5th European Conference on Social Networks EUSN 2021

Naples / online

Workshop Analysing multilevel network dynamics using RSiena

September 6, 2021

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

Don't use Internet Explorer as a browser for these pages. It does not reproduce the R scripts in a nice fashion.

Workshop description

Multilevel network analysis comes in three flavors.

Multilevel analysis of networks ('MAN') where the data consists of a set of multiple networks which are conceptually similar but have disjoint node sets and no connections between them, and regarded as independent replications with respect to the social processes investigated.
Analysis of multilevel networks ('AMN') defined as multiple interdependent networks with several node sets, some of which are shared. The simplest example is a one-mode friendship network between individuals together with a two-mode network of the activities of the same set of individuals.
Analysis of a network on one node set, where the node set has itself a nested structure.

This workshop will treat longitudinal analysis of the first two kinds of multilevel network structures, using stochastic actor-oriented models and the RSiena package. 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). The number of actors (nodes) typically is between 20 and 500.

The first part of the workshop will focus on the first kind (MAN), in particular the random coefficient multilevel longitudinal network analysis implemented in the function sienaBayes in package RSienaTest. The basic idea of this random coefficient model will be presented, with the approach taken by the analysis using sienaBayes. The use of this function will be explained, and guidance will be given for parameter interpretation.

For the second kind of analysis (AMN), the regular estimation function siena07 in RSiena can be used, with multivariate specification of the data set. The simplest case is the co-evolution of a one-mode and a two-mode network, with the question of selection versus influence: are actors influenced to have the same activities as their 'friends', or do they tend to select ties to those having the same activities. This will be elaborated in the second part of the workshop.

Prerequisites

The workshop is intended for participants who have experience in working with RSiena.

Elaboration

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 RSiena 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.

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 RSiena package. 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.

For the first part of the workshop (MAN), the package RSienaTest will be used. Please have the latest version of this installed from the Siena downloads page or from R-Forge.
The R command that can be used is install.packages("RSienaTest", repos="http://R-Forge.R-project.org"). For the second part of the workshop (AMN), the current version of package RSiena will be used, which can be installed in the regular way from CRAN.

Literature

The main background literature for this workshop is Snijders (2016), the 'multiple flavours' chapter below. The rest is given for your interest.

General

Ruth M. Ripley, Tom A.B. Snijders, Zsófia Boda, Andras Vörös, and Paulina Preciado (2021). Manual for SIENA version 4.0. Oxford: University of Oxford, Department of Statistics; Nuffield College.
Snijders, T.A.B., van de Bunt, G.G., and Steglich, C.E.G. (2010). Introduction to actor-based models for network dynamics. Social Networks, 32, 44-60.
DOI: http://dx.doi.org/10.1016/j.socnet.2009.02.004.
Tom A.B. Snijders (2016), The Multiple Flavours of Multilevel Issues for Networks.
Chapter 2 in Emmanuel Lazega and Tom A.B. Snijders (eds.), Multilevel Network Analysis for the Social Sciences, Cham: Springer, 2016.
ISBN 978-3-319-24518-8
ISBN 978-3-319-24520-1 (eBook)
DOI: 10.1007/978-3-319-24520-1
Tom A.B. Snijders. (2017). Stochastic Actor-Oriented Models for Network Dynamics.
Annual Review of Statistics and Its Application, 4, 343-363.
DOI: http://dx.doi.org/10.1146/annurev-statistics-060116-054035
(General overview from a statistical point of view.)

Type I

Tom A.B. Snijders and Chris Baerveldt, A Multilevel Network Study of the Effects of Delinquent Behavior on Friendship Evolution.
Journal of Mathematical Sociology 27 (2003), 123-151.
Tom A.B. Snijders and Johan Koskinen (2012). Multilevel Longitudinal Analysis of Social Networks. Paper presented at the 8th UKSNA Conference, Bristol, June 28-30, 2012.

Type II

Tom A.B. Snijders, Alessandro Lomi, and Vanina Jasmine Torló (2013). A model for the multiplex dynamics of two-mode and one-mode networks, with an application to employment preference, friendship, and advice. Social Networks, 35, 265-276.
Kayo Fujimoto, Tom A.B. Snijders, and Thomas W. Valente (2018). Multivariate dynamics of one-mode and two-mode networks: Explaining similarity in sports participation among friends. Network Science, 6, 370-395.
DOI: http://dx.doi.org/10.1017/nws.2018.11
Peng Wang, Garry Robins, Philippa Pattison, and Emmanuel Lazega (2013). Exponential random graph models for multilevel networks. Social Networks, 35, 96-115.
DOI: http://dx.doi.org/10.1016/j.socnet.2013.01.004

Type III

Tom A.B. Snijders, Malick Faye, and Julien Brailly (2020). Network dynamics with a nested node set: Sociability in seven villages in Senegal. Statistica Neerlandica 74, 300-323.
DOI: http://dx.doi.org/10.1111/stan.12208
From the abstract:
We propose two complementary ways to deal with a nesting structure in the node set of a network; such a structure may be called a multilevel network, with a node set consisting of several groups. First, within-group ties are distinguished from between-group ties by considering them as two distinct but interrelated networks. Second, effects of nodal variables are differentiated according to the levels of the nesting structure, to prevent ecological fallacies.

Back to the main Siena page

	5th European Conference on Social Networks EUSN 2021 Naples / online Workshop Analysing multilevel network dynamics using RSiena September 6, 2021 Tom A.B. Snijders Department of Sociology, University of Groningen Nuffield College, University of Oxford


	Don't use Internet Explorer as a browser for these pages. It does not reproduce the R scripts in a nice fashion. Workshop description Multilevel network analysis comes in three flavors. Multilevel analysis of networks ('MAN') where the data consists of a set of multiple networks which are conceptually similar but have disjoint node sets and no connections between them, and regarded as independent replications with respect to the social processes investigated. Analysis of multilevel networks ('AMN') defined as multiple interdependent networks with several node sets, some of which are shared. The simplest example is a one-mode friendship network between individuals together with a two-mode network of the activities of the same set of individuals. Analysis of a network on one node set, where the node set has itself a nested structure. This workshop will treat longitudinal analysis of the first two kinds of multilevel network structures, using stochastic actor-oriented models and the RSiena package. 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). The number of actors (nodes) typically is between 20 and 500. The first part of the workshop will focus on the first kind (MAN), in particular the random coefficient multilevel longitudinal network analysis implemented in the function sienaBayes in package RSienaTest. The basic idea of this random coefficient model will be presented, with the approach taken by the analysis using sienaBayes. The use of this function will be explained, and guidance will be given for parameter interpretation. For the second kind of analysis (AMN), the regular estimation function siena07 in RSiena can be used, with multivariate specification of the data set. The simplest case is the co-evolution of a one-mode and a two-mode network, with the question of selection versus influence: are actors influenced to have the same activities as their 'friends', or do they tend to select ties to those having the same activities. This will be elaborated in the second part of the workshop. Prerequisites The workshop is intended for participants who have experience in working with RSiena.


	Elaboration 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 RSiena 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. 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 RSiena package. 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. For the first part of the workshop (MAN), the package RSienaTest will be used. Please have the latest version of this installed from the Siena downloads page or from R-Forge. The R command that can be used is install.packages("RSienaTest", repos="http://R-Forge.R-project.org"). For the second part of the workshop (AMN), the current version of package RSiena will be used, which can be installed in the regular way from CRAN.


	Literature The main background literature for this workshop is Snijders (2016), the 'multiple flavours' chapter below. The rest is given for your interest. General Ruth M. Ripley, Tom A.B. Snijders, Zsófia Boda, Andras Vörös, and Paulina Preciado (2021). Manual for SIENA version 4.0. Oxford: University of Oxford, Department of Statistics; Nuffield College. Snijders, T.A.B., van de Bunt, G.G., and Steglich, C.E.G. (2010). Introduction to actor-based models for network dynamics. Social Networks, 32, 44-60. DOI: http://dx.doi.org/10.1016/j.socnet.2009.02.004. Tom A.B. Snijders (2016), The Multiple Flavours of Multilevel Issues for Networks. Chapter 2 in Emmanuel Lazega and Tom A.B. Snijders (eds.), Multilevel Network Analysis for the Social Sciences, Cham: Springer, 2016. ISBN 978-3-319-24518-8 ISBN 978-3-319-24520-1 (eBook) DOI: 10.1007/978-3-319-24520-1 Tom A.B. Snijders. (2017). Stochastic Actor-Oriented Models for Network Dynamics. Annual Review of Statistics and Its Application, 4, 343-363. DOI: http://dx.doi.org/10.1146/annurev-statistics-060116-054035 (General overview from a statistical point of view.) Type I Tom A.B. Snijders and Chris Baerveldt, A Multilevel Network Study of the Effects of Delinquent Behavior on Friendship Evolution. Journal of Mathematical Sociology 27 (2003), 123-151. Tom A.B. Snijders and Johan Koskinen (2012). Multilevel Longitudinal Analysis of Social Networks. Paper presented at the 8th UKSNA Conference, Bristol, June 28-30, 2012. Type II Tom A.B. Snijders, Alessandro Lomi, and Vanina Jasmine Torló (2013). A model for the multiplex dynamics of two-mode and one-mode networks, with an application to employment preference, friendship, and advice. Social Networks, 35, 265-276. Kayo Fujimoto, Tom A.B. Snijders, and Thomas W. Valente (2018). Multivariate dynamics of one-mode and two-mode networks: Explaining similarity in sports participation among friends. Network Science, 6, 370-395. DOI: http://dx.doi.org/10.1017/nws.2018.11 Peng Wang, Garry Robins, Philippa Pattison, and Emmanuel Lazega (2013). Exponential random graph models for multilevel networks. Social Networks, 35, 96-115. DOI: http://dx.doi.org/10.1016/j.socnet.2013.01.004 Type III Tom A.B. Snijders, Malick Faye, and Julien Brailly (2020). Network dynamics with a nested node set: Sociability in seven villages in Senegal. Statistica Neerlandica 74, 300-323. DOI: http://dx.doi.org/10.1111/stan.12208 From the abstract: We propose two complementary ways to deal with a nesting structure in the node set of a network; such a structure may be called a multilevel network, with a node set consisting of several groups. First, within-group ties are distinguished from between-group ties by considering them as two distinct but interrelated networks. Second, effects of nodal variables are differentiated according to the levels of the nesting structure, to prevent ecological fallacies.









	Back to the main Siena page

5th European Conference on Social Networks EUSN 2021 Naples / online Workshop Analysing multilevel network dynamics using RSiena September 6, 2021

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