Evolutionary Biological Data Science Laboratory

profit adjusted h-index

The profit indices (Aziz and Rozing 2013) attempt to measure the effect of collaboration on an author's impact. They use a harmonic weighting algorithm and information on author order (assuming that authors in the middle of an author list had the least impact) to estimate effort for each publication. The effort for the i^th publication is

$$E_i=\frac{1+\left|A_i+1-2a_i\right|}{\frac{1}{2}A_i^2+A_i\left(1-D_i\right)},$$

where

$$D_i=\begin{matrix} 0 & \text{if }A_i\text{ is even} \\ \frac{1}{2A_i} & \text{if }A_i\text{ is odd} \end{matrix}.$$

The sum of E_i for all publications is the number of “monograph equivalents” (a monograph being defined as a single-authored publication). The profit adjusted h-index is calculated by weighting each publications citation count by this effort,

$$C^{*}_i=E_i C_i,$$

reranking the publications based upon these weighted counts, and calculating the index as

$$h_a=\underset{i}{\max}\left(i \leq E_iC_i\right)=\underset{i}{\max}\left(i \leq C^{*}_i\right).$$

Example

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

Citations (Ci)	47	26	11	19	15	2	10	4	1	1	3	1	1	0	0	0	0	0
Authors (Ai)	3	3	1	3	2	1	4	4	1	1	4	2	4	4	2	1	1	1
Author Position (ai)	1	3	1	1	2	1	3	1	1	1	3	1	3	3	1	1	1	1
Author Effort (Ei)	0.43	0.43	1.00	0.43	0.50	1.00	0.17	0.33	1.00	1.00	0.17	0.50	0.17	0.17	0.50	1.00	1.00	1.00
Adjusted Citations (\(C^*_i\))	20.14	11.14	11.00	8.14	7.50	2.00	1.67	1.33	1.00	1.00	0.50	0.50	0.17	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
					ha = 5

The largest rank where \(i \leq C^*_i\) is 5.

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