A modification to Hirsch index allowing comparisons across different scientific fields
Jiří Mazurek Department of Informatics and Mathematics, School of Business Administration in Karvina, Karvina, Czech Republic
[email protected]
Abstract: The aim of this paper is to propose a simple modification to the original measure, the relative Hirsch index, which assigns each researcher a value between 0 (the bottom) and 1 (the top), expressing his/her distance to the top in a given field. By this ‘normalization’ scholars from different scientific disciplines can be compared.
Keywords: citations, citation metric, Hirsch index, relative Hirsch index.
1 Introduction
The Hirsch index (h-index) was introduced by a physicist Jorge E. Hirsch in 2005, originally to determine ‘quality’ of theoretical physicists by citation counts of their publications. Since then, the h-index was used as a measure of scientific proficiency of scholars in various scientific disciplines, university departments, scientific journals, etc. However appealing for its simplicity, the h-index has also several drawbacks. Firstly, it does not enable comparisons across different scientific fields due to different citation habits and numbers of researchers active in different fields. Secondly, the h-index does not account for
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scholars’ age, discriminating younger researchers to their older colleagues. Also, h-index cannot distinguish different positions in authors’ list of collaborative publications and can be biased by self-citations. Therefore, many modification of h-index were proposed in the last decade, see Alonso et al. (2009), Bornmann (2011), Panaretos and Malesios (2009), Prathap, G. (2006), Lehman et al. (2006) or Zhang 2009. The aim of this paper is to propose a new simple modification of the original h-index, the relative Hirsch index (hr-index) which assigns each researcher a value between 0 (the bottom) and 1 (the top), expressing his/her distance to the top in a given field of science. By this ‘normalization’ scientist from different disciplines can be compared. The paper is organized as follows: in the section 2 h-index and its modifications are presented, while section 3 introduces the relative Hirsch index. Conclusions close the article.
2 Hirsch index and other citation metrics
Hirsch index assigns each scientist a positive integer number so that a scientist with an index of h has published h papers, and each of them has been cited at least h times, Hirsch (2005). The number of scholars’ citation is usually acquired from main bibliographic databases such as ISI Web of Knowledge (WoK), Scopus, Google Scholar or REPEC (for economists). However, the data from these sources differ due to different coverage; see e. g. Bar-Ilan (2007). Moreover, SCOPUS and Google Scholar have limited coverage of publications prior to 1990 according to Meho and Young (2007).
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More precise definition of h-index is as follows: Let f be the function assigning each publication i its number of citations, and let the function f be ordered in decreasing order. Then h-index is given as follows: h = max min( f (i ), i ) i
(1)
Table 1 provides several indices derived from h-index that avoid some drawbacks mentioned in the previous section.
Table 1. Selected citation indices. Source: author Index
Explanation A scientist has c-index n if n of his/her N citations are from authors
c-index which are at collaboration distance at least n. The e-index is a complement to the h-index, it takes into account e-index citations beyond h2 core citations, see Zhang (2009). g-index
The g-index can be seen as averaged the h-index The m-index (m-quotient) is defined as h/n, where n is the number of
m-index years since the first published paper The o-index is determined as the geometric mean of the h-index and o-index the most cited paper The s-index, accounts for the non-entropic distribution of citations, s-index see Silagadze (2009) i10-
The i10-index provides the number of publications with at least 10
index
citations
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3 The relative Hirsch index
The relative hr-index of a given scientist active in a scientific field S is defined as the scientist’s h-index (1) divided by the current maximal Hirsch index in the field S:
hr =
h max h
(2)
S
Clearly, hr ∈ [ 0,1] . The relative Hirsch index expresses scholar’s “distance to the top“ in his/her field, as hr = 1 is the top (a case of a scientist with the highest h-index in his/her field) and hr = 0 the bottom (a case of a scientist with no citations). Now consider the following example: Andrei Shleifer is an economist with the highest hindex in his field (h = 81, according to WoK). The best physicist is Edward Witten (h = 132, WoK). Hence, when comparing a physicist with h = 50 (hr = 0.38), and an economist with h = 40 (hr = 0.49), the economist is performing relatively better than the physicist, because he/she is closer to the top of his/her discipline. It should be noted that several other papers attempted to overcome a problem with comparisons in different fields, see e.g. Dias (2012). These measures were based on dividing scholars’ citations by all citations or by the average number of citation in a given discipline, but these measures were not found suitable. Further, they lack illustrative interpretation, such as a distance to the top, as it is the case of the measure proposed in this paper.
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Conclusions
The aim of the article was to propose the relative Hirsch index which enables comparing scholars in different scientific fields. The index evaluates scholar’s distance to the top in his/her discipline. It is a simple measure not accounting for scholar age or a position in authors list, but it can certainly be modified as well. As many other alternatives to original hindex were introduced in the last decade, further research may focus on their (dis)similarity and complementarity.
References
Alonso, S., Cabrerizo, F. J., Herrera-Viedma, E., Herrera, F. (2009) "h-index: A Review Focused in its Variants, Computation and Standardization for Different Scientific Fields" Journal of Informetrics 3 (4), 273–289. Bar-Ilan, J. (2007) "Which h-index? — A comparison of WoS, Scopus and Google Scholar" Scientometrics 74 (2), 257-271. Bornmann, L., Mutz R., Hug, S. E., Daniel, H. D. (2011) "A multilevel meta-analysis of studies reporting correlations between the h-index and 37 different h-index variants". J. of Informetrics 5 (3): 346–359. Dias, L. A. (2009) "Relative h-index to compare the scientific performance of researchers". Genet Mol Res. 11 (2),1738-1740. Hirsch, J. E. (2005). "An index to quantify an individual's scientific research output" PNAS 102 (46), 16569–16572.
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Meho, L. I. and Yang, K. (2007) "Impact of Data Sources on Citation Counts and Rankings of LIS Faculty: Web of Science vs. Scopus and Google Scholar" Journal of the American Society for Information Science and Technology 58 (13), 2105–2125. Panaretos, J. and Malesios, C. (2009) "Assessing Scientific Research Performance and Impact with Single Indices". Scientometrics 81 (3), 635–670. Prathap, G. (2006) "Hirsch-type indices for ranking institutions' scientific research output". Current Science 91 (11), 1439. Silagadze, Z. K. (2010) Citation entropy and research impact estimation. Acta Phys. Polon. B 41, 2325–2333 Lehmann S., Jackson, A. D., Lautrup, B. E. (2006) "Measures for measures". Nature 444 (7122), 1003–4. Zhang, C. T. (2009) "The e-Index, Complementing the h-Index for Excess Citations". PLoS ONE 4 (5), e5429.
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