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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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    References listed on IDEAS

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    1. Bertocchi, Graziella & Gambardella, Alfonso & Jappelli, Tullio & Nappi, Carmela A. & Peracchi, Franco, 2015. "Bibliometric evaluation vs. informed peer review: Evidence from Italy," Research Policy, Elsevier, vol. 44(2), pages 451-466.
    2. Chrisovalantis Malesios, 2015. "Some variations on the standard theoretical models for the h-index: A comparative analysis," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 66(11), pages 2384-2388, November.
    3. Loet Leydesdorff & Tobias Opthof, 2010. "Scopus's source normalized impact per paper (SNIP) versus a journal impact factor based on fractional counting of citations," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 61(11), pages 2365-2369, November.
    4. John Panaretos & Chrisovaladis Malesios, 2009. "Assessing scientific research performance and impact with single indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 81(3), pages 635-670, December.
    5. Seiler, Christian & Wohlrabe, Klaus, 2014. "How robust are journal rankings based on the impact factor? Evidence from the economic sciences," Journal of Informetrics, Elsevier, vol. 8(4), pages 904-911.
    6. Burrell, Quentin L., 2013. "The h-index: A case of the tail wagging the dog?," Journal of Informetrics, Elsevier, vol. 7(4), pages 774-783.
    7. Leo Egghe & Ronald Rousseau, 2012. "The Hirsch index of a shifted Lotka function and its relation with the impact factor," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 63(5), pages 1048-1053, May.
    8. David I. Stern, 2013. "Uncertainty Measures for Economics Journal Impact Factors," Journal of Economic Literature, American Economic Association, vol. 51(1), pages 173-189, March.
    9. Burrell, Quentin L., 2013. "A stochastic approach to the relation between the impact factor and the uncitedness factor," Journal of Informetrics, Elsevier, vol. 7(3), pages 676-682.
    10. Burrell, Quentin L., 2007. "Hirsch's h-index: A stochastic model," Journal of Informetrics, Elsevier, vol. 1(1), pages 16-25.
    11. Schreiber, Michael, 2015. "Restricting the h-index to a publication and citation time window: A case study of a timed Hirsch index," Journal of Informetrics, Elsevier, vol. 9(1), pages 150-155.
    12. Quentin L. Burrell, 2013. "Formulae for the h-index: A lack of robustness in Lotkaian informetrics?," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 64(7), pages 1504-1514, July.
    13. Egghe, L., 2013. "The functional relation between the impact factor and the uncitedness factor revisited," Journal of Informetrics, Elsevier, vol. 7(1), pages 183-189.
    14. Star X. Zhao & Paul L. Zhang & Jiang Li & Alice M. Tan & Fred Y. Ye, 2014. "Abstracting the core subnet of weighted networks based on link strengths," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 65(5), pages 984-994, May.
    15. Vanclay, Jerome K., 2008. "Ranking forestry journals using the h-index," Journal of Informetrics, Elsevier, vol. 2(4), pages 326-334.
    16. Bar-Ilan, Judit, 2010. "Rankings of information and library science journals by JIF and by h-type indices," Journal of Informetrics, Elsevier, vol. 4(2), pages 141-147.
    17. Schreiber, M. & Malesios, C.C. & Psarakis, S., 2012. "Exploratory factor analysis for the Hirsch index, 17 h-type variants, and some traditional bibliometric indicators," Journal of Informetrics, Elsevier, vol. 6(3), pages 347-358.
    18. Hsu, Jiann-wien & Huang, Ding-wei, 2012. "A scaling between Impact Factor and uncitedness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2129-2134.
    19. Schubert, András & Glänzel, Wolfgang, 2007. "A systematic analysis of Hirsch-type indices for journals," Journal of Informetrics, Elsevier, vol. 1(3), pages 179-184.
    20. Peter Vinkler, 2013. "Quantity and impact through a single indicator," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 64(5), pages 1084-1085, May.
    21. András Schubert & András Korn & András Telcs, 2009. "Hirsch-type indices for characterizing networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 78(2), pages 375-382, February.
    22. Waltman, Ludo, 2016. "A review of the literature on citation impact indicators," Journal of Informetrics, Elsevier, vol. 10(2), pages 365-391.
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    Citations

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    Cited by:

    1. Lucio Bertoli-Barsotti & Tommaso Lando, 2017. "The h-index as an almost-exact function of some basic statistics," Scientometrics, Springer;Akadémiai Kiadó, vol. 113(2), pages 1209-1228, November.
    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.
    3. David A. Groneberg & Doris Klingelhöfer & Dörthe Brüggmann & Cristian Scutaru & Axel Fischer & David Quarcoo, 2019. "New quality and quantity indices in science (NewQIS): results of the first decade—project progress review," Scientometrics, Springer;Akadémiai Kiadó, vol. 121(1), pages 451-478, October.
    4. 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.
    5. 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, Open Access Journal, vol. 10(1), pages 1-1, January.
    6. 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.
    7. William Cabos & Juan Miguel Campanario, 2018. "Exploring the Hjif-Index, an Analogue to the H-Like Index for Journal Impact Factors," Publications, MDPI, Open Access Journal, vol. 6(2), pages 1-1, April.
    8. Gangan Prathap, 2018. "Letter to the editor: Dimensionless citation indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 115(3), pages 1433-1435, June.
    9. Lucio Bertoli-Barsotti, 2017. "Reply to the comments of Prathap," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(2), pages 1137-1140, August.
    10. 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;

    JEL classification:

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

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