arXiv subjects

Tom A. B. Snijders

Publications and source records attributed to Tom A. B. Snijders.

7 recordsLinked to original sources

arXiv2024

Stochastic Actor Oriented Model with Random Effects

The stochastic actor oriented model (SAOM) is a method for modelling social interactions and social behaviour over time. It can be used to model drivers of dynamic interactions using both exogenous covariates and endogenous network configurations, but also the co-evolution of behaviour and social interactions. In its standard implementations, it assumes that all individual have the same interaction evaluation function. This lack of heterogeneity is one of its limitations. The aim of this paper is to extend the inference framework for the SAOM to include random effects, so that the heterogeneity of individuals can be modeled more accurately. We decompose the linear evaluation function that models the probability of forming or removing a tie from the network, in a homogeneous fixed part and a random, individual-specific part. We extend the Robbins-Monro algorithm to the estimation of the variance of the random parameters. Our method is applicable for the general random effect formulations. We illustrate the method with a random out-degree model and show the parameter estimation of the random components, significance tests and model evaluation. We apply the method to the Kapferer's Tailor shop study. It is shown that a random out-degree constitutes a serious alternative to including transitivity and higher-order dependency effects.

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arXiv2022

Multilevel Longitudinal Analysis of Social Networks

Stochastic actor-oriented models (SAOM) are a broadly applied modelling framework for analysing network dynamics using network panel data. They have been extended to address co-evolution of multiple networks as well as networks and behaviour. This paper extends the SAOM to the analysis of multiple network panels through a random coefficient multilevel model, estimated with a Bayesian approach. This is illustrated by a study of the dynamic interdependence of friendship and minor delinquency, represented by the combination of a one-mode and a two-mode network, using a sample of 81 school classes in the first year of secondary school.

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arXiv2021

Modeling partitions of individuals

Despite the central role of self-assembled groups in animal and human societies, statistical tools to explain their composition are limited. We introduce a statistical framework for cross-sectional observations of groups with exclusive membership to illuminate the social and organizational mechanisms that bring people together. Drawing from stochastic models for networks and partitions, the proposed framework introduces an exponential family of distributions for partitions. We derive its main mathematical properties and suggest strategies to specify and estimate such models. A case study on hackathon events applies the developed framework to the study of mechanisms underlying the formation of self-assembled project teams.

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arXiv2018

Beyond Homophily: Incorporating Actor Variables in Actor-oriented Network Models

We consider the specification of effects of numerical actor attributes in statistical models for directed social networks. A fundamental mechanism is homophily or assortativity, where actors have a higher likelihood to be tied with others having similar values of the variable under study. But there are other mechanisms that may also play a role in how the attribute values of two actors influence the likelihood of a tie. We discuss three additional mechanisms: aspiration to send ties to others having high values; conformity in the sense of sending more ties to others whose values are close to what may be considered the `social norm'; and sociability, where those having higher values will tend to send more ties generally. These mechanisms may operate jointly, and then their effects will be confounded. We present a specification representing these effects simultaneously by a four-parameter quadratic function of the values of sender and receiver. Greater flexibility can be obtained by a five-parameter extension. We argue that empirical researchers often overlook the possibility that homophily may be confounded with these other mechanisms, and that for actor attributes that have important effects on directed networks, these specifications may provide an improvement. An illustration is given of the dependence of advice ties on academic grades in a network of MBA students, analyzed by the Stochastic Actor-oriented Model.

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arXiv2018

Statistical Power in Longitudinal Network Studies

Longitudinal social network studies can easily suffer from insufficient statistical power. Studies that simultaneously investigate change of network ties and change of nodal attributes (selection and influence studies) are particularly at risk because the number of nodal observations is typically much lower than the number of observed tie variables. This paper presents a simulation-based procedure to evaluate statistical power of longitudinal social network studies in which stochastic actor-oriented models (SAOMs) are to be applied. Two detailed case studies illustrate how statistical power is strongly affected by network size, number of data collection waves, effect sizes, missing data, and participant turnover. These issues should thus be explored in the design phase of longitudinal social network studies.

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arXiv2017

Transitivity Correlation: Measuring Network Transitivity as Comparative Quantity

This paper proposes that common measures for network transitivity, based on the enumeration of transitive triples, do not reflect the theoretical statements about transitivity they aim to describe. These statements are often formulated as comparative conditional probabilities, but these are not directly reflected by simple functions of enumerations. We think that a better approach is obtained by considering the linear regression coefficient of ties $i\,\rightarrow\,j$ on the number of two-paths $i\,\rightarrow\,k\rightarrow\,j$ for the $(n-2)$ possible intermediate nodes $k$. Two measures of transitivity based on correlation coefficients between the existence of a tie and the existence, or the number, of two-paths are developed, and called "Transitivity Phi" and "Transitivity Correlation". Some desirable properties for these measures are studied and compared to existing clustering coefficients, in both random (Erdös-Renyi) and in stylized networks (windmills). Furthermore, it is shown that under the condition of zero Transitivity Correlation, the total number of transitive triples is determined by four underlying features of any directed graph: size, density, reciprocity, and the covariance between indegrees and outdegrees. Also, it is demonstrated that plotting conditional probability of ties, given the number of two-paths, provides valuable insights into empirical regularities and irregularities of transitivity patterns.

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arXiv2010

Maximum likelihood estimation for social network dynamics

A model for network panel data is discussed, based on the assumption that the observed data are discrete observations of a continuous-time Markov process on the space of all directed graphs on a given node set, in which changes in tie variables are independent conditional on the current graph. The model for tie changes is parametric and designed for applications to social network analysis, where the network dynamics can be interpreted as being generated by choices made by the social actors represented by the nodes of the graph. An algorithm for calculating the Maximum Likelihood estimator is presented, based on data augmentation and stochastic approximation. An application to an evolving friendship network is given and a small simulation study is presented which suggests that for small data sets the Maximum Likelihood estimator is more efficient than the earlier proposed Method of Moments estimator.

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