Empirical Bayes approaches to PageRank type algorithms for rating scientific journals

Abstract : Following criticisms against the journal Impact Factor, new journal influence scores have been developed such as the Eigenfactor or the Prestige Scimago Journal Rank. They are based on PageR-ank type algorithms on the cross-citations transition matrix of the citing-cited network. The PageR-ank algorithm performs a smoothing of the transition matrix combining a random walk on the data network and a teleportation to all possible nodes with fixed probabilities (the damping factor being α = 0.85). We reinterpret this smoothing matrix as the mean of a posterior distribution of a Dirichlet-multinomial model in an empirical Bayes perspective. We suggest a simple yet efficient way to make a clear distinction between structural and sampling zeroes. This allows us to contrast cases with self-citations are included or excluded to avoid overvalued journal bias. We estimate the model parameters by maximizing the marginal likelihood with a Majorize-Minimize algorithm. The procedure ends up with a score similar to the PageRank ones but with a damping factor depending on the journal at hand. The procedures are illustrated with an example about cross-citations among 47 statistical journals studied by Varin et al. (2016).