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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)591126161110343112100000
Authors (Ai)313234144114242111
Author Position (ai)113213113113131111
Author Effort (Ei)0.501.000.170.330.500.201.000.400.201.001.000.200.670.200.671.001.001.00
Weight (wi)2.001.006.003.002.005.001.002.505.001.001.005.001.505.001.501.001.001.00
Adjusted Citations (\(C^*_i\))41.7211.0010.619.247.784.473.002.531.341.001.000.890.820.000.000.000.000.00
Rank (i)123456789101112131415161718
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

Yearhap.prop
19970.0000
19981.9365
19992.9669
20004.6230
20015.6452
20026.8571
20038.4718
200411.2500
200514.0000
200615.3181
200717.9785
200820.5000
200921.7922
201023.6004
201125.5922
201227.8357
201330.2563
201431.9179
201532.4596
201632.9730
201733.5324
201833.8349
201935.2568
202035.5907
202136.7500
202237.7608
202337.8267
202438.0589
202538.1657

References