Combining Driving Performance Information in an Index Score

Babaee, Seddigheh; Shen, Yongjun; Hermans, Elke; Wets, Geert; Brijs, Tom; Ariën, Caroline · 2014 · Crossref

DOI: 10.3141/2434-06

archive: archived pipeline: cataloged verified

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Summary

This paper addresses the limitation of single-value bibliometric indicators, such as the h-index, which reduce a researcher’s scientific impact to a one-dimensional observation. The author proposes a refined methodology called Characteristic Scores and Scales (CSS) based on h-type indices. While previous CSS definitions relied on average or median citation data, this work defines CSS using iterative calculations of h-type indices (including the h-index, g-index, Kosmulski’s h(2)-index, and g(2)-index). The goal is to provide a more comprehensive assessment of a researcher’s publication-citation distribution by capturing the impact of highly cited papers that fall outside the initial "h-core." The method involves a recursive truncation process. First, the initial h-type index value (e.g., $h_0$) is calculated for the ranked list of publications. The top $h_0$ papers are then discarded, and the remaining list is re-ranked starting from 1. The h-type index is recalculated for this truncated list to yield $h_1$. This process repeats to generate a sequence of index values ($h_0, h_1, h_2, \dots$). These values define characteristic scales ($\nu_k$), representing cumulative ranks, and characteristic scores ($\beta_k$), representing the citation count at those specific ranks. The author derives mathematical models for these sequences within a Lotkaian framework, proving properties such as the relationship between successive indices. For instance, under Lotka’s law with $\alpha=2$, the second h-index value ($h_1$) is shown to be the Golden Section of the initial h-index ($h_0$). Empirical results are presented using the author’s own citation data from Web of Science. For the h-index, the sequence begins with $h_0=17$, followed by $h_1=12$, $h_2=8$, and so on. Similar sequences are generated for the g-index ($g_0=25, g_1=11, \dots$) and the h(2)-index ($h^{(2)}_0=6, h^{(2)}_1=4, \dots$). The data demonstrate that the ratio of successive index values increases with $k$, consistent with theoretical predictions. The study also notes that the R-index is unsuitable for this CSS construction due to non-integer values and misalignment with truncated lists. The significance of this work lies in its ability to capture the full distribution of citation impact rather than relying on a single threshold. By generating multiple "marks" on the citation distribution, the CSS method accounts for highly cited papers excluded by standard h-type indices, which is particularly relevant for prolific authors with high index values. The paper concludes by suggesting further research into comparing CSS sequences across different authors and defining optimal properties for these scales to better evaluate scientific careers.

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