Evolutionary Biological Data Science Laboratory

pure h-index (proportional credit)

The pure h-index (Wan et al. 2007) is similar to the h_i-index in that it attempts to adjust for multiple authors. The index allows for different methods of assigning authorship credit. 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. Given the credited effort for each publication, the metric is calculated as:

$$h_{p.\text{prop}}=\frac{h}{\sqrt{\frac{\sum\limits_{i=1}^{h}{w_i}}{h}}}.$$

Example

Publications are ordered by number of citations, from highest to lowest.

Citations (Ci)	47	26	19	15	11	10	4	3	2	1	1	1	1	0	0	0	0	0
Rank (i)	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
						h = 6
Authors (Ai)	3	3	3	2	1	4	4	4	1	4	2	1	1	4	2	1	1	1
Author Position (ai)	1	3	1	2	1	3	1	3	1	3	1	1	1	3	1	1	1	1
Author Effort (Ei)	0.50	0.17	0.50	0.33	1.00	0.20	0.40	0.20	1.00	0.20	0.67	1.00	1.00	0.20	0.67	1.00	1.00	1.00
Weight (wi)	2.00	6.00	2.00	3.00	1.00	5.00	2.50	5.00	1.00	5.00	1.50	1.00	1.00	5.00	1.50	1.00	1.00	1.00

The h-index is 6 and the sum of the weights for the publications in the core is 19.0, thus h_p.prop = 3.3717.

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