adapted pure h-index (proportional credit)
The adapted pure h-index (Chai et al. 2008) is very similar to the pure h-index (proportional credit), except that it estimates its own core rather than relying on the standard h-index core. For a given publication, if one has information on author order and assumes the order directly correlates with effort, one can use a proportional (artihmetic) assignment of credit for each publication as:
$$E_i=\frac{2\left(A_i + 1 - a_i\right)}{A_i\left(A_i + 1\right)},$$where ai is the position of the target author within the full author list of publication i (i.e., an integer from 1 to Ai). Each publication can then be weighted by the inverse of the author effort, wi = 1/Ei. The effective number of citations for each publication is then calculated as
$$C^{*}_i = \frac{C_i}{\sqrt{w_i}}.$$Publications are ranked according to these new citation counts and the h-equivalent value, he, is found as the largest rank for which the rank is less than the number of equivalent citations, or
$$h_e = \underset{i}{\max}\left(i \leq C^{*}_i\right).$$The adapted pure h-index is calculated by interpolating between this value and the next largest, as$$h_{ap.\text{prop}}= \frac{\left(h_e+1\right)C^{*}_{h_e}-h_e C^{*}_{h_e +1}}{C^{*}_{h_e}-C^{*}_{h_e+1}+1}.$$Example
Publications are ordered by adjusted number of citations, from highest to lowest.
Citations (Ci) | 59 | 11 | 26 | 16 | 11 | 10 | 3 | 4 | 3 | 1 | 1 | 2 | 1 | 0 | 0 | 0 | 0 | 0 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Authors (Ai) | 3 | 1 | 3 | 2 | 3 | 4 | 1 | 4 | 4 | 1 | 1 | 4 | 2 | 4 | 2 | 1 | 1 | 1 |
Author Position (ai) | 1 | 1 | 3 | 2 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 3 | 1 | 1 | 1 | 1 |
Author Effort (Ei) | 0.50 | 1.00 | 0.17 | 0.33 | 0.50 | 0.20 | 1.00 | 0.40 | 0.20 | 1.00 | 1.00 | 0.20 | 0.67 | 0.20 | 0.67 | 1.00 | 1.00 | 1.00 |
Weight (wi) | 2.00 | 1.00 | 6.00 | 3.00 | 2.00 | 5.00 | 1.00 | 2.50 | 5.00 | 1.00 | 1.00 | 5.00 | 1.50 | 5.00 | 1.50 | 1.00 | 1.00 | 1.00 |
Adjusted Citations (\(C^*_i\)) | 41.72 | 11.00 | 10.61 | 9.24 | 7.78 | 4.47 | 3.00 | 2.53 | 1.34 | 1.00 | 1.00 | 0.89 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Rank (i) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
he = 5 |
The largest rank where \(i \leq C^*_i\) is 5. Interpolating between this and the next largest rank yields hap.prop = 5.6452.
History
Year | hap.prop |
---|---|
1997 | 0.0000 |
1998 | 1.9365 |
1999 | 2.9669 |
2000 | 4.6230 |
2001 | 5.6452 |
2002 | 6.8571 |
2003 | 8.4718 |
2004 | 11.2500 |
2005 | 14.0000 |
2006 | 15.3181 |
2007 | 17.9785 |
2008 | 20.5000 |
2009 | 21.7922 |
2010 | 23.6004 |
2011 | 25.5922 |
2012 | 27.8357 |
2013 | 30.2563 |
2014 | 31.9179 |
2015 | 32.4596 |
2016 | 32.9730 |
2017 | 33.5324 |
2018 | 33.8349 |
2019 | 35.2568 |
2020 | 35.5907 |
2021 | 36.7500 |
2022 | 37.7608 |
2023 | 37.8267 |
2024 | 38.0589 |
2025 | 38.1657 |
References
- Chai, J.-c., P.-h. Hua, R. Rousseau, and J.-k. Wan (2008) The adapted pure h-index. Fourth International Conference on Webometrics, Informetrics and Scientometrics & Ninth COLLNET Meeting, H. Kretschmer and F. Havemann, eds. Humboldt-Universität zu Berlin: Institute for Library and Information Science.