Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-09T02:33:48.786Z Has data issue: false hasContentIssue false
  • English
  • Français

Contemporaneous Statistics for Estimation in Stochastic Actor-Oriented Co-evolution Models

Published online by Cambridge University Press:  01 January 2025

Viviana Amati Open the ORCID record for Viviana Amati [Opens in a new window] ,
Felix Schönenberger  and
Tom A. B. Snijders Open the ORCID record for Tom A. B. Snijders [Opens in a new window]
Viviana Amati*
Affiliation:
ETH Zurich
Felix Schönenberger
Affiliation:
ETH Zurich
Tom A. B. Snijders
Affiliation:
University of Groningen University of Oxford
*
Correspondence should be made to Viviana Amati, Social Networks Lab, Department of Humanities, Social and Political Sciences, ETH Zurich, Weinbergstrasse 109, 8092 Zurich, Switzerland. Email:viviana.amati@gess.ethz.ch
Get access Rights & Permissions [Opens in a new window]

Abstract

Stochastic actor-oriented models (SAOMs) can be used to analyse dynamic network data, collected by observing a network and a behaviour in a panel design. The parameters of SAOMs are usually estimated by the method of moments (MoM) implemented by a stochastic approximation algorithm, where statistics defining the moment conditions correspond in a natural way to the parameters. Here, we propose to apply the generalized method of moments (GMoM), using more statistics than parameters. We concentrate on statistics depending jointly on the network and the behaviour, because of the importance of their interdependence, and propose to add contemporaneous statistics to the usual cross-lagged statistics. We describe the stochastic algorithm developed to approximate the GMoM solution. A small simulation study supports the greater statistical efficiency of the GMoM estimator compared to the MoM.

Keywords

generalized method of momentsnetworksbehaviourpanel datastochastic actor-oriented modelstochastic approximation

Information

Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 4 , December 2019 , pp. 1068 - 1096
Copyright
Copyright © 2019 The Psychometric Society

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.)

Article purchase

Temporarily unavailable

References

Amati, V.,Schönenberger, F. &Snijders, T. A.Estimation of stochastic actor-oriented models for the evolution of networks by generalized method of moments. Journal de la Société Française de Statistique, (2015). 156 (3) 140– 165. Google Scholar
Block, P.Reciprocity, transitivity, and the mysterious three-cycle. Social Networks, (2015). 40 163– 173. CrossRefGoogle Scholar
Bollen, K. A..Kolenikov, S.. & Bauldry, S.Model-implied instrumental variable—generalized method of moments (MIIV-GMM) estimators for latent variable models. Psychometrika, (2014). 79 (1) 20– 50. 24532165 CrossRefGoogle ScholarPubMed
Breusch, T..Qian, H..Schmidt, P.. &Wyhowski, D.Redundancy of moment conditions. Journal of Econometrics, (1999). 91 (1) 89– 111. CrossRefGoogle Scholar
Burguete, J. F..Ronald Gallant, A.. &Souza, G.On unification of the asymptotic theory of nonlinear econometric models. Econometric Reviews, (1982). 1 (2) 151– 190. CrossRefGoogle Scholar
Burk, W. J..Kerr, M.. &Stattin, H.The co-evolution of early adolescent friendship networks, school involvement, and delinquent behaviors. Revue française de sociologie, (2008). 49 (3) 499– 522. CrossRefGoogle Scholar
Ebbers, J. J.,Wijnberg, N. M.Disentangling the effects of reputation and network position on the evolution of alliance networks. Strategic Organization, (2010). 8 (3) 255– 275. CrossRefGoogle Scholar
Gallant, A. R..Hsieh, D.. &Tauchen, G..Estimation of stochastic volatility models with diagnostics. Journal of econometrics, (1997). 81 (1) 159– 192. CrossRefGoogle Scholar
Hall, A. R.Generalized method of moments, (2005). Oxford: Oxford University Press. Google Scholar
Hansen, L.Large sample properties of generalized method of moments estimators. Econometrica, (1982). 50 1029– 1054. CrossRefGoogle Scholar
Hansen, L. P..Singleton, K. J.Generalized instrumental variables estimation of nonlinear rational expectations models. Econometrica, (1982). 50 (5) 1269– 1286. CrossRefGoogle Scholar
Haynie, D. L..Doogan, N. J.. &Soller, B.Gender, friendship networks, and delinquency: A dynamic network approach. Criminology, (2014). 52 (4) 688– 722. 26097241 4469075 CrossRefGoogle ScholarPubMed
Holland, P. W..Leinhardt, S.A dynamic model for social networks. Journal of Mathematical Sociology, (1977). 5 (1) 5– 20. CrossRefGoogle Scholar
Hunter, D. R.Curved exponential family models for social networks. Social Networks, (2007). 29 216– 230. 18311321 2031865 CrossRefGoogle ScholarPubMed
Kim, J-. S..Frees, EW.Multilevel modeling with correlated effects. Psychometrika, (2007). 72 (4) 505– 533. CrossRefGoogle Scholar
Koskinen, J. H.,Snijders, T.A. B.Bayesian inference for dynamic social network data. Journal of Statistical Planning and Inference, (2007). 13 3930– 3938. CrossRefGoogle Scholar
Luce, R.,Suppes, P.Preference, utility, and subjective probability. Handbook of Mathematical Psychology, (1965). 3 249– 410. Google Scholar
Mátyás, L..Generalized method of moments estimation, (1999). Cambridge: Cambridge University Press. CrossRefGoogle Scholar
McFadden, D.Conditional logit analysis of qualitative choice behavior, (1973). Oakland: Institute of Urban and Regional Development, University of California. Google Scholar
McPherson, M.,Smith-Lovin, L.. &Cook, JM.Birds of a feather: Homophily in social networks. Annual Review of Sociology, (2001). 27 (1) 415– 444. CrossRefGoogle Scholar
Meyer, C. D.Matrix analysis and applied linear algebra, (2000). Philadelphia: S.I.A.M. CrossRefGoogle Scholar
Michell, L.,West, P.Peer pressure to smoke: The meaning depends on the method. Health Education Research, (1996). 11 (1) 39– 49. CrossRefGoogle Scholar
Newey, W.,Windmeijer, F.Generalized method of moments with many weak moment conditions. Econometrica, (2009). 77 (3) 687– 719. Google Scholar
Neyman, J.,Pearson, E.S.On the use and interpretation of certain test criteria for purposes of statistical inference: Part II. Biometrika, (1928). 20 263– 294. Google Scholar
Niezink, N.M.D.,Snijders, T.A.B.Co-evolution of social networks and continuous actor attributes. The Annals of Applied Statistics, (2017). 11 (4) 1948– 1973. CrossRefGoogle Scholar
Niezink, Nynke M. D..,Snijders, Tom A. B... &van Duijn, Marijtje A. J..No Longer Discrete: Modeling the Dynamics of Social Networks and Continuous Behavior. Sociological Methodology, (2019). 49 (1) 295– 340. CrossRefGoogle Scholar
Norris, J. R.Markov chains, (1997). Cambridge: Cambridge University Press. CrossRefGoogle Scholar
Pearson, K..On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, (1900). 50 (302) 157– 175. CrossRefGoogle Scholar
Pflug, G. C.Non-asymptotic confidence bounds for stochastic approximation algorithms with constant step size. Monatshefte für Mathematik, (1990). 110 (3–4) 297– 314. CrossRefGoogle Scholar
Polyak, B. T.A new method of stochastic approximation type. Automation and Remote Control, (1990). 51 937– 946. Google Scholar
Ripley, RM..Snijders, T.A. B.,Boda, Z.,András, V.. &Paulina, P.Manual for RSiena, (2019). Groningen: ICS, Department of Sociology, University of Groningen. Google Scholar
Robbins, H.,Monro, S.A stochastic approximation method. The Annals of Mathematical Statistics, (1951). 22 400– 407. CrossRefGoogle Scholar
Ruppert, D. (1988). Efficient estimations from a slowly convergent Robbins–Monro process. Technical report, Cornell University Operations Research and Industrial Engineering.Google Scholar
Schulte, M.,Cohen, NA.. &Klein, KJ.The coevolution of network ties and perceptions of team psychological safety. Organization Science, (2012). 23 (2) 564– 581. CrossRefGoogle Scholar
Schweinberger, M..Snijders, T.A.B.Markov models for digraph panel data: Monte Carlo-based derivative estimation. Computational Statistics & Data Analysis, (2007). 51 (9) 4465– 4483. CrossRefGoogle Scholar
Snijders, T.A.B.Stochastic actor-oriented models for network change. Journal of Mathematical Sociology, (1996). 21 (1–2) 149– 172. CrossRefGoogle Scholar
Snijders, T.A.B.The statistical evaluation of social network dynamics. Sociological Methodology, (2001). 31 (1) 361– 395. CrossRefGoogle Scholar
Snijders, T.A.B., Conte, P.J.C.,Scott, J.. &Wasserman, S.Models for longitudinal network data. Models and methods in social network analysis, (2005). Cambridge: Cambridge University Press. 215– 247. CrossRefGoogle Scholar
Snijders, T.A.B.Stochastic actor-oriented models for network dynamics. Annual Review of Statistics and Its Application, (2017). 4 343– 363. CrossRefGoogle Scholar
Snijders, T. A. B. (2017b). Siena algorithms. Technical report, University of Groningen, University of Oxford. http://www.stats.ox.ac.uk/~snijders/siena/Siena_algorithms.pdf.Google Scholar
Snijders, T.A.B.,Koskinen, J.. &Schweinberger, M.Maximum likelihood estimation for social network dynamics. The Annals of Applied Statistics, (2010). 4 (2) 567– 588. 25419259 4236314 CrossRefGoogle ScholarPubMed
Snijders, T.A.B.,Lomi, A.Beyond homophily: Incorporating actor variables in statistical network models. Network Science, (2019). 7 (1) 1– 19. CrossRefGoogle Scholar
Snijders, T.A.B.,Steglich, C.E.G..Schweinberger, M., van Montfort, K.,Oud, H.. &Satorra, A.Modeling the co-evolution of networks and behavior. Longitudinal models in the behavioral and related sciences, (2007). Mahwah, NJ: Lawrence Erlbaum. 41– 71. Google Scholar
Snijders, T.A.B.,Van de Bunt, G.G., &Steglich, C.E.G.Introduction to stochastic actor-based models for network dynamics. Social Networks, (2010). 32 (1) 44– 60. CrossRefGoogle Scholar
Snijders, T.A.B..van Duijn, M.A.J., Conte, R.,Hegselmann, R.. &Terna, P.Simulation for statistical inference in dynamic network models. Simulating social phenomena, (1997). Berlin: Springer. 493– 512. CrossRefGoogle Scholar
Steglich, C.E.G.,Snijders, T.A.B., &Pearson, M.Dynamic networks and behavior: Separating selection from influence. Sociological Methodology, (2010). 40 (1) 329– 393. CrossRefGoogle Scholar
Strang, G.Linear algebra and its applications, (1976). New York: Academic Press. Google Scholar
Train, K. E.Discrete choice methods with simulation, (2009). Cambridge: Cambridge University Press. Google Scholar