Evolutionary Biological Data Science Laboratory

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 a_i is the position of the target author within the full author list of publication i (i.e., an integer from 1 to A_i). Each publication can then be weighted by the inverse of the author effort, w_i = 1/E_i. 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, h_e, 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)	57	11	26	16	12	10	4	2	3	1	1	1	1	0	0	0	0	0
Authors (Ai)	3	1	3	2	3	4	4	1	4	1	1	2	4	4	2	1	1	1
Author Position (ai)	1	1	3	2	1	3	1	1	3	1	1	1	3	3	1	1	1	1
Author Effort (Ei)	0.50	1.00	0.17	0.33	0.50	0.20	0.40	1.00	0.20	1.00	1.00	0.67	0.20	0.20	0.67	1.00	1.00	1.00
Weight (wi)	2.00	1.00	6.00	3.00	2.00	5.00	2.50	1.00	5.00	1.00	1.00	1.50	5.00	5.00	1.50	1.00	1.00	1.00
Adjusted Citations (\(C^*_i\))	40.31	11.00	10.61	9.24	8.49	4.47	2.53	2.00	1.34	1.00	1.00	0.82	0.45	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 h_ap.prop = 5.6952.

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