Bayesian estimation of the network autocorrelation model

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Abstract

The network autocorrelation model has been extensively used by researchers interested modeling social influence effects in social networks. The most common inferential method in the model is classical maximum likelihood estimation. This approach, however, has known problems such as negative bias of the network autocorrelation parameter and poor coverage of confidence intervals. In this paper, we develop new Bayesian techniques for the network autocorrelation model that address the issues inherent to maximum likelihood estimation. A key ingredient of the Bayesian approach is the choice of the prior distribution. We derive two versions of Jeffreys prior, the Jeffreys rule prior and the Independence Jeffreys prior, which have not yet been developed for the network autocorrelation model. These priors can be used for Bayesian analyses of the model when prior information is completely unavailable. Moreover, we propose an informative as well as a weakly informative prior for the network autocorrelation parameter that are both based on an extensive literature review of empirical applications of the network autocorrelation model across many fields. Finally, we provide new and efficient Markov Chain Monte Carlo algorithms to sample from the resulting posterior distributions. Simulation results suggest that the considered Bayesian estimators outperform the maximum likelihood estimator with respect to bias and frequentist coverage of credible and confidence intervals.
Keywords: Network autocorrelation model, Bayesian inference, Jeffreys rule prior,
Informative prior distribution, Frequentist coverage
Original languageEnglish
Pages (from-to)213-236
JournalSocial Networks
Volume48
DOIs
Publication statusPublished - 2017

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Confidence Intervals
Markov Chains
coverage
confidence
trend
social network
simulation

Keywords

  • Social Networks
  • Social influence
  • Bayesian inference

Cite this

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title = "Bayesian estimation of the network autocorrelation model",
abstract = "The network autocorrelation model has been extensively used by researchers interested modeling social influence effects in social networks. The most common inferential method in the model is classical maximum likelihood estimation. This approach, however, has known problems such as negative bias of the network autocorrelation parameter and poor coverage of confidence intervals. In this paper, we develop new Bayesian techniques for the network autocorrelation model that address the issues inherent to maximum likelihood estimation. A key ingredient of the Bayesian approach is the choice of the prior distribution. We derive two versions of Jeffreys prior, the Jeffreys rule prior and the Independence Jeffreys prior, which have not yet been developed for the network autocorrelation model. These priors can be used for Bayesian analyses of the model when prior information is completely unavailable. Moreover, we propose an informative as well as a weakly informative prior for the network autocorrelation parameter that are both based on an extensive literature review of empirical applications of the network autocorrelation model across many fields. Finally, we provide new and efficient Markov Chain Monte Carlo algorithms to sample from the resulting posterior distributions. Simulation results suggest that the considered Bayesian estimators outperform the maximum likelihood estimator with respect to bias and frequentist coverage of credible and confidence intervals.Keywords: Network autocorrelation model, Bayesian inference, Jeffreys rule prior,Informative prior distribution, Frequentist coverage",
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language = "English",
volume = "48",
pages = "213--236",
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}

Bayesian estimation of the network autocorrelation model. / Dittrich, D.; Leenders, R.T.A.J.; Mulder, J.

In: Social Networks, Vol. 48, 2017, p. 213-236.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Bayesian estimation of the network autocorrelation model

AU - Dittrich, D.

AU - Leenders, R.T.A.J.

AU - Mulder, J.

PY - 2017

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N2 - The network autocorrelation model has been extensively used by researchers interested modeling social influence effects in social networks. The most common inferential method in the model is classical maximum likelihood estimation. This approach, however, has known problems such as negative bias of the network autocorrelation parameter and poor coverage of confidence intervals. In this paper, we develop new Bayesian techniques for the network autocorrelation model that address the issues inherent to maximum likelihood estimation. A key ingredient of the Bayesian approach is the choice of the prior distribution. We derive two versions of Jeffreys prior, the Jeffreys rule prior and the Independence Jeffreys prior, which have not yet been developed for the network autocorrelation model. These priors can be used for Bayesian analyses of the model when prior information is completely unavailable. Moreover, we propose an informative as well as a weakly informative prior for the network autocorrelation parameter that are both based on an extensive literature review of empirical applications of the network autocorrelation model across many fields. Finally, we provide new and efficient Markov Chain Monte Carlo algorithms to sample from the resulting posterior distributions. Simulation results suggest that the considered Bayesian estimators outperform the maximum likelihood estimator with respect to bias and frequentist coverage of credible and confidence intervals.Keywords: Network autocorrelation model, Bayesian inference, Jeffreys rule prior,Informative prior distribution, Frequentist coverage

AB - The network autocorrelation model has been extensively used by researchers interested modeling social influence effects in social networks. The most common inferential method in the model is classical maximum likelihood estimation. This approach, however, has known problems such as negative bias of the network autocorrelation parameter and poor coverage of confidence intervals. In this paper, we develop new Bayesian techniques for the network autocorrelation model that address the issues inherent to maximum likelihood estimation. A key ingredient of the Bayesian approach is the choice of the prior distribution. We derive two versions of Jeffreys prior, the Jeffreys rule prior and the Independence Jeffreys prior, which have not yet been developed for the network autocorrelation model. These priors can be used for Bayesian analyses of the model when prior information is completely unavailable. Moreover, we propose an informative as well as a weakly informative prior for the network autocorrelation parameter that are both based on an extensive literature review of empirical applications of the network autocorrelation model across many fields. Finally, we provide new and efficient Markov Chain Monte Carlo algorithms to sample from the resulting posterior distributions. Simulation results suggest that the considered Bayesian estimators outperform the maximum likelihood estimator with respect to bias and frequentist coverage of credible and confidence intervals.Keywords: Network autocorrelation model, Bayesian inference, Jeffreys rule prior,Informative prior distribution, Frequentist coverage

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KW - Social influence

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