Longitudinal and Dynamic Social Networks

Wasserman/Faust says on p. 731 ""Good, easy-to-use methods for longitudinal network data would be an important addition to the literature."

he also recommends: Wasserman 1978 Iacobucci 1988 Iacobucci 1989,1990 Holland, Leinhardt 1981

More recently <bibtex>@article{snijders2005models,

 title=Template:Models for longitudinal network data,
 author={Snijders, T.A.B.},
 journal={Models and methods in social network analysis},
 pages={215--247},
 year={2005},
 publisher={Cambridge Univ Pr}

}</bibtex>

says "

This chapter treats statistical methods for network evolution. It 

is argued that it is most fruitful to consider models where network evolution is represented as the result of many (usually non-observed) small changes occurring between the consecutively observed networks. Accordingly, the focus is on models where a continuous-time network evolution is assumed although the observations are made at discrete time points (two or more).

Three models are considered in detail, all based on the assump- 

tion that the observed networks are outcomes of a Markov process evolving in continuous time. The independent arcs model is a trivial baseline model. The reciprocity model expresses effects of reciprocity, but lacks other structural effects. The actor-oriented model is based on a model of actors changing their outgoing ties as a consequence of myopic stochastic optimization of an ob jective function. This frame- work offers the flexibility to represent a variety of network effects. An estimation algorithm is treated, based on a Markov chain Monte Carlo implementation of the method of moments. "

recommending: "

Various models have been proposed for the statistical analysis of longitu- 

dinal social network data. Earlier reviews were given by Wasserman (1978), Frank (1991), and Snijders (1995). "

Even more recently he gives this overviews of the area of network dynamics. here is a too big chunk from <bibtex>@article{snijders2007modeling,

 title=Template:Modeling the co-evolution of networks and behavior,
 author={Snijders, T.A.B. and Steglich, C.E.G. and Schweinberger, M.},
 journal={Longitudinal models in the behavioral and related sciences},
 pages={41--71},
 year={2007},
 publisher={Lawrence Erlbaum}

} </bibtex>

" On the other side, actors’ characteristics – indicators of performance and success, attitudes and other cognitions, behavioral tendencies – can depend on the social network the actor is situated in. It is well-known that in many social situations, behavior and attitudes of individuals follow patterns of assimilation to others to whom they are tied. Examples are the diffusion of innovations in a professional community (Valente, 1995), pupils’ copying of ‘chic’ behavior of their friends at school, or traders on a market copying the allegedly successful behavior of their competitors. The change of network structure is often referred to as selection (Lazars- feld and Merton, 1954), and the change of individual characteristics of social actors depending on the characteristics of others to whom they are tied is called influence (Friedkin, 1998). It is assumed here that the group of actors under study has been delineated in such a way that it is meaningful to inves- tigate the selection and influence processes in this group without considering ties to others outside the group. The necessity of studying selection and in- fluence processes in networks simultaneously was discussed both in detailed network investigations (e.g., Padgett and Ansell, 1993) and in theoretical dis- cussion essays (Emirbayer and Goodwin, 1994, Doreian and Stokman, 1997). A concrete example is smoking initiation among adolescents, where it has been established in the literature that friends tend to have similar patterns of smoking behavior, but where it is unknown to which extent this is a mat- ter of selection of friends on the basis of common behavior, or adaptation of 2 behavior towards that of one’s friends (Bauman and Ennett, 1996). This chapter proposes a statistical method for investigating network struc- ture together with relevant actor attributes as joint dependent variables in a longitudinal framework, assuming that data have been collected according to a panel design. This is a more detailed exposition of the proposals sketched in Steglich et al. (2004). In the stochastic model, the network structure and the individual attributes evolve simultaneously in a dynamic process. The method is illustrated by an example on the dynamics of alcohol consumption among adolescent friends. ... The principles of actor-driven, or actor-oriented, modeling were proposed in Snijders (1996). The model for dynamics of only networks, without behav- ior, was formulated in Snijders (2001, 2005). In Steglich et al. (2004), the sociological aspects of the model for dynamics of networks and behavior are discussed, with an extensive example about the interrelationship of the de- velopment of friendship networks and the dynamics in smoking and drinking behavior, on the basis of data from a Scottish high school. This chapter gives an overview of the specification of the stochastic model for dynamics of networks and behavior and then proceeds to parameter estimation and model selection. "

<bibtex> @article{van2007actor,

 title=Template:An actor-oriented dynamic network approach: the case of interorganizational network evolution,
 author={Van de Bunt, G.G. and Groenewegen, P.},
 journal={Organizational Research Methods},
 volume={10},
 number={3},
 pages={463},
 year={2007},
 publisher={Res Methods Div}

}

</bibtex> This is another really good lit review (they get better and better): " A s demonstrated by three special issues in Journal of Mathematical Sociology (Doreian & Stokman, 1996, 2003; Stokman & Doreian, 2001), the study of network dynamics is of growing importance among sociologists, social psychologists, and network statisti- cians. All three issues were devoted to the underlying mechanisms that induce the evolu- tion of social networks: which micro mechanisms (i.e., individual choices) lead to which macro outcomes (i.e., network structures), and how and why do these structures change over time? More recently, research on networks and their dynamics is also flourishing in the strategy and organization literature; see, for instance, review articles by Borgatti and Foster (2003) and Brass, Galaskiewicz, Greve, and Tsai (2004). One emerging and particu- larly important topic is the ongoing dynamics of networks that result from collaborative choices (among others, Ahuja, 2000; Chung, Singh, & Lee, 2000; Ebers, 1999; Gulati, 1995, 1999; Gulati & Gargiulo, 1999; Hagedoorn, 2006; Powell, 1998; Powell, Koput, Smith-Doer, & Owen-Smith, 1999); today’s choice of an alliance partner affects tomorrow’s options as it changes the network structure and thereby the future alternatives and strategies of all fellow network members. For advancements in the latter topic, new statistical techni- ques are required that can analyze these complex longitudinal network data structures (e.g., Hagedoorn, 2006). Most techniques, however, are not able to deal with these data struc- tures in a satisfactorily and statistically sound way. Snijders (1995, 1996, 2001, 2005) and Snijders & Van Duijn (1997) introduced actor-oriented modeling that does not assume statistical independence between observations and combines continuous time Markov analysis and random utility models. Originally these models were designed to model the & Stokman, 1996, 2003; Stokman & Doreian, 2001), the study of network dynamics is of growing importance among sociologists, social psychologists, and network statisti- cians. All three issues were devoted to the underlying mechanisms that induce the evolu- tion of social networks: which micro mechanisms (i.e., individual choices) lead to which macro outcomes (i.e., network structures), and how and why do these structures change over time? More recently, research on networks and their dynamics is also flourishing in the strategy and organization literature; see, for instance, review articles by Borgatti and Foster (2003) and Brass, Galaskiewicz, Greve, and Tsai (2004). One emerging and particu- larly important topic is the ongoing dynamics of networks that result from collaborative choices (among others, Ahuja, 2000; Chung, Singh, & Lee, 2000; Ebers, 1999; Gulati, 1995, 1999; Gulati & Gargiulo, 1999; Hagedoorn, 2006; Powell, 1998; Powell, Koput, Smith-Doer, & Owen-Smith, 1999); today’s choice of an alliance partner affects tomorrow’s options as it changes the network structure and thereby the future alternatives and strategies of all fellow network members. For advancements in the latter topic, new statistical techni- ques are required that can analyze these complex longitudinal network data structures (e.g., Hagedoorn, 2006). Most techniques, however, are not able to deal with these data struc- tures in a satisfactorily and statistically sound way. Snijders (1995, 1996, 2001, 2005) and Snijders & Van Duijn (1997) introduced actor-oriented modeling that does not assume statistical independence between observations and combines continuous time Markov analysis and random utility models. Originally these models were designed to model the evolution of expressive networks consisting of individuals (see van de Bunt, 1999; van de Bunt, Van Duijn, & Snijders, 1999; van de Bunt, Wittek, & De Klepper, 2005; Van Duijn, Zeggelink, Huisman, Stokman, & Wasseur, 2003). However, actor-oriented modeling is also particularly adequate to capture the manner in which interfirm networks evolve as a consequence of interaction between network structure and alliance partner choice. Actor- oriented modeling is also an answer to a call for the application of agent-based modeling to solve the puzzle of the interaction between network (i.e., macro) outcomes and a firm’s (i.e., micro) choices (Macy & Willer, 2002). This is warranted because actor-oriented modeling allows for assessing of the relevant mechanisms based on individual (i.e., firm) choices. These choices are modeled under the assumption that firms are driven by the expected amount of utility derived from the selection of specific partners, taking the present evolution of expressive networks consisting of individuals (see van de Bunt, 1999; van de Bunt, Van Duijn, & Snijders, 1999; van de Bunt, Wittek, & De Klepper, 2005; Van Duijn, Zeggelink, Huisman, Stokman, & Wasseur, 2003). However, actor-oriented modeling is also particularly adequate to capture the manner in which interfirm networks evolve as a consequence of interaction between network structure and alliance partner choice. Actor- oriented modeling is also an answer to a call for the application of agent-based modeling to solve the puzzle of the interaction between network (i.e., macro) outcomes and a firm’s (i.e., micro) choices (Macy & Willer, 2002). This is warranted because actor-oriented modeling allows for assessing of the relevant mechanisms based on individual (i.e., firm) choices. These choices are modeled under the assumption that firms are driven by the expected amount of utility derived from the selection of specific partners, taking the present network configuration and the theoretically desired outcome explicitly into account. "