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A theoretical model of the relationship between the h-index and other simple citation indicators

Author

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  • Lucio Bertoli-Barsotti

    (University of Bergamo)

  • Tommaso Lando

    (University of Bergamo
    VŠB -TU Ostrava)

Abstract

Of the existing theoretical formulas for the h-index, those recently suggested by Burrell (J Informetr 7:774–783, 2013b) and by Bertoli-Barsotti and Lando (J Informetr 9(4):762–776, 2015) have proved very effective in estimating the actual value of the h-index Hirsch (Proc Natl Acad Sci USA 102:16569–16572, 2005), at least at the level of the individual scientist. These approaches lead (or may lead) to two slightly different formulas, being based, respectively, on a “standard” and a “shifted” version of the geometric distribution. In this paper, we review the genesis of these two formulas—which we shall call the “basic” and “improved” Lambert-W formula for the h-index—and compare their effectiveness with that of a number of instances taken from the well-known Glänzel–Schubert class of models for the h-index (based, instead, on a Paretian model) by means of an empirical study. All the formulas considered in the comparison are “ready-to-use”, i.e., functions of simple citation indicators such as: the total number of publications; the total number of citations; the total number of cited paper; the number of citations of the most cited paper. The empirical study is based on citation data obtained from two different sets of journals belonging to two different scientific fields: more specifically, 231 journals from the area of “Statistics and Mathematical Methods” and 100 journals from the area of “Economics, Econometrics and Finance”, totaling almost 100,000 and 20,000 publications, respectively. The citation data refer to different publication/citation time windows, different types of “citable” documents, and alternative approaches to the analysis of the citation process (“prospective” and “retrospective”). We conclude that, especially in its improved version, the Lambert-W formula for the h-index provides a quite robust and effective ready-to-use rule that should be preferred to other known formulas if one’s goal is (simply) to derive a reliable estimate of the h-index.

Suggested Citation

  • Lucio Bertoli-Barsotti & Tommaso Lando, 2017. "A theoretical model of the relationship between the h-index and other simple citation indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 111(3), pages 1415-1448, June.
    • Handle: RePEc:spr:scient:v:111:y:2017:i:3:d:10.1007_s11192-017-2351-9
    DOI: 10.1007/s11192-017-2351-9
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    Cited by:

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    2. Deming Lin & Tianhui Gong & Wenbin Liu & Martin Meyer, 2020. "An entropy-based measure for the evolution of h index research," Scientometrics, Springer;Akadémiai Kiadó, vol. 125(3), pages 2283-2298, December.
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    5. Brito, Ricardo & Navarro, Alonso Rodríguez, 2021. "The inconsistency of h-index: A mathematical analysis," Journal of Informetrics, Elsevier, vol. 15(1).
    6. Wei, Shelia X. & Tong, Tong & Rousseau, Ronald & Wang, Wanru & Ye, Fred Y., 2022. "Relations among the h-, g-, ψ-, and p-index and offset-ability," Journal of Informetrics, Elsevier, vol. 16(4).
    7. Fassin, Yves, 2024. "The internal dynamics of journals’ h-cores over time," Journal of Informetrics, Elsevier, vol. 18(2).
    8. Bertoli-Barsotti, Lucio & Lando, Tommaso, 2019. "How mean rank and mean size may determine the generalised Lorenz curve: With application to citation analysis," Journal of Informetrics, Elsevier, vol. 13(1), pages 387-396.
    9. Huchang Liao & Ming Tang & Li Luo & Chunyang Li & Francisco Chiclana & Xiao-Jun Zeng, 2018. "A Bibliometric Analysis and Visualization of Medical Big Data Research," Sustainability, MDPI, vol. 10(1), pages 1-18, January.
    10. Linying Jia & Ao Cheng & Naqash Alam & Yuxuan Qian & Zeyao Ma & Honghao Ren & Rong Wang & Enqi Liu, 2021. "Global Trends in Atherosclerosis Research in the Epigenetics Field: Bibliometric and Visualization Studies," IJERPH, MDPI, vol. 18(24), pages 1-12, December.
    11. Biró, Tamás S. & Telcs, András & Józsa, Máté & Néda, Zoltán, 2023. "Gintropic scaling of scientometric indexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    12. Wojciech Charemza & Michal Lewandowski & Lukasz Wozny, 2021. "Efficiency in rewarding academic journal publications. The case of Poland," KAE Working Papers 2021-062, Warsaw School of Economics, Collegium of Economic Analysis.
    13. Mingyang Wang & Shijia Jiao & Kah-Hin Chai & Guangsheng Chen, 2019. "Building journal’s long-term impact: using indicators detected from the sustained active articles," Scientometrics, Springer;Akadémiai Kiadó, vol. 121(1), pages 261-283, October.
    14. William Cabos & Juan Miguel Campanario, 2018. "Exploring the Hjif-Index, an Analogue to the H-Like Index for Journal Impact Factors," Publications, MDPI, vol. 6(2), pages 1-11, April.
    15. Gangan Prathap, 2018. "Letter to the editor: Dimensionless citation indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 115(3), pages 1433-1435, June.
    16. Lucio Bertoli-Barsotti, 2017. "Reply to the comments of Prathap," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(2), pages 1137-1140, August.
    17. Gangan Prathap, 2017. "Letter to the editor: comments on the paper of Lucio Bertoli-Barsotti and Tommaso Lando: a theoretical model of the relationship between the h-index and other simple citation indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(2), pages 1133-1136, August.

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    More about this item

    Keywords

    Journal ranking; h-index for journals; Journal impact factor; Glänzel–Schubert formula; Geometric distribution; Lambert W function;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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