Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-24T12:25:13.417Z Has data issue: false hasContentIssue false
  • English
  • Français

Relative importance of effects in stochastic actor-oriented models*

Published online by Cambridge University Press:  07 January 2014

NATALIE INDLEKOFER  and
ULRIK BRANDES
NATALIE INDLEKOFER
Affiliation:
Department of Computer & Information Science, University of Konstanz, Konstanz, Germany (e-mail: natalie.indlekofer@uni-konstanz.de, ulrik.brandes@uni-konstanz.de)
ULRIK BRANDES
Affiliation:
Department of Computer & Information Science, University of Konstanz, Konstanz, Germany (e-mail: natalie.indlekofer@uni-konstanz.de, ulrik.brandes@uni-konstanz.de)
Get access Rights & Permissions [Opens in a new window]

Abstract

A measure of relative importance of network effects in the stochastic actor-oriented model (SAOM) is proposed. The SAOM is a parametric model for statistical inference in longitudinal social networks. The complexity of the model makes the interpretation of inferred results difficult. So far, the focus is on significance tests while the relative importance of effects is usually ignored. Indeed, there is no established measure to determine the relative importance of an effect in a SAOM. We introduce such a measure based on the influence effects have on decisions of individual actors in the network. We demonstrate its utility on empirical data by analyzing an evolving friendship network of university freshmen.

Keywords

longitudinal networkssocial networksstatistical modelsinterpretation of stochastic actor-oriented models
Type
Research Article
Information
Network Science , Volume 1 , Issue 3 , December 2013 , pp. 278 - 304
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

The electronic version of this article contains color figures.

References

Agresti, A. (2002). Categorical data analysis. Hoboken, NJ: John Wiley.Google Scholar
Amati, V., & Brandes, U. (2012). On ERGMs as the outcome of network formation games. Paper presented at the XXXII Sunbelt Social Networks Conference, March 13–18, Redondo Beach, California.Google Scholar
Frank, O., & Strauss, D. (1986). Markov graphs. Journal of the American Statistical Association, 81, 832–842.CrossRefGoogle Scholar
Grömping, U. (2007). Estimators of relative importance in linear regression based on variance decomposition. American Statistician, 61 (2), 139–147.Google Scholar
Healy, M. J. R. (1990). Measuring importance. Statistics in Medicine, 9 (6), 633–637.Google Scholar
Hosmer, D. W., & Lemeshow, S. (2000). Applied logistic regression. Hoboken, NJ: John Wiley.CrossRefGoogle Scholar
Karlson, K. B., Holm, A., & Breen, R. (2012). Comparing regression coefficients between same-sample nested models using logit and probit: A new method. Sociological Methodology, 42, 286–313.Google Scholar
Khinchin, A. I. (1957). Mathematical foundations of information theory. New York: Dover.Google Scholar
Koskinen, J. H., & Snijders, T. A. B. (2007). Bayesian inference for dynamic social network data. Journal of Statistical Planning and Inference, 137 (12), 3930–3938.CrossRefGoogle Scholar
Kruskal, W. (1987). Relative importance by averaging over orderings. American Statistician, 41 (1), 6–10.Google Scholar
Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22 (1), 79–86.Google Scholar
Lerner, J., Indlekofer, N., Nick, B., & Brandes, U. (2013). Conditional independence in dynamic networks. Journal of Mathematical Psychology, 57 (6), 275–283.Google Scholar
Lospinoso, J. A., Schweinberger, M., Snijders, T. A. B., & Ripley, R. M. (2011). Assessing and accounting for time heterogeneity in stochastic actor oriented models. Advances in Data Analysis and Classification, 5, 147–176. doi:http://dx.doi.org/10.1007/s11634-010-0076-1.Google Scholar
Maddala, G. D. (1983). Limited-dependent and qualitative variables in econometrics. Cambridge, UK: Cambridge University Press.Google Scholar
Mayer, L. S., & Younger, M. S. (1976). Estimation of standardized regression coefficients. Journal of the American Statistical Association, 71 (353), 154–157.Google Scholar
McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In Zarembka, P. (Ed.), Frontiers in econometrics (Chap. 4, pp. 105–142). New York: Academic Press.Google Scholar
Menard, S. (2004). Six approaches to calculating standardized logistic regression coefficients. American Statistician, 58 (3), 218–223.Google Scholar
Menard, S. (2011). Standards for standardized logistic regression coefficients. Social Forces, 89 (4), 1409–1428.Google Scholar
Pratt, J. W. (1987). Dividing the indivisible: Using simple symmetry to partition variance explained. In Pukkila, T. & Puntanen, S. (Eds.), Proceedings of second Tampere conference in statistics (pp. 245–260). Finland: University of Tampere.Google Scholar
Ripley, R., Snijders, T. A. B., & Preciado, P. (2011). Manual for SIENA version 4.0 (version April 19, 2013). Oxford: University of Oxford, Department of Statistics; Nuffield College. (http://www.stats.ox.ac.uk/siena/).Google Scholar
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.Google Scholar
Snijders, T. A. B. (1996). Stochastic actor-oriented models for network change. Journal of Mathematical Sociology, 21, 149–172.Google Scholar
Snijders, T. A. B. (2001). The statistical evaluation of social network dynamics. Sociological Methodology, 31 (1), 361–395.Google Scholar
Snijders, T. A. B. (2004). Explained variation in dynamic network models. Mathematiques, informatiques et sciences humaines, 168 (4), 5–15.Google Scholar
Snijders, T. A. B. (2005). Models for longitudinal network data. In Carrington, P. J., Scott, J., & Wasserman, S. (Eds.), Models and methods in social network analysis (Chap. 4, pp. 215–247). New York: Cambridge University Press.CrossRefGoogle Scholar
Snijders, T. A. B., & Bearveldt, C. (2003). A multilevel network study of the effects of delinquent behavior on friendship evolution. Journal of Mathematical Sociology, 27 (2), 123–151.Google Scholar
Snijders, T. A. B., Koskinen, J., & Schweinberger, M. (2010b). Maximum likelihood estimation for social network dynamics. Annals of Applied Statistics, 4 (2), 567–588.Google Scholar
Snijders, T. A. B., Lomi, A. & Torló, V. J. (2013). A model for the multiplex dynamics of two-mode and one-mode networks with an application to employment preference, friendship and advice. Social Networks, 35 (2), 265–276.Google Scholar
Snijders, T. A. B., Pattison, P. E., Robins, G. L., & Handcock, M. S. (2006). New specifications for exponential random graph models. Sociological Methodology, 36, 99–153.Google Scholar
Snijders, T. A. B., & Steglich, C. E. G. (2013). Representing micro-macro linkages by actor-based dynamic network models. Sociological Methods & Research. doi:10.1177/0049124113494573.Google Scholar
Snijders, T. A. B., Steglich, C., & Schweinberger, M. (2007). Modeling the co-evolution of networks and behavior. In van Montfort, K., Oud, H., & Satorra, A., (Eds.), Longitudinal models in behavioral and related sciences (pp. 41–71). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
Snijders, T. A. B., van de Bunt, G. G., & Steglich, C. (2010a). Introduction to stochastic actor-based models for network dynamics. Social Networks, 32 (1), 44–60.Google Scholar
Steglich, C., Snijders, T. A. B., & Pearson, M. (2010). Dynamic networks and behavior: Separating selection from influence. Sociological Methodology, 40 (1), 329–393.Google Scholar
Train, K. E. (2009). Discrete choice methods with simulation. New York: Cambridge University Press.Google Scholar
Van de Bunt, G. G. (1999). Friends by choice: An actor-oriented statistical network model for friendship networks through time. Amsterdam: Thesis Publisher.Google Scholar
Van de Bunt, G. G., Van Van Duijn, M. A. J., & Snijders, T. A. B. (1999). Friendship networks through time: An actor-oriented dynamic statistical network model. Computational and Mathematical Organization Theory, 5 (2), 167–192.Google Scholar
Wasserman, S., & Pattison, P. (1996). Logit models and logistic regressions for social networks: I. An introduction to Markov graphs and p*. Psychometrika, 61 (3), 401–425.CrossRefGoogle Scholar