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MCMC estimation for the p(2) network regression model with crossed random effects.
Br J Math Stat Psychol. 2009 Feb; 62(Pt 1):143-66.BJ

Abstract

The p(2) model is a statistical model for the analysis of binary relational data with covariates, as occur in social network studies. It can be characterized as a multinomial regression model with crossed random effects that reflect actor heterogeneity and dependence between the ties from and to the same actor in the network. Three Markov chain Monte Carlo (MCMC) estimation methods for the p(2) model are presented to improve iterative generalized least squares (IGLS) estimation developed earlier, two of which use random walk proposals. The third method, an independence chain sampler, and one of the random walk algorithms use normal approximations of the binary network data to generate proposals in the MCMC algorithms. A large-scale simulation study compares MCMC estimates with IGLS estimates for networks with 20 and 40 actors. It was found that the IGLS estimates have a smaller variance but are severely biased, while the MCMC estimates have a larger variance with a small bias. For networks with 20 actors, mean squared errors are generally comparable or smaller for the IGLS estimates. For networks with 40 actors, mean squared errors are the smallest for the MCMC estimates. Coverage rates of confidence intervals are good for the MCMC estimates but not for the IGLS estimates.

Authors+Show Affiliations

Department of Educational Sciences/IOPS, University of Amsterdam, Amsterdam, The Netherlands. B.J.H.Zijlstra@uva.nlNo affiliation info availableNo affiliation info available

Pub Type(s)

Journal Article

Language

eng

PubMed ID

19208289

Citation

Zijlstra, Bonne J H., et al. "MCMC Estimation for the P(2) Network Regression Model With Crossed Random Effects." The British Journal of Mathematical and Statistical Psychology, vol. 62, no. Pt 1, 2009, pp. 143-66.
Zijlstra BJ, van Duijn MA, Snijders TA. MCMC estimation for the p(2) network regression model with crossed random effects. Br J Math Stat Psychol. 2009;62(Pt 1):143-66.
Zijlstra, B. J., van Duijn, M. A., & Snijders, T. A. (2009). MCMC estimation for the p(2) network regression model with crossed random effects. The British Journal of Mathematical and Statistical Psychology, 62(Pt 1), 143-66. https://doi.org/10.1348/000711007X255336
Zijlstra BJ, van Duijn MA, Snijders TA. MCMC Estimation for the P(2) Network Regression Model With Crossed Random Effects. Br J Math Stat Psychol. 2009;62(Pt 1):143-66. PubMed PMID: 19208289.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - MCMC estimation for the p(2) network regression model with crossed random effects. AU - Zijlstra,Bonne J H, AU - van Duijn,Marijtje A J, AU - Snijders,Tom A B, PY - 2009/2/12/entrez PY - 2009/2/12/pubmed PY - 2009/5/12/medline SP - 143 EP - 66 JF - The British journal of mathematical and statistical psychology JO - Br J Math Stat Psychol VL - 62 IS - Pt 1 N2 - The p(2) model is a statistical model for the analysis of binary relational data with covariates, as occur in social network studies. It can be characterized as a multinomial regression model with crossed random effects that reflect actor heterogeneity and dependence between the ties from and to the same actor in the network. Three Markov chain Monte Carlo (MCMC) estimation methods for the p(2) model are presented to improve iterative generalized least squares (IGLS) estimation developed earlier, two of which use random walk proposals. The third method, an independence chain sampler, and one of the random walk algorithms use normal approximations of the binary network data to generate proposals in the MCMC algorithms. A large-scale simulation study compares MCMC estimates with IGLS estimates for networks with 20 and 40 actors. It was found that the IGLS estimates have a smaller variance but are severely biased, while the MCMC estimates have a larger variance with a small bias. For networks with 20 actors, mean squared errors are generally comparable or smaller for the IGLS estimates. For networks with 40 actors, mean squared errors are the smallest for the MCMC estimates. Coverage rates of confidence intervals are good for the MCMC estimates but not for the IGLS estimates. SN - 0007-1102 UR - https://www.unboundmedicine.com/medline/citation/19208289/MCMC_estimation_for_the_p_2__network_regression_model_with_crossed_random_effects_ L2 - https://doi.org/10.1348/000711007X255336 DB - PRIME DP - Unbound Medicine ER -