Temporal dynamics of Hirsch index

Yu. Yu. Tarasevich   ; T. S. Shinyaeva

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 1, pp. 32-45

Résumé

We performed the analysis of the data from the Scopus database regarding temporal dynamics of $h$-index and $h_s(2015)$-index of a group of the continuously and consistently working scientists. We propose a model describing the temporal dynamics of $h$-index. Temporal dynamics of $h_s(2015)$-index demonstrates sigmoidal behaviour. The model takes into account: 1) changing the publication activity of the scientist (sigmoidal growth of number of publications at the early stages of scientific career is assumed); 2) the distribution of articles by the number of citations; 3) the dynamics of each specific article citation (typically, the number of citations at first increases and then gradually decreases). The dynamics of the $h$-index as a function of average productivity (number of articles published per year) is investigated. We used two types of citations distributions, i.e. Lotka distribution and geometric distribution. Both distributions lead to a qualitatively correct temporal dynamics of Hirsch index.

Détail

Keywords: $h$-index; modelling.

Bibliographie

[1] Hirsch J. E., “An Index to Quantify an Individual's Scientific Research Output”, Proceedings of the National Academy of Sciences of the United States of America, 102:46 (2005), 16569–16572 | DOI

[2] Schreiber M., “A Modification of The $h$-index: The $h_m$-index Accounts for Multi-Authored Manuscripts”, Journal of Informetrics, 2:3 (2008), 211–216 | DOI | MR

[3] Hirsch J. E., “An Index to Quantify an Individual's Scientific Research Output That Takes Into Account the Effect of Multiple Coauthorship”, Scientometrics, 85:3 (2010), 741–754 | DOI

[4] Schreiber M., “Twenty Hirsch Index Variants and Other Indicators Giving More or Less Preference to Highly Cited Papers”, Annalen der Physik, 522:8 (2010), 536–554 | DOI | MR

[5] Burrell Q. L., “Hirsch's $h$-index: A Stochastic Model”, Journal of Informetrics, 1:1 (2007), 16–25 | DOI

[6] Burrell Q. L., “Hirsch Index or Hirsch Rate? Some Thoughts Arising From Liang's Data”, Scientometrics, 73:1 (2007), 19–28 | DOI

[7] Wu J., “Empirical Study of the Growth Dynamics in Real Career $h$-index Sequences”, Journal of Informetrics, 5:4 (2011), 489–497 | DOI

[8] Egghe L., Rousseau R., “An Informetric Model for the Hirsch-Index”, Scientometrics, 69:1 (2006), 121–129 | DOI | MR

[9] Egghe L., “Dynamic $h$-index: The Hirsch Index in Function of Time”, Journal of the American Society for Information Science and Technology, 58:3 (2007), 452–454 | DOI

[10] Egghe L., “Item-time-dependent Lotkaian Informetrics and Applications to the Calculation of the Time-Dependent $h$-index and $g$-index”, Mathematical and Computer Modelling, 45:7–8 (2007), 864–872 | DOI | MR | Zbl

[11] Guns R., Rousseau R., “Simulating Growth of the $h$-index”, Journal of the American Society for Information Science and Technology, 60:2 (2009), 410–417 | DOI

[12] Schreiber M., “How Relevant is the Predictive Power of the $h$-index? A Case Study of the Time-Dependent Hirsch Index”, Journal of Informetrics, 7:2 (2013), 325–329 | DOI

[13] Vieira E.S, Gomes J. A. N. F., “Citations to Scientific Articles: Its Distribution and Dependence on the Article Features”, Journal of Informetrics, 4:1 (2010), 1–13 | DOI

[14] Sangwal K., “Growth Dynamics of Citations of Cumulative Papers of Individual Authors According to Progressive Nucleation Mechanism: Concept of Citation Acceleration”, Information Processing Management, 49:4 (2013), 757–772 | DOI

[15] Amancio D. R., Oliveira O. N. (Jr.), da Fontoura Costa L., “Three-Feature Model to Reproduce the Topology of Citation Networks and the Effects from Authors' Visibility on Their $h$-index”, Journal of Informetrics, 6:3 (2012), 427–434 | DOI

[16] Amin M., Mabe M. A., “Impact Factors: Use and Abuse”, Medicina, 63:4 (2003), 347–354

[17] Egghe L., Ravichandra Rao I. K., “Theory of First-Citation Distributions and Applications”, Mathematical and Computer Modelling, 34:1–2 (2001), 81–90 | DOI | MR | Zbl

[18] Tsay M.-Y., “An Analysis and Comparison of Scientometric Data Between Journals of Physics, Chemistry and Engineering”, Scientometrics, 78:2 (2009), 279–293 | DOI

[19] Bouabid H., “Revisiting Citation Aging: a Model for Citation Distribution and Life-Cycle Prediction”, Scientometrics, 88:1 (2011), 199–211 | DOI

[20] Sangwal K., “Distributions of Citations of Papers of Individual Authors Publishing in Different Scientific Disciplines: Application of Langmuir-Type Function”, Journal of Informetrics, 8:4 (2014), 972–984 | DOI

[21] Egghe L., “Mathematical Study of $h$-index Sequences”, Information Processing Management, 45:2 (2009), 288–297 | DOI

[22] McCarty C., Jawitz J. W., Hopkins A., Goldman A., “Predicting Author $h$-index Using Characteristics of the Co-author Network”, Scientometrics, 96:2 (2013), 467–483 | DOI | MR

[23] Schreiber M., “The Predictability of the Hirsch Index Evolution. Translational Twists and Turns: Science as a Socio-Economic Endeavor”, Proceedings of 18th International Conference on Science and Technology Indicators (Berlin, Germany, September 4–6, 2013), Institute for Research Information and Quality Assurance, Berlin, 2013, 366–372