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The discretised lognormal and hooked power law distributions for complete citation data: Best options for modelling and regression

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  • Thelwall, Mike

Abstract

Identifying the statistical distribution that best fits citation data is important to allow robust and powerful quantitative analyses. Whilst previous studies have suggested that both the hooked power law and discretised lognormal distributions fit better than the power law and negative binomial distributions, no comparisons so far have covered all articles within a discipline, including those that are uncited. Based on an analysis of 26 different Scopus subject areas in seven different years, this article reports comparisons of the discretised lognormal and the hooked power law with citation data, adding 1 to citation counts in order to include zeros. The hooked power law fits better in two thirds of the subject/year combinations tested for journal articles that are at least three years old, including most medical, life and natural sciences, and for virtually all subject areas for younger articles. Conversely, the discretised lognormal tends to fit best for arts, humanities, social science and engineering fields. The difference between the fits of the distributions is mostly small, however, and so either could reasonably be used for modelling citation data. For regression analyses the best option is to use ordinary least squares regression applied to the natural logarithm of citation counts plus one, especially for sets of younger articles, because of the increased precision of the parameters.

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  • Thelwall, Mike, 2016. "The discretised lognormal and hooked power law distributions for complete citation data: Best options for modelling and regression," Journal of Informetrics, Elsevier, vol. 10(2), pages 336-346.
    • Handle: RePEc:eee:infome:v:10:y:2016:i:2:p:336-346
    DOI: 10.1016/j.joi.2015.12.007
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    8. Zahedi, Zohreh & Haustein, Stefanie, 2018. "On the relationships between bibliographic characteristics of scientific documents and citation and Mendeley readership counts: A large-scale analysis of Web of Science publications," Journal of Informetrics, Elsevier, vol. 12(1), pages 191-202.
    9. Thelwall, Mike & Nevill, Tamara, 2018. "Could scientists use Altmetric.com scores to predict longer term citation counts?," Journal of Informetrics, Elsevier, vol. 12(1), pages 237-248.
    10. Thelwall, Mike, 2016. "Are there too many uncited articles? Zero inflated variants of the discretised lognormal and hooked power law distributions," Journal of Informetrics, Elsevier, vol. 10(2), pages 622-633.
    11. Thelwall, Mike, 2016. "Are the discretised lognormal and hooked power law distributions plausible for citation data?," Journal of Informetrics, Elsevier, vol. 10(2), pages 454-470.
    12. Donner, Paul, 2018. "Effect of publication month on citation impact," Journal of Informetrics, Elsevier, vol. 12(1), pages 330-343.
    13. Mrowinski, Maciej J. & Gagolewski, Marek & Siudem, Grzegorz, 2022. "Accidentality in journal citation patterns," Journal of Informetrics, Elsevier, vol. 16(4).
    14. Mike Thelwall, 2017. "Avoiding obscure topics and generalising findings produces higher impact research," Scientometrics, Springer;Akadémiai Kiadó, vol. 110(1), pages 307-320, January.
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    16. Gómez-Déniz, Emilio & Dorta-González, Pablo, 2024. "Modeling citation concentration through a mixture of Leimkuhler curves," Journal of Informetrics, Elsevier, vol. 18(2).
    17. Mike Thelwall, 2016. "Interpreting correlations between citation counts and other indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 108(1), pages 337-347, July.
    18. Banshal, Sumit Kumar & Gupta, Solanki & Lathabai, Hiran H & Singh, Vivek Kumar, 2022. "Power Laws in altmetrics: An empirical analysis," Journal of Informetrics, Elsevier, vol. 16(3).
    19. Guillermo Armando Ronda-Pupo & J. Sylvan Katz, 2018. "The power law relationship between citation impact and multi-authorship patterns in articles in Information Science & Library Science journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 114(3), pages 919-932, March.
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    21. Guillermo Armando Ronda-Pupo, 2017. "The citation-based impact of complex innovation systems scales with the size of the system," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(1), pages 141-151, July.

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