Advertisement

Evaluating Complex Educational Systems with Quadratic Assignment Problem and Exponential Random Graph Model Methods

  • Russ Marion
  • Craig Schreiber
Chapter

Abstract

This chapter has three objectives: (1) to describe how social network analyses (SNA) can be used to explore complexity dynamics in education; (2) to provide a primer on SNA methods; and (3) to explore statistical procedures for hypothesis testing with SNA. SNA has experienced increasing popularity in recent years, but resources available to researchers wanting to learn about this methodology are sparse. That which is available typically fails to link SNA to complexity theory, although this would seem an obvious context. This chapter briefly describes major principles of complexity theory and how network analyses are useful for exploring social dynamics. We then explain what SNA is, the types of analyses it performs, and its various uses. This section delves into issues such as designing SNA analyses, data collection procedures, and converting non-matrix data for use in SNA. Lastly, the chapter describes statistical procedures for analyzing network data. In particular, we explain how to conduct multiple regression quadratic assignment procedures and p* to test hypotheses about network dynamics. Issues of using network coefficients with traditional, variable-based statistics are discussed. Examples of applicable research questions and research studies are provided to help readers formulate questions and research designs.

Keywords

Quadratic assignment problem Exponential random graph model Statistical modeling Network analysis Network survey Dyadic relationships Network measures QAP examples ERGM examples p* 

References

  1. Blackwell, B. (2014). South Carolina public high schools: Leadership, network dynamics and innovation. PhD, Clemson University, Clemson, SC.Google Scholar
  2. Bojanowski, M., & Corten, R. (2014). Measuring segregation in social networks. Social Networks, 39, 14–32. doi: 10.1016/j.socnet.2014.04.001.CrossRefGoogle Scholar
  3. Bonabeau, E. (2002). Agent-based modeling: Methods and techniques for simulating human systems. Paper presented at the Colloquim of the National Academy of Sciences.Google Scholar
  4. Borgatti, S. P., Carley, K., & Krackhardt, D. (2006). On the robustness of centrality measures under conditions of imperfect data. Social Networks, 28(2), 124–136. doi: 10.1016/j.socnet.2005.05.001.CrossRefGoogle Scholar
  5. Borgatti, S. P., Everett, M. G., & Johnson, J. (2013). Analyzing social networks. Thousand Oaks, CA: Sage.Google Scholar
  6. Bowler, W. M., & Brass, D. J. (2006). Relational correlates of interpersonal citizenship behavior: A social network perspective. Journal of Applied Psychology, 9(1), 70–82.CrossRefGoogle Scholar
  7. Brewer, D., & Webster, C. (1999). Forgetting of friends and its effects on measuring friendship networks. Social Networks, 21, 361–373.CrossRefGoogle Scholar
  8. Burkard, R. E., Çela, E., Karisch, S. E., & Rendl, F. (2013). Quadratic assignment problem. Journal of Global Optimization. Retrieved from http://www.neos-guide.org/content/quadratic-assignment-problem doi: 10:391–403, 1997.
  9. Chiles, T. H., Meyer, A. D., & Hench, T. J. (2004). Organizational emergence: The origin and transformation of Branson, Missouri’s musical theaters. Organization Science, 15(5), 499–519.CrossRefGoogle Scholar
  10. Cilliers, P. (1998). Complexity and postmodernism: Understanding complex systems. London: Routledge.Google Scholar
  11. Coveney, P. (2003). Self-organization and complexity: A new age for theory, computation and experiment. Paper presented at the Nobel symposium on self-organization, Karolinska Institutet, Stockholm.Google Scholar
  12. Dansereau, F., Yammarino, F. J., & Kohles, J. C. (1999). Multiple levels of analysis from a longitudinal perspective: Some implications for theory building. Academy of Management Review, 24(2), 346–357.Google Scholar
  13. Davis, J. A., & Leinhardt, S. (1972). The structure of positive interpersonal relations in small groups. In J. Berger (Ed.), Sociological theories in progress (Vol. 2, pp. 218–251). Boston: Houghton Mifflin.Google Scholar
  14. Dekker, D., Krackhardt, D., & Snijders, T. (2007). Sensitivity of MRQAP tests to collinearity and autocorrelation conditions. Psychometrika, 72(4), 563–581. doi: 10.1007/s11336-007-9016-1.CrossRefGoogle Scholar
  15. Ellwardt, L., Labianca, G., & Wittek, R. (2012). Who are the objects of positive and negative gossip at work?: A social network perspective on workplace gossip. Social Networks, 34(2), 193–205. doi: 10.1016/j.socnet.2011.11.003.CrossRefGoogle Scholar
  16. Fields, A. (2009). Discovering statistics using SPSS (3rd ed.). Thousand Oaks, CA: Sage Publishing.Google Scholar
  17. Frank, O., & Strauss, D. (1986). Markov graphs. Journal of the American Statistical Association, 81(395), 832–842.CrossRefGoogle Scholar
  18. Friedkin, N. E., & Slater, M. R. (1994). School leadership and performance: A social network approach. Sociology of Education, 67(2), 139–157.CrossRefGoogle Scholar
  19. Goodreau, S. M., Handcock, M. S., Hunter, D. R., Butts, C. T., & Morris, M. (2008). A Statnet tutorial. Journal of Statistical Software, 24(9), 1–26.CrossRefGoogle Scholar
  20. Graen, G. B., & Uhi-Bien, M. (1995). The transformation of professionals into self-managing and partially self-designing contributors: Toward a theory of leadership-making. Journal of Management Systems, 3(3), 25–39.Google Scholar
  21. Gupta, A. K., Tesluk, P. E., & Taylor, M. S. (2007). Innovation at and across multiple levels of analysis. Organization Science, 18(6), 885–897.CrossRefGoogle Scholar
  22. Handcock, M. S., Hunter, D. R., Butts, C. T., Goodreau, S. M., & Morris, M. (2008). Statnet: Software tools for the representation, visualization, analysis and simulation of network data. Journal of Statistical Software, 24(1), 1–11.CrossRefGoogle Scholar
  23. Harris, J. K. (2014). An introduction to exponential random graph modeling. London: Sage.CrossRefGoogle Scholar
  24. Hogue, M., & Lord, R. G. (2007). A multilevel, complexity theory approach to understanding gender bias in leadership. The Leadership Quarterly, 18(4), 370–390.CrossRefGoogle Scholar
  25. 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.CrossRefGoogle Scholar
  26. 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.CrossRefGoogle Scholar
  27. Hunter, D. R., & Handcock, M. S. (2006). Inference in curved exponential family models for networks. Journal of Computational and Graphical Statistics, 15(3), 565–583.CrossRefGoogle Scholar
  28. Kauffman, S. A. (1993). The origins of order. New York: Oxford University Press.Google Scholar
  29. Kenny, D. A., & La Voie, L. (1984). The social relations model. In L. Berkowitz (Ed.), Advances in experimental social psychology (Vol. 18). New York: Academic.Google Scholar
  30. Koopmans, T. C., & Beckmann, M. J. (1957). Assignment problems and the location of economic activities. Econometrica, 25, 53–76.CrossRefGoogle Scholar
  31. Krackhardt, D. (1987). QAP partialling as a test of spuriousness. Social Networks, 9(2), 171–186.CrossRefGoogle Scholar
  32. Krackhardt, D. (1998). Simmelian ties: Super strong and sticky. In R. M. Kramer & M. A. Neale (Eds.), Power and influence in organizations (pp. 21–38). Thousand Oaks, CA: Sage.CrossRefGoogle Scholar
  33. Krackhardt, D. (1999). The ties that torture: Simmelian tie analysis in organizations. Research in the Sociology of Organizations, 16, 183–210.Google Scholar
  34. Krivitsky, P. N. (2012). Exponential-family random graph models for valued networks. Electronic Journal of Statistics, 6, 1100–1128.CrossRefGoogle Scholar
  35. Lusher, D., Koskinen, J., & Robins, G. (2013). Exponential random graph models for social networks. New York, NY: Cambridge University Press.Google Scholar
  36. Marineau, J. E., & Labianca, G. J. (2010). Work and personal based conflict and advise and knowledge seeking relationships. Academy of Management Proceedings, 2010(1), 1–6. doi: 10.5465/ambpp.2010.54501343.CrossRefGoogle Scholar
  37. Marion, R., Schreiber, C., Klar, H., Christiansen, J., & Reese, K. (2014). Collectivist analysis of adaptive leadership, interaction, and cliques on organizational capacity. Paper presented at the Academy of Management, Philadelphia, PA.Google Scholar
  38. Moody, J., Brynildsen, W. D., Osgood, D. W., Feinberg, M. E., & Gest, S. (2011). Popularity trajectories and substance use in early adolescence. Social Networks, 33(2), 101–112. doi: 10.1016/j.socnet.2010.10.001.CrossRefGoogle Scholar
  39. Pattison, P. E., & Robbins, G. L. (2002). Neighborhood-based models for social networks. Sociological Methodology, 32(1), 301–337.CrossRefGoogle Scholar
  40. Plowman, D., Solansky, S., Beck, T., Baker, L., Kulkarni, M., & Travis, D. (2007). The role of leadership in emergent, self-organization. The Leadership Quarterly, 18, 341–356.CrossRefGoogle Scholar
  41. Robins, G., & Lusher, D. (2013). Simplified account of an exponential random graph model as a statistical model. In D. Lusher, J. Koskinen, & G. Robins (Eds.), Exponential random graph models for social networks (pp. 29–36). New York, NY: Cambridge University Press.Google Scholar
  42. 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. doi: 10.1016/j.socnet.2006.08.002.CrossRefGoogle Scholar
  43. Scott, J., & Carrington, P. J. (Eds.). (2011). The Sage handbook of social network analysis. London, UK: Sage.Google Scholar
  44. Smith, S., Maas, I., & van Tubergen, F. (2014). Ethnic ingroup friendships in schools: Testing the by-product hypothesis in England, Germany, the Netherlands and Sweden. Social Networks, 39, 33–45. doi: 10.1016/j.socnet.2014.04.003.CrossRefGoogle Scholar
  45. Snijders, T. A. B., Pattison, P. E., Robbins, G. L., & Handcock, M. S. (2006). New specifications for exponential random graph models. Sociological Methodology, 36(1), 99–153.CrossRefGoogle Scholar
  46. Solow, D., Burnetas, A., Piderit, S., & Leenawong, C. (2003). Mathematical models for studying the value of motivational leadership in teams. Computational and Mathematical Organization Theory, 9(1), 61–81.CrossRefGoogle Scholar
  47. Sterman, J. D. (1994). Learning in and about complex systems. System Dynamics Review, 10, 291–330.CrossRefGoogle Scholar
  48. Tortoriello, M., & Krackhardt, D. (2010). Activating cross-boundary knowledge: The role of Simmelian ties in the generation of innovations. [Article]. Academy of Management Journal, 53(1), 167–181.CrossRefGoogle Scholar
  49. Tsai, W., & Ghoshal, S. (1998). Social capital and value creation: The role of intrafirm networks. Academy of Managemenl Journal, 41(4), 464–476. doi: 10.2307/257085.CrossRefGoogle Scholar
  50. van Duijn, M. A. J., & Huisman, M. (2011). Statistical models for ties and actors. In J. Scott & P. J. Carrington (Eds.), The Sage handbook of social network analysis (pp. 459–483). London, UK: Sage.CrossRefGoogle Scholar
  51. Wang, P., Robins, G. L., & Pattison, P. E. (2009). Pnet: Program for the simulation and estimation of p* exponential random graph models. Retrieved from http://sna.unimelb.edu.au/
  52. Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  53. Wasserman, S., & Pattison, P. (1996). Logit models and logistic regression for social networks: I. An introduction to Markov graphs and p*. Psychometrika, 61(3), 401–425.CrossRefGoogle Scholar
  54. Weick, K. E. (1976). Educational organizations as loosely coupled systems. Administrative Science Quarterly, 21, 1–19.CrossRefGoogle Scholar
  55. White, L., Currie, G., & Lockett, A. (2014). The enactment of plural leadership in a health and social care network: The influence of institutional context. The Leadership Quarterly, 25(4), 730–745. doi: 10.1016/j.leaqua.2014.04.003.CrossRefGoogle Scholar
  56. Windzio, M. (2015). Immigrant children and their parents: Is there an intergenerational interdependence of integration into social networks? Social Networks, 40, 197–206. doi: 10.1016/j.socnet.2014.11.002.CrossRefGoogle Scholar
  57. Yap, J., & Harrigan, N. (2015). Why does everybody hate me? Balance, status, and homophily: The triumvirate of signed tie formation. Social Networks, 40, 103–122.CrossRefGoogle Scholar
  58. Zhu, M., Huang, Y., & Contractor, N. S. (2013). Motivations for self-assembling into project teams. Social Networks, 35(2), 251–264. doi: 10.1016/j.socnet.2013.03.001.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Clemson UniversityClemsonUSA
  2. 2.Lenoir-Rhyne UniversityHickoryUSA

Personalised recommendations