### Abstract

Original language | English |
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Journal | Sociological Methodology |

Publication status | Accepted/In press - 2020 |

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*Sociological Methodology*.

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

Research output: Contribution to journal › Article › Scientific › peer-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 -