Abstract
Countless bibliometric indexes have been proposed to assess researchers’ productivities, in particular, in fields where the author sequence is regarded helpful in determining authors’ individual credits. Unfortunately, the most popular h-index ignores author ranks and leads to bias with multi-author publications; and of the many bibliometric counting methods proposed for assigning credit to authors, such as harmonic or geometric counting, none seems to have been widely adopted yet. In this work, I challenge the assumption that the total credit for a publication be equal to 1. This total-credit normalization assumption diminishes first-author credit and may impede adoption of multi-author-aware credit assignment rules. Other than on relative contributions, author credit could be based on variables such as accountability, which remains unchanged for the first (and potentially, the last) author regardless of additional coauthors. Therefore, I study the adequacy of several counting methods for first-author-normalized credit, giving full credit to the first author while also crediting coauthors. Harmonic counting has been shown to agree well with empirical data; however, unlike geometric counting, harmonic counting results in unbounded total credit for a publication with first-author-credit normalization in the limit of many authors. I therefore propose adaptable geometric counting and evaluate how it combines the advantages of harmonic and geometric counting through an additional parameter. I show that the golden ratio is a parameter for geometric counting that agrees as well as harmonic counting with empirical data for total-credit normalization; and I discuss the impact of using adaptable geometric counting with first-author-normalized credit. In particular, the latter features bounded total credits even when full credit is given to first authors. In conclusion, geometric counting with the golden ratio can be used for credit assignment without having to choose a parameter value, yet offers customization potential and can be combined with either normalization assumption.
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Notes
Other sources of bias include the coverage of the data base (Bar-Ilan 2008), in particular, literature reviews; self citations (Engqvist and Frommen 2008); salami publications (Šupak Smolčić 2013); and academic age. With regard to the latter, any index can be differentiated to obtain an annual increase (Harzing et al. 2014), or divided by the academic age (compare the m-number; Hirsch 2005). Alternatively, the source data \(c_p\) can be weighted by each publication’s age (AR-index, Jin et al. 2007; contemporary h-index, Sidiropoulos et al. 2007); an extreme case is the binary weighting currently used by Google Scholar, which shows h-index and i10 not only for all publications, but also for those younger than five years.
Yet not necessarily illegitimately.
Despite the term, by definition, illegitimate.
This is also true for variables such as experience gained, which I do not discuss further in this work.
With some, e.g., fractional, counting methods, even the same credit as the first author.
Awarding author credit based on accountability may seem debatable based on relative-contribution-based credit; however, it is not necessarily incompatible with accepted standards for scientific authorship. For example, the recommendations of the International Committee of Medical Journal Editors (2016) define four mandatory authorship criteria, one of which is the “[a]greement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved”. Similarly, the Council of Science Editors (2012) states that there is general consensus that “[t]he ultimate reason for identification of authors and other contributors is to establish accountability for the reported work”. Nonetheless, this should not imply that any of those recommendations can be followed simply through a counting method.
Note that first-author-credit normalization may only be valid when evaluating or comparing individual researchers: by contrast, when groups of researchers such as departments, universities, or countries are aggregated, the total credit for a publication should not exceed 1 per group, since each group cannot be more than “fully accountable”.
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Acknowledgements
I thank Jessica Mueller and Dr. Benjamin Goldschmidt for critically reading an earlier version of the manuscript, and several anonymous reviewers for their suggestions to improve the focus of this manuscript. The work leading to this publication was supported by the German Academic Exchange Service (DAAD) (Grant No. 57178382) with funds from the German Federal Ministry of Education and Research (BMBF) and the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA Grant Agreement No. 605728 (P.R.I.M.E.—Postdoctoral Researchers International Mobility Experience).
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Berker, Y. Golden-ratio as a substitute to geometric and harmonic counting to determine multi-author publication credit. Scientometrics 114, 839–857 (2018). https://doi.org/10.1007/s11192-017-2632-3
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DOI: https://doi.org/10.1007/s11192-017-2632-3