016 Socioeconomic correlations and stratification in social-communication networks. J. R. Soc. Interface 13, 20160598. (doi:10.1098/rsif.2016.0598) Blau P, Schwartz J. 1984 Crosscutting social circles: testing a macrostructual theory of integroup relations. New York, NY: Routledge. Chang J, Rosen I, Backstrom L, Marlow C. 2010 ePluribus: ethnicity on social networks. In ICWSM. Marsden PV. 1988 Homogeneity in confiding relations. Soc. Netw. 10, 57-76. (doi:10.1016/0378-8733(88)90010-X) Smith JA, McPherson M, Smith-Lovin L. 2014 Social distance in the United States: sex, race, religion, age, and education homophily among confidants, 1985 to 2004. Am. Sociol. Rev. 79, 432-456. (doi:10.1177/0003122414531776) Blumenstock J, Fratamico L. 2013 Social and spatial ethnic segregation: a framework for analyzing segregation with large-scale spatial network data. In ACM DEV-4 '13: Proceedings of the 4th Annual Symposium on Computing for Development, Cape Town, South Africa, December, pp. 1–10, art. no.: 11. New York, NY: ACM. See https://doi.org/10.1145/2537052.2537061. Johnson MA. 1989 Variables associated with friendship in an adult population. J. Soc. Psychol. 129, 379-390. (doi:10.1080/00224545.1989.9712054) Chan TW, Goldthorpe JH. 2004 Is there a status order in contemporary british society? Evidence from the occupational structure of friendship. Eur. Sociol. Rev. 20, 383-401. (doi:10.1093/esr/jch033) Platt L. 2012 Exploring social spaces of Muslims. In Muslims in Britain: making social and political space, pp. 53–83. London, UK: Routledge. Kalmijn M, Vermunt JK. 2007 Homogeneity of social networks by age and marital status: a multilevel analysis of ego-centered networks. Soc. Netw. 29, 25-43. (doi:10.1016/j.socnet.2005.11.008) Lambiotte R, Blondel VD, De Kerchove C, Huens E, Prieur C, Smoreda Z, Van Dooren P. 2008 Geographical dispersal of mobile communication networks. Physica A 387, 5317-5325. (doi:10.1016/j.physa.2008.05.014) Expert P, Evans TS, Blondel VD, Lambiotte R. 2011 Uncovering space-independent communities in spatial networks. Proc. Natl Acad. Sci. USA 108, 7663-7668. (doi:10.1073/pnas.1018962108) Backstrom L, Sun E, Marlow C. 2010 Find me if you can: improving geographical prediction with social and spatial proximity. In WWW '10: Proceedings of the 19th international conference on World Wide Web, April, pp. 61-70. (doi:10.1145/1772690.1772698) Scellato S, Noulas A, Lambiotte R, Mascolo C. 2011 Socio-spatial properties of online location-based social networks. In 5th Int. AAAI Conf. on Weblogs and Social Media (ICWSM-11), Barcelona, Spain, 17–21 July. See https://www.aaai.org/ocs/index.php/ICWSM/ICWSM11/paper/view/2751. Illenberger J, Nagel K, Flötteröd G. 2013 The role of spatial interaction in social networks. Netw. Spat. Econ. 13, 255-282. (doi:10.1007/s11067-012-9180-4) Rodriguez-Moral A, Vorsatz M. 2016 An overview of the measurement of segregation: classical approaches and social network analysis. In Complex networks and dynamics, pp. 93–119. New York, NY: Springer. Bojanowski M, Corten R. 2014 Measuring segregation in social networks. Soc. Netw. 39, 14-32. (doi:10.1016/j.socnet.2014.04.001) Orfield G, Frankenberg E. 2014 Brown at 60: great progress, a long retreat and an uncertain future. Tech. rep. Civil Rights Project. See https://civilrightsproject.ucla.edu/research/k-12-education/integration-and-diversity/brown-at-60-great-progress-a-long-retreat-and-an-uncertain-future/Brown-at-60-051814.pdf. Popielarz PA. 1999 (In)voluntary association: a multilevel analysis of gender segregation in voluntary organizations. Gender Soc. 13, 234-250. (doi:10.1177/089124399013002005) Charles M, Grusky DB. 1995 Models for describing the underlying structure of sex segregation. Am. J. Sociol. 100, 931-971. (doi:10.1086/230605) Reardon SF, O’Sullivan D. 2004 Measures of spatial segregation. Sociol. Methodol. 34, 121-162. (doi:10.1111/j.0081-1750.2004.00150.x) Moody J. 2001 Race, school integration, and friendship segregation in America. Am. J. Sociol. 107, 679-716. (doi:10.1086/338954) Newman MEJ. 2003 Mixing patterns in networks. Phys. Rev. E 67, 026126. (doi:10.1103/PhysRevE.67.026126) Lam Morgan D. 2012 A spatial econometric approach to the study of social influence. PhD thesis. University of Texas Austin. Kim M, Leskovec J. 2012 Multiplicative attribute graph model of real-world networks. Internet Math. 8, 113-160. (doi:10.1080/15427951.2012.625257) Pelechrinis K, Wei D. 2016 VA-index: quantifying assortativity patterns in networks with multidimensional nodal attributes. PLoS ONE 11, e0146188. Butts CT, Acton RM, Hipp JR, Nagle NN. 2012 Geographical variability and network structure. Soc. Netw. 34, 82-100. (doi:10.1016/j.socnet.2011.08.003) Golder SA, Macy MW. 2014 Digital footprints: opportunities and challenges for online social research. Annu. Rev. Sociol. 40, 129-152. (doi:10.1146/annurev-soc-071913-043145) Blumenstock J, Cadamuro G, On R. 2015 Predicting poverty and wealth from mobile phone metadata. Science 350, 1073-1076. (doi:10.1126/science.aac4420) Luo S, Morone F, Sarraute C, Travizano M, Makse HA. 2017 Inferring personal economic status from social network location. Nat. Commun. 8, 15227. (doi:10.1038/ncomms15227) Wang Y, Kosinski M. 2017 Deep neural networks are more accurate than humans at detecting sexual orientation from facial images. Open Sci. Framework 114, zn79k. Kosinski M, Stillwell D, Graepel T. 2013 Private traits and attributes are predictable from digital records of human behavior. Proc. Natl Acad. Sci. USA 110, 5802-5805. (doi:10.1073/pnas.1218772110) Backstrom L, Dwork C, Kleinberg J. 2011 Wherefore art thou R3579X?: anonymized social networks, hidden patterns, and structural steganography. Commun. ACM 54, 133-141. (doi:10.1145/2043174.2043199) Narayanan A, Shmatikov V. 2008 Robust de-anonymization of large sparse datasets. In Symp. on Security and Privacy, pp. 111–125. (doi:10.1109/SP.2008.33) Huckfeldt RR. 1983 Social contexts, social networks, and urban neighborhoods: environmental constraints on friendship choice. Am. J. Sociol. 89, 651-669. (doi:10.1086/227908) Marsden PV. 1987 Core discussion networks of Americans. Am. Sociol. Rev. 52, 122-131. (doi:10.2307/2095397) Banerjee A, Chandrasekhar AG, Duflo E, Jackson MO. 2013 The diffusion of microfinance. Science 341, 1236498. (doi:10.1126/science.1236498) Marin A. 2004 Are respondents more likely to list alters with certain characteristics? Implications for name generator data. Soc. Netw. 26, 289-307. (doi:10.1016/j.socnet.2004.06.001) Eagle DE, Proeschold-Bell RJ. 2015 Methodological considerations in the use of name generators and interpreters. Soc. Netw. 40, 75-83. (doi:10.1016/j.socnet.2014.07.005) Eveland WP, Appiah O, Beck PA. 2017 Americans are more exposed to difference than we think: capturing hidden exposure to political and racial difference. Soc. Netw. 52, 192-200. (doi:10.1016/j.socnet.2017.08.002) Snijders TAB. 2011 Statistical models for social networks. Annu. Rev. Sociol. 37, 131-153. (doi:10.1146/annurev.soc.012809.102709) Hoff PD, Raftery AE, Handcock MS. 2002 Latent space approaches to social network analysis. J. Am. Stat. Assoc. 97, 1090-1098. (doi:10.1198/016214502388618906) Hoff PD. 2008 Multiplicative latent factor models for description and prediction of social networks. Comput. Math. Organ. Theory 15, 261-272. (doi:10.1007/s10588-008-9040-4) Ball B, Newman MEJ. 2013 Friendship networks and social status. Netw. Sci. 1, 16-30. (doi:10.1017/nws.2012.4) Fienberg SE. 2012 A brief history of statistical models for network analysis and open challenges. J. Comput. Graph. Stat. 21, 825-839. (doi:10.1080/10618600.2012.738106) Barnett L, Di Paolo E, Bullock S. 2007 Spatially embedded random networks. Phys. Rev. E 76, 056115. (doi:10.1103/PhysRevE.76.056115) Caron F, Fox EB. 2017 Sparse graphs using exchangeable random measures. J. R. Stat. Soc. B 79, 1295-1366. (doi:10.1111/rssb.12233) Freeman LC. 1978 Segregation in social networks. Sociol. Methods Res. 6, 411-429. (doi:10.1177/004912417800600401) Krackhardt D, Stern RN. 1988 Informal networks and organizational crises: an experimental simulation. Soc. Psychol. Q. 51, 123-140. (doi:10.2307/2786835) Hastie T, Tibshirani R, Friedman J. 2009 The elements of statistical learning: data mining, inference and prediction. New York, NY: Springer. Wilson WA. 1931 On semi-metric spaces. Am. J. Math. 53, 361-373. (doi:10.2307/2370790) Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. 2013 Bayesian data analysis. Boca Raton, FL: Chapman and Hall/CRC. King G, Zeng L. 2001 Logistic regression in rare events data. Pol. Anal. 9, 137-163. (doi:10.1093/oxfordjournals.pan.a004868) Pigott TD. 2001 A review of methods for missing data. Educ. Res. Eval. 7, 353-383. (doi:10.1076/edre.7.4.353.8937) Gelman A. 2008 Scaling regression inputs by dividing by two standard deviations. Stat. Med. 27, 2865-2873. (doi:10.1002/sim.3107) Gelman A, Jakulin A, Pittau MG, Su Y-S. 2008 A weakly informative default prior distribution for logistic and other regression models. Ann. Appl. Stat. 2, 1360-1383. (doi:10.1214/08-AOAS191) Hastings WK. 1970 Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109. (doi:10.1093/biomet/57.1.97) Pollard M, Baird MD. 2017 The RAND American Life Panel. Research Report. Santa Monica, CA: RAND. See https://doi.org/10.7249/RR1651. Mihaly K. 2009 American Life Panel: well-being 86 questionnaire. Santa Monica, CA: RAND corporation. Hutcheon JA, Chiolero A, Hanley JA. 2010 Random measurement error and regression dilution bias. BMJ 340, 1402-1406. (doi:10.1136/bmj.c2289) Institute for Social and Economic Research. 2000 British Household Panel Survey Questionnaire Wave 10. See https://www.iser.essex.ac.uk/bhps/documentation/pdf_versions/questionnaires/bhpsw10q.pdf. Institute for Social and Economic Research. 2017 UK Household Longitudinal Study Mainstage Questionnaire Wave 3. See https://www.understandingsociety.ac.uk/documentation/mainstage/questionnaire/questionnaire-documents/mainstage/wave-3/Understanding_Society_Wave_3_Questionnaire_v03.pdf. Understanding Society User Support. 2016 Unusual age distribution after conditioning on wJBSTATT in wave R. See https://www.understandingsociety.ac.uk/support/issues/687. Understanding Society User Support. 2017 Unexpectedly strong gender homophily in Understanding Society compared with the BHPS. See https://www.understandingsociety.ac.uk/support/issues/869. Borg I, Groenen P. 1996 Modern multidimensional scaling: theory and applications. New York, NY: Springer. Franz S, Marsili M, Pin P. 2010 Observed choices and underlying opportunities. Sci. Cult. 76, 471-476. Shalizi CR, Thomas AC. 2011 Homophily and contagion are generically confounded in observational social network studies. Sociol. Methods Res. 40, 211-239. (doi:10.1177/0049124111404820) Biernacki P, Waldorf D. 1981 Snowball sampling: problems and techniques of chain referral sampling. Sociol. Methods Res. 10, 141-163. (doi:10.1177/004912418101000205) Bruch E, Feinberg F, Lee KY. 2016 Extracting multistage screening rules from online dating activity data. Proc. Natl Acad. Sci. USA 113, 10 530-10 535. (doi:10.1073/pnas.1522494113) Po JYT, Finlay JE, Brewster MB, Canning D. 2012 Estimating household permanent income from ownership of physical assets. PGDA Working Papers 9712, Program on the Global Demography of Aging. See https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1288/2013/10/PGDA_WP_97.pdf. Wimmer A, Lewis K. 2010 Beyond and below racial homophily: ERG models of a friendship network documented on facebook. Am. J. Sociol. 116, 583-642. (doi:10.1086/653658) Bhattacharya K, Ghosh A, Monsivais D, Dunbar RIM, Kaski K. 2016 Sex differences in social focus across the life cycle in humans. Open Sci. 3, 160097. Stouffer SA. 1940 Intervening opportunities: a theory relating mobility and distance. Am. Sociol. Rev. 5, 845-867. (doi:10.2307/2084520) Frölich M. 2006 Non-parametric regression for binary dependent variables. Econ. J. 9, 511-540. (doi:10.1111/j.1368-423X.2006.00196.x)