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Related Experiment Video

Updated: Jun 25, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

MCMC estimation for the p(2) network regression model with crossed random effects.

Bonne J H Zijlstra¹, Marijtje A J van Duijn, Tom A B Snijders

¹Department of Educational Sciences/IOPS, University of Amsterdam, Amsterdam, The Netherlands. B.J.H.Zijlstra@uva.nl

The British Journal of Mathematical and Statistical Psychology

|February 12, 2009

Summary

Markov chain Monte Carlo (MCMC) methods improve statistical analysis of social networks. MCMC estimates for the p(2) model show less bias than IGLS, especially in larger networks.

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Last Updated: Jun 25, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

Social network analysis
Statistical modeling
Computational statistics

Background:

The p(2) model is a statistical tool for analyzing binary relational data in social networks.
It accounts for actor heterogeneity and tie dependence using crossed random effects.
Existing iterative generalized least squares (IGLS) estimation methods have limitations.

Purpose of the Study:

To develop and compare Markov chain Monte Carlo (MCMC) estimation methods for the p(2) model.
To evaluate the performance of MCMC methods against IGLS estimation.
To assess estimation accuracy and bias in social network analysis.

Main Methods:

Development of three MCMC estimation methods for the p(2) model.
Two MCMC methods utilize random walk proposals.
One MCMC method employs an independence chain sampler with normal approximations.

Main Results:

IGLS estimates exhibit smaller variance but significant bias.
MCMC estimates demonstrate larger variance but minimal bias.
MCMC methods provide better confidence interval coverage rates, especially for larger networks (40 actors).

Conclusions:

MCMC estimation methods offer a more accurate approach for the p(2) model in social network analysis.
MCMC methods are particularly advantageous for larger network sizes.
The developed MCMC techniques address limitations of previous estimation strategies.