Description

Networks are quite complicated entities already, but combined with the word ‘multilevel’ they become even more complex. To limit the curse of everything depending on everything else, a longitudinal approach gives a bit of support; but more specific structuring is needed for cutting through the complexities.

A variety of multilevel network structures are possible. In this course several of such structures are treated, with a focus on three main types. Some principles of longitudinal approaches are presented that can be carried out using Stochastic Actor-oriented Models, implemented in the Siena software. These are illustrated by examples. Much of this is current research, or potentialities that have been little explored, and some loose threads are to be expected. In all cases, the data is supposed to consist of network panel data: repeated observations (2 or a few waves) of a network on a constant actor set (where some turnover and some missing data are allowed).

Type I, for the ‘multilevel analysis of networks’, refers to a set of unrelated networks, for each of which the same model is applicable, but with different parameters. This is a nested structure of parallel networks. One possible approach is a two-step procedure, where the first step is to estimate parameters for each network separately, and the second step to combine these results in a meta analysis. Another approach uses a random effects multilevel network model, where a common model specification is used for the individual networks, and the network-level parameters are modelled as a sample from a population, similar to use of the hierarchical linear model to combine linear regression models across multiple “parallel” groups. A multivariate normal distribution may be assumed for the distribution of the parameter vector across the “parallel” networks. The analysis of each network then borrows strength from the data for the other networks, much like in the hierarchical linear model. A Bayesian approach may be followed for the estimation of parameters in such a random effects multilevel model for combining actor-oriented models for network dynamics.

Type II, for the ‘analysis of multilevel networks’ as defined by Wang et al. (2013), refers to a structure with several distinct node sets, and networks on or between several of these node sets. The networks on a node set are one-mode networks, those between node sets are two-mode networks. This can be regarded mathematically as one network on the union of the node sets, but also as multiple networks on various combinations of the node sets. A simple case is the co-evolution of a one-mode and a two-mode network for a given set of actors. In all its simplicity this is a particularly rich type of network structure, because the two types of network allow to represent the combination of two (or more) different kinds of social context of actors.

Type III, for ‘network analysis on a multilevel node set’, refers to a network on one node set, where the node set has itself a nested structure. This is one network on a nested node set. Here one may distinguish between an exogenous nesting structure, e.g., networks between students in classrooms in schools, and an endogenous structure, such as represented in the Settings Model, a new variety of the Stochastic Actor-oriented Model.

Panel data for multilevel networks of all these kinds can be analysed using Stochastic Actor-oriented Models, implemented in the Siena software. Such models can be extended with dependent nodal variables, which for Type II could be given for one or several of the node sets, and for Type III can be distinguished by the nesting levels for the nodes. Examples for the various Types will be discussed, and procedures will be presented for how to analyse this using Siena.

Requirements

For this workshop, some prior basic knowledge of the Stochastic Actor-oriented Model is assumed, and it will be helpful for participants to have some knowledge of the RSiena package in R. The Bayesian analysis of Type I data can be done by the function sienaBayes which is available only in the RSienaTest package. This can be downloaded from R-Forge http://r-forge.r-project.org/R/?group_id=461

The command that can be used is:

install.packages("RSienaTest", repos="http://R-Forge.R-project.org")