# A statistical sound method for joint estimation of the attachment function and node fitness in a temporal complex network by maximizing a suitable penalized log-likelihood function

### Description

A method for estimating jointly the attachment function *A_k* and node fitness *η_i* of a temporal complex network is implemented in this package. The network's growth is assumed to follow a modified version of the fitness model, in which newly added edges, including newly edges between existed nodes, are connected to a degree *k* node *v_i* with probability proportional to the product of the attachment value *A_k* and the fitness value *η_i*. The method makes no assumption on the functional form of either *A_k* or *η_i*. By choosing suitable regularizations, good estimations of *A_k* and *η_i* can be obtained by maximizing the corresponding penalized log-likelihood function. We also implement a fast estimation of confidence intervals based on the Hessian of the penalized log likelihood. See the accompanying vignette for a tutorial.

For a list of references, please run the command: citation("PAFit").

### Details

Package: | PAFit |

Type: | Package |

Version: | 0.8.7 |

Date: | 2016-10-18 |

License: | GPL-3 |

PAFit: estimates the Preferential Attachment function and fitness function in a temporal complex network.

GenerateNet: generates simulated networks based on the Barabasi-Albert model or the fitness model.

GetStatistics: summarizes a matrix of edges into summary statistics ready for applying the PAFit function.

### Author(s)

Thong Pham, Paul Sheridan, Hidetoshi Shimodaira. Maintainer: Thong Pham thongpham@thongpham.net

### References

1. Pham, T., Sheridan, P. & Shimodaira, H. (2016). Nonparametric Estimation of the Preferential Attachment Function in Complex Networks: Evidence of Deviations from Log Linearity, Proceedings of ECCS 2014, 141-153 (Springer International Publishing) (http://dx.doi.org/10.1007/978-3-319-29228-1_13).

2. Pham, T., Sheridan, P. & Shimodaira, H. (2015). PAFit: A Statistical Method for Measuring Preferential Attachment in Temporal Complex Networks. PLoS ONE 10(9): e0137796. doi:10.1371/journal.pone.0137796 (http://dx.doi.org/10.1371/journal.pone.0137796).

3. Pham, T., Sheridan, P. & Shimodaira, H. (2016). Joint Estimation of Preferential Attachment and Node Fitness in Growing Complex Networks. Scientific Reports 6, Article number: 32558. doi:10.1038/srep32558 (www.nature.com/articles/srep32558).

### Examples

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