Measuring the citation impact of journals with generalized Lorenz curves

Abstract

To improve comparisons of journals, which are typically based on single-value indicators, such as the journal impact factor (JIF), this paper proposes a functional approach. We discuss interpretatively three progressively finer dominance relations. The first one corresponds to a comparison between the quantile functions of the citation distributions. The second one consists in comparing the integrals of the quantile functions namely, the generalized Lorenz curves (GLCs). The third one consists in comparing the integrals of the GLCs, where the integration is designed to emphasize the role of the "central body" of the articles of the journal. Although dominance relations are generally not complete orders, we demonstrate with an empirical analysis that it is possible to increase significantly the proportion of pairs of journals that are comparable by moving from the first to the second criterion, and then from the second to the third.

Because, in practical applications, it may be convenient to reduce such a functional comparison to a scalar comparison between indicators, we follow an axiomatic approach to identify classes of indicators that are isotonic with the criteria introduced. We demonstrate that the established JIF may be usefully improved if it is corrected simply by multiplying it by one minus the Gini coefficient. The resulting index, defined as stabilized-JIF, has many attractive features and it is isotonic with all the dominance relations introduced.