Volume 9, no. 1Pages 32 - 45

Temporal Dynamics of Hirsch Index

Yu.Yu. Tarasevich, T.S. Shinyaeva
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.
Full text
h-index; modelling.
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, 2005, vol. 102, no. 46, pp. 16569-16572. DOI: 10.1073/pnas.0507655102
2. Schreiber M. A Modification of The h-index: The hm-index Accounts for Multi-Authored Manuscripts. Journal of Informetrics, 2008, vol. 2, no. 3, pp. 211-216. DOI: 10.1016/j.joi.2008.05.001
3. Hirsch J.E. An Index to Quantify an Individual's Scientific Research Output That Takes Into Account the Effect of Multiple Coauthorship. Scientometrics, 2010, vol. 85, no. 3, pp. 741-754. DOI: 10.1007/s11192-010-0193-9
4. Schreiber M. Twenty Hirsch Index Variants and Other Indicators Giving More or Less Preference to Highly Cited Papers. Annalen der Physik, 2010, vol. 522, no. 8, pp. 536-554. DOI: 10.1002/andp.201000046
5. Burrell Q.L. Hirsch's h-index: A Stochastic Model. Journal of Informetrics, 2007, vol. 1, no. 1, pp. 16-25. DOI: 10.1016/j.joi.2006.07.001
6. Burrell Q.L. Hirsch Index or Hirsch Rate? Some Thoughts Arising From Liang's Data. Scientometrics, 2007, vol. 73, no. 1, pp. 19-28. DOI: 10.1007/s11192-006-1774-5
7. Wu J. Empirical Study of the Growth Dynamics in Real Career h-index Sequences. Journal of Informetrics, 2011, vol. 5, no. 4. pp. 489-497. DOI: 10.1016/j.joi.2011.02.003
8. Egghe L., Rousseau R. An Informetric Model for the Hirsch-Index. Scientometrics, 2006, vol. 69, no. 1, pp. 121-129. DOI: 10.1007/s11192-006-0143-8
9. Egghe L. Dynamic h-index: The Hirsch Index in Function of Time. Journal of the American Society for Information Science and Technology, 2007, vol. 58, no. 3, pp. 452-454. DOI: 10.1002/asi.20473
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, 2007, vol. 45, no. 7-8, pp. 864-872. DOI: 10.1016/j.mcm.2006.08.006
11. Guns R., Rousseau R. Simulating Growth of the h-index. Journal of the American Society for Information Science and Technology, 2009, vol. 60, no. 2, pp. 410-417. DOI: 10.1002/asi.20973
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, 2013, vol. 7, no. 2, pp. 325-329. DOI: 10.1016/j.joi.2013.01.001
13. Vieira E.S, Gomes J. A. N. F. Citations to Scientific Articles: Its Distribution and Dependence on the Article Features. Journal of Informetrics, 2010, vol. 4, no. 1, pp. 1-13. DOI: 10.1016/j.joi.2009.06.002
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, 2013, vol. 49, no. 4, pp. 757-772. DOI: 10.1016/j.ipm.2013.01.003
15. Amancio D.R., Oliveira Jr. O.N., L. da Fontoura Costa. Three-Feature Model to Reproduce the Topology of Citation Networks and the Effects from Authors' Visibility on Their h-index. Journal of Informetrics, 2012, vol. 6, no. 3, pp. 427-434. DOI: 10.1016/j.joi.2012.02.005
16. Amin M., Mabe M.A. Impact Factors: Use and Abuse. Medicina, 2003, vol. 63, no. 4, pp. 347-354.
17. Egghe L., Ravichandra Rao I.K. Theory of First-Citation Distributions and Applications. Mathematical and Computer Modelling, 2001, vol. 34, no. 1-2, pp. 81-90. DOI: 10.1016/S0895-7177(01)00050-4
18. Tsay M.-Y. An Analysis and Comparison of Scientometric Data Between Journals of Physics, Chemistry and Engineering. Scientometrics, 2009, vol. 78, no. 2, pp. 279-293. DOI: 10.1007/s11192-007-1996-1
19. Bouabid H. Revisiting Citation Aging: a Model for Citation Distribution and Life-Cycle Prediction. Scientometrics, 2011, vol. 88, no. 1, pp. 199-211. DOI: 10.1007/s11192-011-0370-5
20. Sangwal K. Distributions of Citations of Papers of Individual Authors Publishing in Different Scientific Disciplines: Application of Langmuir-Type Function. Journal of Informetrics, 2014, vol. 8, no. 4, pp. 972-984. DOI: 10.1016/j.joi.2014.09.009
21. Egghe L. Mathematical Study of h-index Sequences. Information Processing & Management, 2009, vol. 45, no. 2, pp. 288-297. DOI: 10.1016/j.ipm.2008.12.002
22. McCarty C., Jawitz J.W., Hopkins A., Goldman A. Predicting Author h-index Using Characteristics of the Co-author Network. Scientometrics, 2013, vol. 96, no. 2, pp. 467-483. DOI: 10.1007/s11192-012-0933-0
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. Berlin, Institute for Research Information and Quality Assurance, 2013, pp. 366-372.