Description Usage Arguments Details Value Author(s) References Examples

Model-based clustering and cluster-specific parameter estimation through the mixed membership Exponential-Family Random Graph Models (ERGMs) for the different number of clusters. Model selection is based on maximum value of Integrated Classification Likelihood (ICL).

1 2 | ```
ergmclust.ICL(adjmat, Kmax = 5, directed = FALSE,
thresh = 1e-06, iter.max = 200, coef.init = NULL)
``` |

`adjmat` |
An object of class matrix of dimension (N x N) containing the adjacency matrix, where N is the number of nodes in the network. |

`Kmax` |
Maximum number of clusters. |

`directed` |
If |

`thresh` |
Optional user-supplied convergence threshold for relative error in the objective in Variational Expectation-Maximization (VEM) algorithm. The default value is set as 1e-06. |

`iter.max` |
The maximum number of iterations after which the algorithm is terminated. The default value is set as 200. |

`coef.init` |
Optional user-supplied network canonical parameter vector (K-dimensional). Default is |

ergmclust.ICL is an R implementation for the model selection for an appropriate number of clusters in the mixed membership Exponential-Family Random Graph Models (ERGMs). The Integrated Classification Likelihood (ICL) was proposed by Biernacki et al. (2000) and Daudin, et. al. (2008) to assess the model-based clustering.

Returns a list of `ergmclust`

object. Each object of class `ergmclust`

is a `list`

with the following components:

`Kselect` |
Optimum number of clusters chosen after model selection through Integrated Classification Likelihood (ICL). |

`coefficients` |
An object of class vector of size (Kselect x 1) containing the canonical network parameters of the model. |

`probability` |
An object of class matrix of size (N x Kselect) containing the mixed membership probabilities of the model for N nodes distributed in Kselect clusters. |

`clust.labels` |
An object of class vector of size (N x 1) containing the cluster membership labels in {1, ..., Kselect} for N nodes. |

`ICL` |
Integrated Classification Likelihood (ICL) score calculated from completed data log-likelihood and penalty terms. |

Authors: Amal Agarwal [aut, cre], Kevin Lee [aut], Lingzhou Xue [aut, cre], Anna Yinqi Zhang [cre]

Maintainer: Lingzhou Xue <lzxue@psu.edu>

Biernacki, C., Celeux, G., and Govaert, G. (2000) *Assessing a mixture model for clustering with the integrated completed likelihood*, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 22(7), 719-725

https://ieeexplore.ieee.org/document/865189

Daudin, J. J., Picard, F., and Robin, S. (2008) *A Mixture Model for Random Graphs*, Statistics and Computing, Vol. 18(2), 173–183

https://link.springer.com/article/10.1007/s11222-007-9046-7

1 2 3 4 5 6 7 8 9 10 11 | ```
## undirected network:
data(tradenet)
## Model selection for Kmax = 3
ergmclust.ICL(adjmat = tradenet, Kmax = 3, directed = FALSE,
thresh = 1e-06, iter.max = 120, coef.init = NULL)
## directed network:
data(armsnet)
## Model selection for Kmax = 3
ergmclust.ICL(adjmat = armsnet, Kmax = 3, directed = TRUE,
thresh = 1e-06, iter.max = 60, coef.init = NULL)
``` |

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