### Abstract

The exponential random graph model (ERGM) plays a major role in social network analysis. However, parameter estimation for the ERGM is a hard problem due to the intractability of its normalizing constant and the model degeneracy. The existing algorithms, such as Monte Carlo maximum likelihood estimation (MCMLE) and stochastic approximation, often fail for this problem in the presence of model degeneracy. In this article, we introduce the varying truncation stochastic approximation Markov chain Monte Carlo (SAMCMC) algorithm to tackle this problem. The varying truncation mechanism enables the algorithm to choose an appropriate starting point and an appropriate gain factor sequence, and thus to produce a reasonable parameter estimate for the ERGM even in the presence of model degeneracy. The numerical results indicate that the varying truncation SAMCMC algorithm can significantly outperform the MCMLE and stochastic approximation algorithms: for degenerate ERGMs, MCMLE and stochastic approximation often fail to produce any reasonable parameter estimates, while SAMCMC can do; for nondegenerate ERGMs, SAMCMC can work as well as or better than MCMLE and stochastic approximation. The data and source codes used for this article are available online as supplementary materials.

Original language | English |
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Pages (from-to) | 927-952 |

Number of pages | 26 |

Journal | Journal of Computational and Graphical Statistics |

Volume | 22 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2013 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Discrete Mathematics and Combinatorics
- Statistics, Probability and Uncertainty

### Cite this

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*Journal of Computational and Graphical Statistics*, vol. 22, no. 4, pp. 927-952. https://doi.org/10.1080/10618600.2012.680851

**Fitting social network models using varying truncation stochastic approximation MCMC algorithm.** / Jin, Ick Hoon; Liang, Faming.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Fitting social network models using varying truncation stochastic approximation MCMC algorithm

AU - Jin, Ick Hoon

AU - Liang, Faming

PY - 2013/1/1

Y1 - 2013/1/1

N2 - The exponential random graph model (ERGM) plays a major role in social network analysis. However, parameter estimation for the ERGM is a hard problem due to the intractability of its normalizing constant and the model degeneracy. The existing algorithms, such as Monte Carlo maximum likelihood estimation (MCMLE) and stochastic approximation, often fail for this problem in the presence of model degeneracy. In this article, we introduce the varying truncation stochastic approximation Markov chain Monte Carlo (SAMCMC) algorithm to tackle this problem. The varying truncation mechanism enables the algorithm to choose an appropriate starting point and an appropriate gain factor sequence, and thus to produce a reasonable parameter estimate for the ERGM even in the presence of model degeneracy. The numerical results indicate that the varying truncation SAMCMC algorithm can significantly outperform the MCMLE and stochastic approximation algorithms: for degenerate ERGMs, MCMLE and stochastic approximation often fail to produce any reasonable parameter estimates, while SAMCMC can do; for nondegenerate ERGMs, SAMCMC can work as well as or better than MCMLE and stochastic approximation. The data and source codes used for this article are available online as supplementary materials.

AB - The exponential random graph model (ERGM) plays a major role in social network analysis. However, parameter estimation for the ERGM is a hard problem due to the intractability of its normalizing constant and the model degeneracy. The existing algorithms, such as Monte Carlo maximum likelihood estimation (MCMLE) and stochastic approximation, often fail for this problem in the presence of model degeneracy. In this article, we introduce the varying truncation stochastic approximation Markov chain Monte Carlo (SAMCMC) algorithm to tackle this problem. The varying truncation mechanism enables the algorithm to choose an appropriate starting point and an appropriate gain factor sequence, and thus to produce a reasonable parameter estimate for the ERGM even in the presence of model degeneracy. The numerical results indicate that the varying truncation SAMCMC algorithm can significantly outperform the MCMLE and stochastic approximation algorithms: for degenerate ERGMs, MCMLE and stochastic approximation often fail to produce any reasonable parameter estimates, while SAMCMC can do; for nondegenerate ERGMs, SAMCMC can work as well as or better than MCMLE and stochastic approximation. The data and source codes used for this article are available online as supplementary materials.

UR - http://www.scopus.com/inward/record.url?scp=84901767980&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84901767980&partnerID=8YFLogxK

U2 - 10.1080/10618600.2012.680851

DO - 10.1080/10618600.2012.680851

M3 - Article

AN - SCOPUS:84901767980

VL - 22

SP - 927

EP - 952

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

SN - 1061-8600

IS - 4

ER -