Short Course

Multilevel Network Dynamics

October 28, 2019 in Vietri sul Mare, on the Amalfi Coast, near Salerno (Italy),

part of the ARS'19 International Workshop Multilayer, Multilevel and Multimode Networks

Tom A.B. Snijders
Department of Sociology, University of Groningen
Nuffield College, University of Oxford


Johan Koskinen
School of Psychological Sciences, University of Melbourne


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Overview

Networks are quite complicated entities already by themselves, 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. (Social Networks 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. 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.

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. See Snijders, van de Bunt and Steglich (2010) and the Siena website.
The RSienaTest version of the package is preferable here, because the Bayesian analysis of Type I data can be done by the function sienaBayes which is available only in the RSienaTest package. The current version of both packages can be downloaded from R-Forge.
The R command that can be used is install.packages("RSienaTest", repos="http://R-Forge.R-project.org")


Literature

The main specific literature for this short course is Snijders (2016), the 'multiple flavours' chapter below. The rest is for further study.

General

Type I

Type II

Type III

  • ...


Materials

The materials all are work in progress.

Texts

For the course

  1. Multilevel Longitudinal Network Analysis (general introduction) (slides).

    Handout version of the same .

  2. The Multiple Flavours of Multilevel Issues for Networks (slides).

    Overview of the course.

  3. Multilevel analysis of network dynamics (slides).

    Handout version of the same.

  4. The co-evolution of multiple networks, one-mode and two-mode (slides).

    Handout version of the same .

  5. Longitudinal Analysis of Multilevel Networks (slides).

    Handout version of the same .

  6. Network dynamics with a structured node set: Sociability in seven villages in Senegal (slides).

    Handout version of the same .

Some further material for Type I

Scripts

Type I

Type II




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