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Health Services and Outcomes Research Methodology

Published in:

01-12-2008

The analysis of social networks

Authors: A. James O’Malley, Peter V. Marsden

Published in: Health Services and Outcomes Research Methodology | Issue 4/2008

Abstract

Many questions about the social organization of medicine and health services involve interdependencies among social actors that may be depicted by networks of relationships. Social network studies have been pursued for some time in social science disciplines, where numerous descriptive methods for analyzing them have been proposed. More recently, interest in the analysis of social network data has grown among statisticians, who have developed more elaborate models and methods for fitting them to network data. This article reviews fundamentals of, and recent innovations in, social network analysis using a physician influence network as an example. After introducing forms of network data, basic network statistics, and common descriptive measures, it describes two distinct types of statistical models for network data: individual-outcome models in which networks enter the construction of explanatory variables, and relational models in which the network itself is a multivariate dependent variable. Complexities in estimating both types of models arise due to the complex correlation structures among outcome measures.

Available only for authorised users

To aid readers in applying these methods, we provide some references to network software throughout, but our coverage of software is not comprehensive. Huisman and Van Duijn (2005) review software resources available earlier in this decade.

The extent to which distances in a graphical representation correspond to the data on which they rest—dyadic measurements of social distance or proximity—depends on the objective function that serves as a fitting criterion when the plot is constructed. The most widely-used “nonmetric” multidimensional scaling algorithm requires an ordinal correspondence between data and plotted distances; “metric” scaling uses a stronger (linear) criterion. Objective functions used by many spring-embedder methods involve a “node repulsion” term that simplifies the visual representation by discouraging co-location of vertices within a plot, but simultaneously limits the extent to which data and plotted distances correspond. Moreover, a low (ordinarily 2)-dimensional Cartesian plot may do more or less well in representing data on the relationships among N actors, which may in principle be (N − 1)-dimensional.

Note that some or all of the intermediaries along these geodesic paths may be physicians 11–33.

Recall that the undirected physician network is identical to that shown in Fig. 1, except that ties lack directionality.

We calculated centrality scores using the software package UCINET 6 (Borgatti, Everett, and Freeman, 2002).

Eigenvalue centrality can in principle be calculated for a nonsymmetric matrix, but the routine in UCINET 6 handles only the symmetric case.

Because two actors have outdegrees of 0, the associated rows of W sum to 0 as opposed to 1. Therefore, although these actors contribute to the estimation of β and σ², they do not directly contribute any information about the autocorrelation parameters α and ρ. We retained these actors in the analysis because they were cited by other physicians as influencing them and so removing them would omit information about how other actors were influenced.

Computations were performed using the StOCNET software package (Boer et al. 2006).

Under p₁, the estimate of a receiver parameter is infinitely small for actors with indegree 0; likewise, the estimate of a sender parameter is -∞ when the corresponding outdegree is 0.

The p₂ model is closely related to a social relations model developed by Kenny and La Voie (1984) for quantitative network variables.

The large number of terms in κ(θ) complicates the estimation of ERGMs. There are 2^N(N−1)possible directed binary-valued networks; for example, with N = 10, the number of possible networks—hence terms in κ(θ)—is 1.238 × 10²⁷.

For example, an actor with degree 3 contributes 1 3-star, 3 2-stars, and 3 1-stars; 1-stars are equivalent to individual edges.

The set of k-star statistics is equivalent to the set of degree statistics (the number of nodes of degree k, k = 1,2,3,…) in that a bijection exists between the two sets of the statistics (Snijders et al. 2006).

An analogous “sender covariate” statistic allows the density effect to depend on an attribute of the sender (i).

\( {\mathbf{y}}_{ij}^{ + } \)is the realization of the complement network with y _ij = 1, while \( {\mathbf{y}}_{ij}^{ - } \) is the realization of the complement network with y _ij = 0.

An equivalent statistic based on the degree distribution itself is known as the “geometrically weighted degree” statistic; see Hunter and Handcock (2006).

No mutuality term is included, since this is redundant with the edges term in an undirected network. Constraining the value of ρ when fitting the model with the GWESP term is often helpful; attaining adequate convergence is more difficult when it is estimated as a free parameter. We found that setting ρ = 1.2 served well here; the likelihood surface is relatively flat, so that using a value between 1.0 and 1.5 did not affect inferences about other parameters. Note, however, ρ was estimated at 0.93 when we left it as a free parameter in the third model in Table 9.

Although the missing values are replaced with non-missing values during model fitting, the statistics measuring model fit are only evaluated using actors with non-missing values throughout the corresponding interval of time. Thus, standard imputation is not performed.

Anderson, C., Wasserman, S., Crouch, B.: A p* primer: logit models for social networks. Soc. Networks 21(1), 37–66 (1999). doi:10.1016/S0378-8733(98)00012-4

Anselin, L.: Spatial Econometrics: Methods and Models. Kluwer Academic Publishers, Dordrecht, The Netherlands (1988)

Anselin, L.: Some robust approaches to testing and estimation in spatial econometrics. Reg. Sci. Urban Econ. 20(2), 141–163 (1990). doi:10.1016/0166-0462(90)90001-J

Banerjee, S., Carlin, B., Gelfand, A.: Hierarchical Modeling and Analysis for Spatial Data. Chapman and Hall, Boca Raton, FL (2004)

Barabási, A.-L.: Linked: The New Science of Networks. Perseus, New York (2002)

Bartholomew, D., Steele, F., Moustaki, I., Galbraith, J.: The Analysis and Interpretation of Multivariate Data for Social Scientists. Chapman and Hall, New York (2002)

Batagelj, V., Mrvar, A.: Pajek: analysis and visualization of large networks. In: Jünger, M., Mutzel, P. (eds.) Graph Drawing Software, pp. 77–103. Springer, New York (2003)

Beauchamp, M.: An improved index of centrality. Behav. Sci. 10, 161–163 (1965). doi:10.1002/bs.3830100205 PubMed

Behrman, J., Kohler, H.-P., Watkins, S.: Social networks and changes in contraceptive use over time: evidence from a longitudinal study in rural Kenya. Demography 39, 713–738 (2002). doi:10.1353/dem.2002.0033 PubMed

Berkman, L., Glass, T.: Social integration, social methods, social support, and health. In: Berkman, L., Kawachi, I. (eds.) Social Epidemiology, pp. 137–173. Oxford University Press, New York (2000)

Berkman, L., Syme, S.: Social networks, host resistance, and mortality: a nine-year follow-up study of Alameda County residents. Am. J. Epidemiol. 109, 86–204 (1979)

Besag, J.: Spatial interaction and statistical-analysis of lattice systems. J. Roy. Stat. Soc. B Met. 36(2), 192–236 (1974)

Besag, J.: Statistical analysis of non-lattice data. J. Inst. Statisticians 24, 179–196 (1975)

Best, N., Cowles, M., Vines, K.: Convergence Diagnosis and Output Analysis Software for Gibbs Sampling Output. MRC Biostatistics Unit, Institute of Public Health, Robinson Way, Cambridge CB2 2SR, UK (1995)

Boer, P., Huisman, M., Snijders, T., Steglich, M., Wicher, L., Zeggelink, E.: StOCNET User’s Manual, Version 1.7. ICS, Groningen, NL (2006)

Bonacich, P.: Power and centrality: a family of measures. Am. J. Sociol. 92, 1170–1182 (1987). doi:10.1086/228631

Borgatti, S.: NetDraw: Graph Visualization Software. Analytical Technologies, Lexington, KY (2008)

Borgatti, S., Everett, M., Freeman, L.: UCINET 6 for Windows: Software for Social Network Analysis. Analytical Technologies, Lexington, KY (2002)

Burt, R.: Structural Holes: The Social Structure of Competition. Harvard University Press, Cambridge, MA (1992)

Burt, R., Doreian, P.: Testing a structural model of perception: conformity and deviance with respect to journal norms in elite sociological methodology. Qual. Quant. 16, 109–150 (1982). doi:10.1007/BF00166880

Butts, C.: sna: Tools for Social Network Analysis (release 1.5) (2007)

Christakis, N.: Social networks and collateral health effects. BMJ 329(7459), 184–185 (2004). doi:10.1136/bmj.329.7459.184 PubMed

Christakis, N., Fowler, J.: The spread of obesity in a large social network over 32 years. N. Engl. J. Med. 357, 370–379 (2007). doi:10.1056/NEJMsa066082 PubMed

Christakis, N., Fowler, J.: The collective dynamics of smoking in a large social network. N. Engl. J. Med. 358, 2249–2258 (2008). doi:10.1056/NEJMsa0706154 PubMed

Coleman, J., Katz, E., Menzel, H.: Medical Innovation: A Diffusion Study. Bobbs-Merrill, Indianapolis (1966)

Doreian, P.: Linear-models with spatially distributed data-spatial disturbances or spatial effects. Sociol. Method. Res. 9(1), 29–60 (1980). doi:10.1177/004912418000900102

Doreian, P.: Estimating linear models with spatially distributed data. In: Leinhardt, S. (ed.) Sociological Methodology, pp. 359–388. Jossey-Bass, San Francisco (1981)

Doreian, P.: Network autocorrelation models: problems and prospects. In: Griffith, D.A. (ed.) Spatial Statistics: Past, Present, Future, pp. 369–389. Michigan Document Services, Ann Arbor (1989)

Doreian, P., Stokman, F.: Evolution of social networks: processes and principles. In: Doreian, P., Stokman, F. (eds.) Evolution of Social Networks, pp. 233–250. Gordon and Breach Publishers, Amsterdam (1997)

Dow, M.: A biparametric approach to network autocorrelation. Sociol. Method. Res. 13, 201–217 (1984). doi:10.1177/0049124184013002002

Erdös, P., Rényi, A.: On random graphs. Pub. Math. 6, 290–297 (1959)

Fienberg, S., Wasserman, S.: Categorical data analysis of single sociometric relations. In: Leinhardt, S. (ed.) Sociological Methodology, pp. 156–192. Jossey-Bass, San Francisco (1981)

Frank, O.: Statistical Inference in Graphs. Stockholm: FOA Repro, Stockholm (1971)

Frank, O.: Sampling and estimation in large social networks. Soc. Networks 11, 91–101 (1978)

Frank, O.: A survey of statistical methods for graph analysis. In: Leinhardt, S. (ed.) Sociological Methodology, pp. 110–155. Jossey-Bass, San Francisco (1981)

Frank, O.: Random sampling and social networks: a survey of various approaches. Math. Informatique Sci. Hum. 26, 19–33 (1988)

Frank, O., Strauss, D.: Markov graphs. J. Am. Stat. Assoc. 81(395), 832–842 (1986). doi:10.2307/2289017

Freeman, L.: Centrality in social networks, I. Conceptual clarification. Soc. Networks 1, 215–239 (1979). doi:10.1016/0378-8733(78)90021-7

Freeman, L.: Social networks and the structure experiment. In: Freeman, L., White, D., Romney, A. (eds.) Research Methods in Social Network Analysis, pp. 11–40. George Mason University Press, Fairfax, VA (1989)

Freeman, L.: The Development of Social Network Analysis: A Study in the Sociology of Science. Empirical Press, Vancouver, BC (2004)

Friedkin, N.: Social networks in structural equations models. Soc. Psychol. Q. 53, 316–328 (1990). doi:10.2307/2786737

Friedkin, N., Cook, K.: Peer group influence. Sociol. Method. Res. 19(1), 122–143 (1990). doi:10.1177/0049124190019001006

Fruchterman, T., Reingold, E.: Graph drawing by force-directed placement. Software Pract. Exper. 21(11), 1129–1164 (1991). doi:10.1002/spe.4380211102

Geyer, C., Thompson, E.: Constrained Monte Carlo maximum likelihood for dependent data. J. Roy. Stat. Soc. B Met. 54(3), 657–699 (1992)

Gill, P., Swartz, T.: Bayesian analysis of directed graphs data with applications to social networks. J. Roy. Stat. Soc. C-App. Stat. 53, 249–260 (2004)

Goodreau, S.: Advances in exponential random graph (p*) models applied to a large social network. Soc. Networks 29, 231–248 (2007). doi:10.1016/j.socnet.2006.08.001 PubMed

Haines, V., Hurlbert, J.: Network range and health. J. Health Soc. Behav. 33, 254–266 (1992). doi:10.2307/2137355 PubMed

Handcock, M.: Assessing Degeneracy in Statistical Models of Social Networks. Center for Statistics and Social Sciences, University of Washington, Seattle (2003)

Handcock, M., Hunter, D., Butts, C., Goodreau, S., Morris, M.: Statnet: Software tools for the Statistical Modeling of Network Data (release Version 2.1). Center for Statistics and Social Sciences, University of Washington, Seattle, WA; Project home page at http://statnetproject.org; Software available at http://CRAN.R-project.org/package=statnet (2003)

Handcock, M., Raftery, A., Tantrum, J.: Model-based clustering for social networks. J. R. Stat. Soc. [Ser A] 170(2), 301–354 (2007). doi:10.1111/j.1467-985X.2007.00471.x

Harville, D.: Matrix Algebra from a Statistician’s Perspective. Springer-Verlag Inc, New York (1997)

Hoff, P.: Bilinear mixed-effects models for dyadic data. J. Am. Stat. Assoc. 100, 286–295 (2005). doi:10.1198/016214504000001015

Hoff, P., Raftery, A., Handcock, M.: Latent space approaches to social network analysis. J. Am. Stat. Assoc. 97, 1090–1098 (2002). doi:10.1198/016214502388618906

Holland, P., Leinhardt, S.: Local structure in social networks. In: Heise, D. (ed.) Sociological Methodology, pp. 1–45. Jossey-Bass, San Francisco (1976)

Holland, P., Leinhardt, S.: A dynamic model for social networks. J. Math. Sociol. 5, 5–20 (1977)

Holland, P., Leinhardt, S.: An exponential family of probability-distributions for directed-graphs. J. Am. Stat. Assoc. 76(373), 33–50 (1981). doi:10.2307/2287037

Holland, P., Laskey, K., Leinhardt, S.: Stochastic blockmodels: first steps. Soc. Networks 5, 109–137 (1983). doi:10.1016/0378-8733(83)90021-7

House, J., Kahn, R.: Measures and concepts of social support. In: Cohen, S., Syme, S. (eds.) Social Support and Health, pp. 83–108. Academic Press, New York (1985)

Huisman, M., Van Duijn, M.: Software for statistical analysis of social networks. In: Van Dijkum, C., Blasius, J., Kleijer, H., Van Hilten, B. (eds.) The Sixth International Conference on Logic and Methodology, Amsterdam, The Netherlands (2004)

Huisman, M., Snijders, T.: Statistical analysis of longitudinal network data with changing composition. Sociol. Method. Res. 32, 253–287 (2003). doi:10.1177/0049124103256096

Huisman, M.,Van Duijn, M.: Software for social networks analysis. In: Carrington, P.J., Scott, J., Wasserman, S. (eds.) Models and Methods in Social Network Analysis, pp. 270–316. Cambridge University Press, Cambridge (2005)

Hunter, D.: Curved exponential family models for social networks. Soc. Networks 29, 216–230 (2007). doi:10.1016/j.socnet.2006.08.005 PubMed

Hunter, D., Goodreau, S., Handcock, M.: Goodness of fit of social network models. J. Am. Stat. Assoc. 103, 248–258 (2008). doi:10.1198/016214507000000446

Hunter, D., Handcock, M.: Inference in curved exponential family models for networks. J. Comput. Graph. Stat. 15, 565–583 (2006)

Katz, L., Powell, J.: Probability distributions of random variables associated with a structure of the sample space of sociometric investigations. Ann. Math. Stat. 28, 442–448 (1957). doi:10.1214/aoms/1177706972

Keating, N., Ayanian, J., Cleary, P., Marsden, P.: Factors affecting influential discussions among physicians: a social network analysis of a primary care practice. J. Gen. Intern. Med. 22(6), 794–798 (2007). doi:10.1007/s11606-007-0190-8 PubMed

Kenny, D., La Voie, L.: The social relations model. In: Berkowitz, L. (ed.) Advances in Experimental Social Psychology, pp. 142–182. Academic Press, New York (1984)

Klovdahl, A.: Social networks and the spread of infectious diseases. Soc. Sci. Med. 21, 1203–1216 (1985). doi:10.1016/0277-9536(85)90269-2 PubMed

Land, K., Deane, G.: On the large-sample estimation of regression models with spatial or network effects terms: a two-stage least-squares approach. In: Marsden, P.V. (ed.) Sociological Methodology, pp. 221–248. Basil Blackwell, Ltd., Oxford (1992)

Laumann, E., Youm, Y.: Racial/ethnic group differences in the prevalence of sexually transmitted diseases in the United States: a network explanation. Sex. Transm. Dis. 26, 250–261 (1999). doi:10.1097/00007435-199905000-00003 PubMed

Laumann, E., Marsden, P., Prensky, D.: The boundary specification problem in network analysis. In: Burt, R., Minor, M. (eds.) Applied Network Analysis A Methodological Introduction, pp. 18–34. Sage Publications, Beverly Hills, CA (1983)

Laumann, E., Mahay, J., Paik, A., Youm, Y.: Network data collection and its relevance for the analysis of STDs: the NHSLS and CHSLS. In: Morris, M. (ed.) Network Epidemiology: A Handbook for Survey Design and Data Collection, pp. 27–41. Oxford University Press, New York (2004)

Leenders, R.: Modeling social influence through network autocorrelation: constructing the weight matrix. Soc. Networks 24(1), 21–47 (2002). doi:10.1016/S0378-8733(01)00049-1

Marsden, P.: Core discussion networks of Americans. Am. Sociol. Rev. 52(1), 122–131 (1987). doi:10.2307/2095397

Marsden, P.: Network data and measurement. Annu. Rev. Sociol. 16, 435–463 (1990). doi:10.1146/annurev.so.16.080190.002251

Marsden, P.: Egocentric and sociocentric measures of network centrality. Soc. Networks 24, 407–422 (2002). doi:10.1016/S0378-8733(02)00016-3

Marsden, P.: Network methods in social epidemiology. In: Oakes, J.M., Kaufman, J.S. (eds.) Methods in Social Epidemiology, pp. 267–286. Jossey-Bass, San Francisco (2006)

McGrath, C., Blythe, J., Krackhardt, D.: The effect of spatial arrangement on judgments and errors in interpreting graphs. Soc. Networks 19(3), 223–242 (1997). doi:10.1016/S0378-8733(96)00299-7

McPherson, M., Smith-Lovin, L., Cook, J.: Birds of a feather: homophily in social networks. Annu. Rev. Sociol. 27, 415–444 (2001). doi:10.1146/annurev.soc.27.1.415

Miguel, E., Kremer, M.: Networks, Social Learning, and Technology Adoption: The Case of Deworming Drugs in Kenya. Poverty Action Laboratory (2003)

Morris, M., Handcock, M., Miller, W., Ford, C., Schmitz, J., Hobbs, M., Cohen, M., Harris, K., Udry, J.: Prevalence of HIV infection among young adults in the U.S.: results from the add health study. Am. J. Public Health 96(6), 1091–1097 (2006). doi:10.2105/AJPH.2004.054759 PubMed

Nowicki, K., Snijders, T.A.B.: Estimation and prediction for stochastic blockstructures. J. Am. Stat. Assoc. 96, 1077–1087 (2001). doi:10.1198/016214501753208735

Pattison, P., Wasserman, S.: Logit models and logistic regressions for social networks: II. Multivariate relations. Br. J. Math. Stat. Psychol. 52(Pt 2), 169–193 (1999). doi:10.1348/000711099159053 PubMed

Robins, G., Pattison, P., Wasserman, S.: Logit models and logistic regressions for social networks: III. Valued relations. Psychometrika 64(3), 371–394 (1999). doi:10.1007/BF02294302

Robins, G., Pattison, P., Woolcock, J.: Small and other worlds: global network structures from local processes. Am. J. Sociol. 110(4), 894–936 (2005). doi:10.1086/427322

Robins, G., Pattison, P., Kalish, Y., Lusher, D.: An introduction to exponential random graph (p*) models for social networks. Soc. Networks 29(2), 173–191 (2007). doi:10.1016/j.socnet.2006.08.002

Rothenberg, R., Potterat, J., Woodhouse, D., Muth, S., Darrow, W., Klovdahl, A.: Social network dynamics and HIV transmission. AIDS 12, 1529–1536 (1998). doi:10.1097/00002030-199812000-00016 PubMed

Salganik, M., Heckathorn, D.: Sampling and estimation in hidden populations using respondent-driven sampling. Sociol. Methodol. 34, 193–239 (2004). doi:10.1111/j.0081-1750.2004.00152.x

Snijders, T.: The degree variance: an index of graph heterogeneity. Soc. Networks 3, 163–174 (1981). doi:10.1016/0378-8733(81)90014-9

Snijders, T.: Enumeration and simulation methods for 0–1 matrices with given marginals. Psychometrika 56(3), 397–417 (1991). doi:10.1007/BF02294482

Snijders, T.: Stochastic actor-oriented models for network change. J. Math. Sociol. 21, 149–172 (1996)

Snijders, T.: The statistical evaluation of social network dynamics. In: Sobel, M.E., Becker, M.P. (eds.) Sociological Methodology, pp. 361–395. Basil Blackwell, Boston (2001)

Snijders, T.: Models for longitudinal social network data. In: Carrington, P., Scott, J., Wasserman, S. (eds.) Models and Methods in Social Network Analysis, pp. 215–247. Cambridge University Press, Cambridge (2005)

Snijders, T.: Markov Chain Monte Carlo estimation of exponential random graph models. J. Soc. Struct. 3(2) (2002). Available at: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.5323

Snijders, T., Pattison, P., Robins, G., Handcock, M.: New specifications for exponential random graph models. In: Stolzenberg, R. (ed.) Sociological Methodology, pp. 99–153. Blackwell, Boston, MA (2006)

Snijders, T., Steglich, C., Schweinberger, M., Huisman, M.: Manual for SIENA Version 3.2. University of Groningen, Groningen, The Netherlands (2007)

Strauss, D., Ikeda, M.: Pseudolikelihood estimation for social networks. J. Am. Stat. Assoc. 85, 204–212 (1990). doi:10.2307/2289546

Sudman, S., Kalton, G.: New developments in the sampling of special populations. Annu. Rev. Sociol. 12, 401–429 (1986). doi:10.1146/annurev.so.12.080186.002153

Thompson, S.: Adaptive web sampling. Biometrics 62(4), 1224–1234 (2006)PubMed

Travers, J., Milgram, S.: An experimental study of the small world problem. Sociometry 32(4), 425–443 (1969). doi:10.2307/2786545

Unger, J., Chen, X.: The role of social networks and media receptivity in predicting age of smoking initiation: a proportional hazards model of risk and protective factors. Addict. Behav. 24, 371–381 (1999). doi:10.1016/S0306-4603(98)00102-6 PubMed

Valente, T., Watkins, S., Jato, M., van der Straten, A., Tsitol, L.: Social network associations with contraceptive use among Cameroonian women in voluntary associations. Soc. Sci. Med. 45, 1837–1843 (1997). doi:10.1016/S0277-9536(96)00385-1

Van Duijn, M., van Busschbach, J., Snijders, T.: Multilevel analysis of personal networks as dependent variables. Soc. Networks 21, 187–209 (1999). doi:10.1016/S0378-8733(99)00009-X

Van Duijn, M., Snijders, T., Zijlstra, B.: P2: a random effects model with covariates for directed graphs. Stat. Neerl. 58(2), 234–254 (2004). doi:10.1046/j.0039-0402.2003.00258.x

Waller, L., Gotway, C.: Applied Spatial Statistics for Public Health Data. Wiley Interscience, Hoboken, NJ (2004)

Wang, P., Robins, G., Pattison, P.: PNet: Program for the Simulation and Estimation of P* Exponential Random Graph Models (release: Department of Psychology, University of Melbourne (2008)

Wang, W., Wong, G.: Stochastic blockmodels for directed graphs. J. Am. Stat. Assoc. 82, 8–19 (1987). doi:10.2307/2289119

Wasserman, S.: A stochastic model for directed graphs with transition rates determined by reciprocity. In: Schuessler, K.F. (ed.) Sociological Methodology, pp. 392–412. Jossey-Bass, San Francisco (1979)

Wasserman, S.: Analyzing social networks as stochastic processes. J. Am. Stat. Assoc. 75, 280–294 (1980). doi:10.2307/2287447

Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge (1994)

Wasserman, S., Pattison, P.: Logit models and logistic regressions for social networks: I. An introduction to Markov graphs and p*. Psychometrika 61, 401–425 (1996). doi:10.1007/BF02294547

Wellman, B., Frank, K.: Network capital in a multilevel world: getting support from personal communities. In: Lin, K., Cook, K., Burt, R. (eds.) Social Capital: Theory and Research, pp. 233–273. Aldine de Gruyter, New York (2001)

White, D., Harary, F.: The cohesiveness of blocks in social networks: node connectivity and conditional density. In: Becker, M.P. (ed.) Sociological Methodology, pp. 140–148. Blackwell, Boston (2001)

Wolfram, S.: A New Kind of Science. Wolfram Media (2002)

Wong, G.: Bayesian models for directed graphs. J. Am. Stat. Assoc. 82, 140–148 (1987)

Zeggelink, E.: Dynamics of structure—an individual oriented approach. Soc. Networks 16(4), 295–333 (1994). doi:10.1016/0378-8733(94)90014-0

Zijlstra, B., Van Duijn, M., Snijders, T.: The multilevel p2 model: a random effects model for the analysis of multiple social networks. Methodology 21, 42–47 (2006)

Title: The analysis of social networks
Authors: A. James O’Malley
Peter V. Marsden
Publication date: 01-12-2008
Publisher: Springer US
Published in: Health Services and Outcomes Research Methodology / Issue 4/2008
Print ISSN: 1387-3741
Electronic ISSN: 1572-9400
DOI: https://doi.org/10.1007/s10742-008-0041-z

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The analysis of social networks

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Keynote webinar | Spotlight on medication adherence

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