The function summarizes input data into sufficient statistics for estimating the attachment function and node fitness, together with additional information about the data, such as the total number of nodes, the number of time-steps, the maximum degree, and the final degree of the network, etc. . It also provides mechanisms to automatically deal with very large datasets by binning the degree, setting a degree threshold, or discarding time-steps.
From a PAFitData object, which contains summary statistics summerized from the dataset, PAFit estimates the attachment function A_k and node fitness f_i by penalized log-likelihood maximization. It also calculates confidence intervals for A_k and f_i. Estimation of the attachment function in isolation (while fixing f_i = 1) can be specified by setting only_PA = TRUE. Estimation of node fitness in isolation (fixing either A_k = k or A_k = 1) can be specified by setting only_f = TRUE.
● Data Source:
CranContrib
● Keywords: Barabasi-Albert model, Bianconi-Barabasi model, MM algorithims, Minorize-Maximization algorithms, Preferential Attachment function, fitness, fitness model, maximum likelihood function, package
● Alias: PAFit
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This function generates networks from the Barabasi-Albert model or the fitness model. The number of edges of the new node at each time-step can be specified to be fixed, or followed a Poisson distribution. In the latter case, the mean of the Poisson distribution is either held fixed or increased with time.
This function plots the estimated attachment function A_k and node fitness f_i, together with additional information such as their confidence intervals.
PAFit-package
(Package: PAFit) :
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
A method for estimating jointly the attachment function A_k and node fitness f_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 f_i. The method makes no assumption on the functional form of either A_k or f_i. By choosing suitable regularizations, good estimations of A_k and f_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.
● Data Source:
CranContrib
● Keywords: Barabasi-Albert model, Bianconi-Barabasi model, MM algorithims, Minorize-Maximization algorithms, Preferential Attachment function, fitness, fitness model, maximum likelihood function, package
● Alias: PAFit-package
●
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