You are here

Actor-Based Models for Longitudinal Networks


Alberto Caimo, Nial Friel

Publication Type: 
Refereed Original Article
The study of longitudinal networks has become a major topic of interest and dynamic modelling approaches have been pursued in much of social network analysis. Important applications range from friendship networks (see for example, Pearson and West (2003) and Burk et al (2007)) to inter-organizational networks (see for example, Brass et al (2004)). However many of the classical statistical models proposed have focused mainly on single static network analysis. One of the reasons why network dynamics was not tackled until a couple of decades ago is that the complex dependence structures that characterize networks could not allow an exact inferential calculations and estimation procedures cannot be dealt without computer simulation algorithms. These powerful tools have allowed researchers to focus to the analysis of the underlying mechanisms that induce the characteristics of network dynamics from the \micro dynamics" such as the individual actor choices to the \macro properties" such as the network connectivity structure. Key research topics concern the structural positions of the actors, their connectivity evolution, belief development, friendship formation, di usion of innovations, the spread of a particular behaviour, etc. Modeling the dynamics of social networks is therefore of crucial importance but it is also extremely dicult, due to the temporal dependence, but also since network data, at any given time instance, are not composed of independent observations but each tie variable between two actors is dependent on the presence or absence of ties in the other dyads. Consequently the network dynamics is greatly a ected by the global connectivity structure. For this reason standard statistical models cannot give an adequate representation of this dependence feature. Various models have been proposed for the statistical analysis of longitudinal social network data and some earlier reviews were given by Wasserman (1979) and Frank (1991). An actor-oriented approach to this type of modelling was pioneered by Snijders Snijders (1996, 2001, 2005) and Snijders and van Duijn (1997) under the assump- tion of statistical dependence between observations evolving over time according to a continuous time Markov process. These models were originally designed to model the evolution of expressive networks consisting of individuals but they can provide a general framework for the analysis of many di erent kinds of relations. Some applications were presented by van de Bunt (1999), de Nooy (2002), Huisman and Steglich (2008) and van Duijn et al (2003). The actor-based models are a family of statistical models aiming to describe network dynamics according to some typical network dependencies such as reciprocation of ties, transitivity, etc. They represent one of the most prominent class of models for the analysis of network dynamics as they allow a exible analysis of the complex social network dependencies among the actors over the time. In this context, the network dynamic is assumed to be driven by di erent e ects modelled by network statistics which operate simultaneously. The stochastic process de ned by these e ects can provide a good representation of the changes of the network connectivity structure over time. The model parameter estimates allow one to understand the strength of the e ects included in the model. The actor-based models are exible as they allow to incorporate a wide variety of network statistics. The main objectives of this approach consist in representing a wide variety of e ects or tendencies on network evolution, estimate parameters expressing such tendencies and test corresponding hypotheses so as to understand the structuring of social networks over time. These e ects are various and can be created based on the application. The parameter estimates obtained from the inferential process can be used to simulate network structures compatible with the tendencies observed in the network changes under study. This chapter does not give a review of this literature concerning modelling approaches for longitudinal network data but it focuses only on the class of stochastic actor-based models. In this chapter we describe the basic features of the actor-based models by providing the theoretical assumptions and methodology requirements needed. We give some basic insights con- cerning the inferential analysis for the parameters and goodness of t procedures. Next we carry out an illustration of the capabilities of these models through their applica- tion to an ethnographic study of community structure in a New England monastery by Sampson (1968). A brief discussion on the future directions is given at the end of the chapter
Digital Object Identifer (DOI): 
1 0 . 1 0 0 7 / 9 7 8 - 1 - 4 6 1 4 - 6 1 7 0 - 8 _ 1 6 6
Publication Status: 
Publication Date: 
Encyclopedia of Social Network Analysis and Mining, Springer
National University of Ireland, Dublin (UCD)
Open access repository: