Bayesian analysis of higher-order network autocorrelation models

D. Dittrich*, Roger Leenders, Joris Mulder

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

The network autocorrelation model has been the workhorse for estimating and testing the strength of theories of social influence in a network. In many network studies, different types of social influence are present simultaneously and can be modeled using various connectivity matrices. Often, researchers have expectations about the order of strength of these different influence mechanisms. However, currently available methods cannot be applied to test a specific order of social influence in a network. In this chapter, we first present flexible Bayesian techniques for estimating network autocorrelation models with multiple network autocorrelation parameters. Second, we develop new Bayes factors that allow researchers to test hypotheses with order constraints on the network autocorrelation parameters in a direct manner. Concomitantly, we give efficient algorithms for sampling from the posterior distributions and for computing the Bayes factors. Simulation results suggest that frequentist properties of Bayesian estimators based on non-informative priors for the network autocorrelation parameters are overall slightly superior to those based on maximum likelihood estimation. Furthermore, when testing statistical hypotheses, the Bayes factors show consistent behavior with evidence for a true data-generating hypothesis increasing with the sample size. Finally, we illustrate our methods using a data set from the economic growth theory.
Original languageEnglish
JournalSociological Methodology
Publication statusAccepted/In press - 2020

Fingerprint

growth theory
economic theory
economic growth
simulation
present
evidence

Cite this

@article{61debb5d7c504a3fbdfefcc67823edbe,
title = "Bayesian analysis of higher-order network autocorrelation models",
abstract = "The network autocorrelation model has been the workhorse for estimating and testing the strength of theories of social influence in a network. In many network studies, different types of social influence are present simultaneously and can be modeled using various connectivity matrices. Often, researchers have expectations about the order of strength of these different influence mechanisms. However, currently available methods cannot be applied to test a specific order of social influence in a network. In this chapter, we first present flexible Bayesian techniques for estimating network autocorrelation models with multiple network autocorrelation parameters. Second, we develop new Bayes factors that allow researchers to test hypotheses with order constraints on the network autocorrelation parameters in a direct manner. Concomitantly, we give efficient algorithms for sampling from the posterior distributions and for computing the Bayes factors. Simulation results suggest that frequentist properties of Bayesian estimators based on non-informative priors for the network autocorrelation parameters are overall slightly superior to those based on maximum likelihood estimation. Furthermore, when testing statistical hypotheses, the Bayes factors show consistent behavior with evidence for a true data-generating hypothesis increasing with the sample size. Finally, we illustrate our methods using a data set from the economic growth theory.",
author = "D. Dittrich and Roger Leenders and Joris Mulder",
year = "2020",
language = "English",
journal = "Sociological Methodology",
issn = "0081-1750",
publisher = "Wiley-Blackwell",

}

Bayesian analysis of higher-order network autocorrelation models. / Dittrich, D.; Leenders, Roger; Mulder, Joris.

In: Sociological Methodology, 2020.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Bayesian analysis of higher-order network autocorrelation models

AU - Dittrich, D.

AU - Leenders, Roger

AU - Mulder, Joris

PY - 2020

Y1 - 2020

N2 - The network autocorrelation model has been the workhorse for estimating and testing the strength of theories of social influence in a network. In many network studies, different types of social influence are present simultaneously and can be modeled using various connectivity matrices. Often, researchers have expectations about the order of strength of these different influence mechanisms. However, currently available methods cannot be applied to test a specific order of social influence in a network. In this chapter, we first present flexible Bayesian techniques for estimating network autocorrelation models with multiple network autocorrelation parameters. Second, we develop new Bayes factors that allow researchers to test hypotheses with order constraints on the network autocorrelation parameters in a direct manner. Concomitantly, we give efficient algorithms for sampling from the posterior distributions and for computing the Bayes factors. Simulation results suggest that frequentist properties of Bayesian estimators based on non-informative priors for the network autocorrelation parameters are overall slightly superior to those based on maximum likelihood estimation. Furthermore, when testing statistical hypotheses, the Bayes factors show consistent behavior with evidence for a true data-generating hypothesis increasing with the sample size. Finally, we illustrate our methods using a data set from the economic growth theory.

AB - The network autocorrelation model has been the workhorse for estimating and testing the strength of theories of social influence in a network. In many network studies, different types of social influence are present simultaneously and can be modeled using various connectivity matrices. Often, researchers have expectations about the order of strength of these different influence mechanisms. However, currently available methods cannot be applied to test a specific order of social influence in a network. In this chapter, we first present flexible Bayesian techniques for estimating network autocorrelation models with multiple network autocorrelation parameters. Second, we develop new Bayes factors that allow researchers to test hypotheses with order constraints on the network autocorrelation parameters in a direct manner. Concomitantly, we give efficient algorithms for sampling from the posterior distributions and for computing the Bayes factors. Simulation results suggest that frequentist properties of Bayesian estimators based on non-informative priors for the network autocorrelation parameters are overall slightly superior to those based on maximum likelihood estimation. Furthermore, when testing statistical hypotheses, the Bayes factors show consistent behavior with evidence for a true data-generating hypothesis increasing with the sample size. Finally, we illustrate our methods using a data set from the economic growth theory.

M3 - Article

JO - Sociological Methodology

JF - Sociological Methodology

SN - 0081-1750

ER -